SlideShare una empresa de Scribd logo
1 de 187
Descargar para leer sin conexión
Advanced Nuclear Physics


                                         MOHAMMAD IMRAN AZIZ
                                            Assistant Professor
                                          PHYSICS DEPARTMENT
                                  SHIBLI NATIONAL COLLEGE, AZAMGARH
                                                  (India).



                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Nuclides

        The total number of protons in the nucleus of an atom is called the atomic
        number of the atom and is given the symbol Z. The number of electrons in an
        electrically-neutral atom is the same as the number of protons in the nucleus.
        The number of neutrons in a nucleus is known as the neutron number and is
        given the symbol N. The mass number of the nucleus is the total number of
        nucleons, that is, protons and neutrons in the nucleus. The mass number is
        given the symbol A and can be found by the equation Z + N = A.
        .




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
why electrons cannot exist inside a nucleus:
                     Nuclear constituents and their properties
                      This can be explained mathematically also using Heisenberg's
                      uncertainty principle as follows




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Confinement Calculation




         Electtron is not found in the nucleus, it means we are talking about free electron. That is free
         electron does not exist.n ....> p + e, here this is beta deacy and electron that becomes free is
         emitted out of the nucleus as free electron as can not exist due to Heisenberg uncertainty.

                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
It is common practice to represent the total angular momentum of a
                                                          Nuclear Spin
                  nucleus by the symbol I and to call it "nuclear spin". For electrons in
                  atoms we make a clear distinction between electron spin and electron
                  orbital angular momentum, and then combine them to give the total
                  angular momentum. But nuclei often act as if they are a single entity
                  with intrinsic angular momentum I. Associated with each nuclear spin
                  is a nuclear magnetic moment which produces magnetic interactions
                  with its environment.
                  The nuclear spins for individual protons and neutrons parallels the
                  treatment of electron spin, with spin 1/2 and an associated magnetic
                  moment. The magnetic moment is much smaller than that of the
                  electron. For the combination neutrons and protons into nuclei, the
                  situation is more complicated.




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
• A characteristic of the collection of protons and
        neutrons (which are fermions) is that a nucleus of
        odd mass number A will have a half-integer spin and
        a nucleus of even A will have integer spin. The
        suggestion that the angular momenta of nucleons
        tend to form pairs is supported by the fact that all
        nuclei with even Z and even N have nuclear spin I=0.
        The half-integer spins of the odd-A nuclides suggests
        that this is the nuclear spin contributed by the odd
        neutron
                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Nuclear Magnetic Moments

      • Associated with each nuclear spin is a magnetic moment
        which is associated with the angular momentum of the
        nucleus. It is common practice to express these magnetic
        moments in terms of the nuclear spin in a manner parallel to
        the treatment of the magnetic moments of electron spin and
        electron orbital angular momentum.
      • For the electron spin and orbital cases, the magnetic
        moments are expressed in terms of a unit called a Bohr
        magneton which arises naturally in the treatment of
        quantized angular momentum



                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Electric Quadrupole Moments of
                          Nuclei
                   The nuclear electric quadrupole moment is a parameter which
                   describes the effective shape of the ellipsoid of nuclear charge
                   distribution. A non-zero quadrupole moment Q indicates that the
                   charge distribution is not spherically symmetric. By convention, the
                   value of Q is taken to be positive if the ellipsoid is prolate and
                   negative if it is oblate.




                      The quantity Q0 is the classical form of the calculation
                      represents the departure from spherical symmetry in the rest
                      frame of the nucleus.


                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Generally, the measured quantity is proportional to the z-component of the
           magnetic moment (the component along the experimentally determined
           direction such as the direction of an applied magnetic field, etc. ). In this
           treatment, the use of a "gyromagnetic ratio" or "g-factor" is introduced. The g-
           factor for orbital is just gL = 1, but the electron spin g-factor is approximately
           gS = 2




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
For free protons and neutrons with spin I =1/2, the magnetic moments
            are of the form




                                            where
                                            Proton: g = 5.5856912 +/- 0.0000022
                                            Neutron: g = -3.8260837 +/- 0.0000018
                  The proton g-factor is far from the gS = 2 for the electron, and even the uncharged
                  neutron has a sizable magnetic moment! For the neutron, this suggests that there is
                  internal structure involving the movement of charged particles, even though the net
                  charge of the neutron is zero. If g=2 were an expected value for the proton and g=0
                  were expected for the neutron, then it was noted by early researchers that the the
                  proton g-factor is 3.6 units above its expected value and the neutron value is 3.8 units
                  below its expected value. This approximate symmetry was used in trial models of the
                  magnetic moment, and in retrospect is taken as an indication of the internal structure
                  of quarks in the standard model of the proton and neutron




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Note that the maximum effective magnetic moment of a nucleus in
                nuclear magnetons will be the g-factor multiplied by the nuclear
                spin. For a proton with g = 5.5857 the quoted magnetic moment is m
                = 2.7928 nuclear magnetons.

                                                                                 Nuclear                              Magnetic moment
                                          Nuclide
                                                                                  spin I                                  m in mN




                                             n                                     1/2                   -1.9130418



                                             p                                     1/2                   +2.7928456



                                           2H(D)                                    1                    +0.8574376



                                            17O                                    5/2                   -1.89279



                                            57Fe                                   1/2                   +0.09062293



                                           57Co                                    7/2                   +4.733



                                           93Nb                                    9/2                   +6.1705




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Nuclei

                      • Parameters of nuclei
                      • Strong Interaction
                      • Binding Energy
                      • Stable and Unstable Nuclei
                      • Liquid-Drop Model




                                                                     Numerous Applications:
                                                                  • nuclear power
                                                                  • applications in                         medicine,   biology   and
                                                                            chemistry
                                                                  • evolution of stars and the Universe
                                                                  • nuclear weapons



                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Size of Nuclei and Rutherford Scattering
                     1/3
 R  R0 A
                                 - depends weakly on A
                                 (number of nucleons in
                                      the nucleus)

 R0  1.2 1015 m  1.2 fm                                                                                             Geiger, Marsden,

      238                                         1/3
                                                                                                                        Rutherford,1910
R    92    U   1.2 fm   238                        7.4 fm
                                                                          Scattering pattern was consistent with that expected for
-particles: bare He nuclei                                               scattering of  particles by pointlike objects having a charge
                                                                          of +79e (the charge of the gold nucleus). This allowed
                                                                          Rutherford to put an upper limit on the size of the nucleus
                                                                          (<310-14m for gold).
                                                        Calculations were strictly classical. However, because of the Coulomb
                                                        interaction between alpha-particles and nucleus, the result
                                                        miraculously coincides with the exact quantum-mechanical one
                                                        (recall the success of the Bohr model for atoms).

                                                    To measure the size of a nucleus, one
                                                    has to use more energetic  particles
                                                    (or electrons, which are more                                        R – the fitting
                                                    commonly used these days) that get                                    parameter
                                                pdfMachine
                                                    close enough to get inside the nucleus.
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Nuclear Mass
                                                                                A                                               12
                                                                                     X                                               C
           number of nucleons in the nucleus                                                         chemical symbol
                                                                                                                                6
                                                                                Z
             (mass number of the nucleus)                                                            for the element
              number of protons in the nucleus                                                                         6 protons + 6 neutrons

                                                                                                                N  A Z
               (atomic number of the element)
                                                                           The neutron number:

            Atomic Mass (the mass of a neutral atom):

                 M  Z  m p  N  mn  U nucleus / c 2  Z  me  U el .nucl . / c 2
               U nucleus ,U el .nucl .  0 - attraction between nucleons in the nucleus and between
                                                                                       electrons and the nucleus
               U el .nucl .  U nucleus  mp c 2                                      - we can neglect Uel.-nucl. and introduce a
                                                                                                  convenient mass unit:
                                                         M 12 C
                                             1u              6
                                                                      1.66054 1027 kg  931.49MeV / c 2
                                                           12
                   Mass Unit


                                             m p  proton mass  1.007277u
                                            mn  neutron mass  1.008665u
                                            m  electron mass  0.000549u
                                                pdfMachine
                                                e
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Nuclear Density


                                                                                     MA  1au      1au
                                                                            3 3 3 3                 3 3
                                                                                               
                                                                              R         R0 A         R0
                                                                            4         4             4
                                                                              1.66 1027 kg
                                                                                                    2.4 1017 kg / m3
                                                                            3             15    3
                                                                          
                                                                               1.2 10 m 
                                                                            4
                                                                                                                               !
                                                                     The density of neutron stars is comparable with that of
                                                                                             nuclei.



(Unstable) isotopes of tin and zinc.




                                                 pdfMachine
                          A pdf writer that produces quality PDF files with ease!
                                                                      aziz_muhd33@yahoo.co.in
 Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
     nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                          “Broadgun pdfMachine printer” and that’s it! Get yours now!
The Need for a “Strong Force”
    Which interaction controls the size of nucleons? This cannot be electromagnetic interaction:
    protons have the same electric charge (they would repel each other) and also there are attractive
    forces between protons and electrically neutral neutrons.
    Strong Interaction:
       binds protons to protons, neutrons to neutrons, and protons to neutrons with roughly the
                same force
       does not affect certain other kinds of particles (specifically electrons)
       is short-ranged (the range ~ 2 fm). Nucleons separated by a larger distance exert no strong
    forces on each other.
                                                    These observations are explained by the quark model of nucleons.

                      g
                                                    Nucleons are the combination of quarks that are strong-interaction-

                           u
                                                    neutral (like an electrically-neutral atom). Two nucleons interact only if
                                                    they are close enough that the distances between various pairs of

                                       d
                                                    quarks are significantly different.
             u
 quarks
  and
 gluons


                 ~ 10-15 m



                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Structure of Matter

                                                                                                                                   g
                                                                                                                                         u
                                                         El.-mag. interaction

                                                                                                                             u               d
                                                        determines the size of
                                                                                                                    quarks
                                                               atoms
                                                                                                                     and
                                                                                                                    gluons


                                                                                                                                 ~ 10-15 m

                ~ 10-10 - 10-9 m                                                                                      Protons & Neutrons (nucleons)
                                                                                                                      are almost an empty space (the
          Atom is almost an
                                                                                                                          quark size is <10-18 m)
          empty space (the
        nuclear volume is ~10-
           15 of the atomic

               volume)                                                                                            Strong interaction
                                                                                                                determines the size of
                                                                                                                 nuclei and nucleons


                                                pdfMachine
                         A pdf writer that produces quality PDF files with -15    ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
                                                                        ~ 10       - 10   -14m
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Binding Energy

Binding energy:                    Esys  EB  E parts                          EB  E parts  Esys             -the binding energy is positive for
                                                                                                                         a bound system
            Recall a H atom: the binding energy is 13.6 eV (the ground state energy with sign “minus”).


                                                                                              n
                                                                                                                     n                 p
                                                                                                          p
                                                       add EB
                                                                                                                    n                      n
                                                                                     E parts   mi  c 2
                   Esys                                                                                                     p


             We can compute the binding energy if we know masses of a system and its constituents:


       EB   mass of all particles consituting the atom    mass of the atom    c 2
                                                                                  
        Z  m1 H  N  mn  M A X   c 2                                                                     EB  M  c 2
              1                Z   
                                                                                                                      mass deficit
                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Binding Energy curve
    Because of the short-range character of strong interaction (basically, between nearest and next-to-
    nearest neighbors), the interaction energy per nucleon with increasing Z saturates at the level ~
    (Z/2)(# of neighbors).
                    Binding energy per nucleon (EB/A), MeV




                                                              increasing Z is caused by the long-range Coulomb B   Z 2
                                                                   The decrease of the binding energy with

                                                                             repulsion of protons:




                                                                                                                Mass number, A
                    The binding energy ~ 10MeV/nucleon is ~1% of the nucleon’s rest energy: we can
                                     pdfMachine
                                 consider the nucleus as a system of individual nucleons
                         A pdf writer that produces quality PDF files with ease!
                                                                    aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Liquid-Drop Model
                                                                                                                        2                2
             A “semi-classical” model of the
                                                                            EB  aV A  as A2/3  ac
                                                                                                                  Z
                                                                                                                        aa
                                                                                                                             A  2Z 
                                                                                                                  A1/3           A
             nucleus: describes reasonably well
             the dependence EB(A):

                                                                                                                                             dq  r 
                                                                                                                               q r
                                                                                                        - charge density



                                                                                                                q r       dq  r 

                                                                                                       4 3              2
                                                                                                          r    4 r  dr
                                                                                                          R0
                                                                                                           3
                                                                                         U  R0             
                                                                                                    0
                                                                                                               4 0 r




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Liquid-Drop Model (cont’d)




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Limitations of Liquid-Drop Model




          Maria Goeppert-Mayer, J.H.D.Jensen


                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Stable Nuclei
                                                                                   Isotopes: all nuclei that have the same number of
                                                                                   protons (Z) but different number of neutrons (N).
                                                                                   Since the chemical properties of an atom are
                                                                                   determined by the number of its electrons,
                                                                                   isotopes of the same element have almost
                                                                                   identical chemical properties.

                                                                                   Example: naturally occurring isotopes of oxygen
                                                                                                        16       17       19
                                                                                                        8    0   8    0   8    0

                                                                                   Related questions:
                                                                                   - What makes unstable nuclei unstable?
                                                                                   - What are the mechanisms by which they
                                                                                   transform themselves into stable nuclei?
                                                                                   -Why do light stable nuclei tend to have N  Z?
                                                                                   - Why do heavier nuclei tend to have more
                                                                                   neutrons than protons?
                                                                                   - Why are there no stable nuclei with Z>83?




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
What makes unstable nuclei unstable?
                                                           Both protons - and neutrons are                            energy
                                                           fermions (they obey the exclusion
                                                           principle).   Nuclei   are    two-                   0
                                                                                                                                            r
                                                           component Fermi systems. Each
                                                           nuclear energy level can contain
                                                           four particles: two protons (s=½)

                                                                                                                                       12
                                                           and two neutrons (s=½).

                                                                                                                                       6    C
      The potential experienced by nucleons is a 3D potential well. The
           ground-state configuration of the carbon-16 nucleus :

 If a nucleus is allowed to decrease its energy by transforming “excessive”
 protons (neutrons) into neutrons (protons), it will do it!                                                         protons neutrons

   The processes responsible for these transformations are driven by weak interaction (the fourth
   fundamental interaction):
       The weak interaction (unlike the strong interaction) affects both quarks and leptons, (unlike the
   el.-mag. interaction) can affect electrically neutral particles, and (unlike gravity) does not affect
   photons.
       The effective range of the weak interaction is ~ 10-18m.

    Some important transformation processes driven by weak interaction:

                        n  e  p           pdfMachine                p   n  e 
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in                        p   e  n 
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Why N  Z for light nuclei
13                                                                       13
8    O             energy                                                7    N            energy
                                                                                                                If the electrostatic repulsion
                                             t1/2  8.9ms                                                       of protons can be neglected
                                                                                                                (this is the case of light
                                                                                                                nuclei: recall that the
                                                                                                                positive electrostatic energy
                                                                                                                Z2), the nucleus tends to
                                                                                                                keep approximately equal
                                                                                                                numbers of protons and
                                                                                                                neutrons.
   protons            neutrons                                              protons            neutrons

14                                                                       14
6    C             energy                                                7    N            energy
                                                                                                                Even in this case, the nucleus

                                           t1/2  5730 y
                                                                                                                can still lower its total
                                                                                                                energy: the rest energy of
                                                                                                                neutron is slightly more than
                                                                                                                the rest energy of a proton
                                                                                                                and an electron.



                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
   protons            neutrons                                              protons
                                                                     aziz_muhd33@yahoo.co.in   neutrons
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Why N > Z for heavy nuclei
44                                                       44
22   Ti            energy                                20   Ca             energy                     In the heavy nuclei, the electrostatic
                                                                                                        energy cannot be neglected. As a
                                                                                                        result, the protons’ energy levels are
                                                                                                        “pushed up” with respect to the
                                                                                                        neutrons’ levels. In the “otherwise
                                                                                                        stable” 44Ti, two protons undergo
                                                                                                        the transformation into neutrons,
                                                                                                        the end product is stable 44Ca.

         .                                                         .
         .                  .                                      .                  .
         .                  .                                      .                  .
   protons            neutrons                                protons           neutrons


      The proton-neutron disbalance                                    becomes             more
      pronounced with increasing Z.




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Nuclear Masses and Sizes
      • Masses and binding energies
               – Absolute values measured with mass
                 spectrometers.
               – Relative values from reactions and decays.
      • Nuclear Sizes
               – Measured with scattering experiments (leave
                 discussion until after we have looked at
                 Rutherford scattering).
               – Isotope shifts
                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Nuclear Mass Measurements
      • Measure relative masses by energy released
        in decays or reactions.
               – X  Y +Z + DE
               – Mass difference between X and Y+Z is DE/c2.
      • Absolute mass by mass spectrometers (next
        transparency).
      • Mass and Binding energy:
      • B = [Z MH + N Mn – M(A,Z)]/c2

                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Mass Spectrometer
      • Ion Source
      • Velocity selector                                                                                                 Detector
        electric and magnetic
        forces equal and
        opposite                                                                                                Velocity
         – qE=qvB  v=E/B                                                          Ion Source
                                                                                                                selector
      • Momentum selector,
        circular orbit satisfies:
         – Mv=qBr
         – Measurement r gives
           M.


                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Binding Energy vs A
      • B increases with A up to 56Fe and then slowly
        decreases. Why?
      • Lower values and not smooth at small A.




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Nuclear Sizes & Isotope Shift
      • Coulomb field modified by finite size of nucleus.
      • Assume a uniform charge distribution in the nucleus.
         Gauss’s law 

                                                                              r 3Ze
        integrate and apply boundary conditions
                                                                E          ( )
                                                                            2 R
                                                                    4 0 r
      • Difference between actual potential and Coulomb
                                                                                    Zer 2       3Ze
                                                                        V (r )           3
                                                                                   8 0 R     8 0 R
                                                                                             

      • Use 1st order perturbation theory
                                Zer 2              3Ze     Ze
              V ( r )                  3
                                                                           (r  R )
                              8 0 R             8 0 R 4 0r
                                                        


                        R                                                                           Z 3/ 2                     Z
                                 2    *
             E   4r  ( r )[ eV ( r )] ( r )dr                              ( r )  2(         )   exp( Zr / a0 )  2( )3 / 2
                        0
                                                                                                    a0                         a0
                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Isotope Shifts
                                R
                                             2              3Ze   3 Ze                     Zer 2
                 E   4r 4( Z / a ) (  e)[        3
                                                                          ] dr
                                                8 0R     8 0 R 4 0r
                                                                 
                      0

R                4R 5                                     R            4R 3                                   R      1
  4 r 2 r 2dr                                                   2
                                                             4 r dr 
                                                                                                                    2
                                                                                                                 4 r dr  2R
                                                                                                                                2
0                  5                                        0             3                                     0      r


                          Ze     2    4  4  3    3
    E  ( 4e)( Z / a )       R [        2 ]
                         4 0       10  3  2 
                                                                  2        2
                                     2 Ze R            3
                                E         ( Z / a0 )
                                       5 0
                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Isotope Shifts
      • Isotope shift for optical spectra
      • Isotope shift for X-ray spectra (bigger effect
        because electrons closer to nucleus)
      • Isotope shift for X-ray spectra for muonic
        atoms. Effect greatly enhanced because mm~
        207 me and a0~1/m.
      • All data consistent with R=R0 A1/3 with
        R0=1.25fm.

                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Liquid Drop Model Nucleus
      • Phenomenological model to understand binding energies.
      • Consider a liquid drop
               – Ignore gravity and assume no rotation
               – Intermolecular force repulsive at short distances, attractive at
                 intermediate distances and negligible at large distances  constant
                 density.
               E=-an + 4pR2T B=an-bn2/3
      • Analogy with nucleus
               – Nucleus has constant density
               – From nucleon nucleon scattering experiments: Nuclear force has
                 short range repulsion and attractive at intermediate distances.
               – Assume charge independence of nuclear force, neutrons and protons
                 have same strong interactions check with experiment!




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Mirror Nuclei
      • Compare binding energies of mirror nuclei (nuclei n
        p). Eg 73Li and 74Be.
      • Mass difference due to n/p mass and Coulomb
                      R
        energy.
                         Q( r )
             E                dQ
                      0 4 0 r

            Q( r )  Ze( r / R ) 3 dQ  3 Zer 2 / R 3

                3( Ze ) 2 r 5
                    R
                                            ( Ze ) 2
            E             6
                              dr  ( 3 / 5)
              0 4 0 r R                   4 0 R
                         3 e2
     E c ( Z , Z  1)            [ Z ( Z  1)  ( Z  1)( Z  2)] ; Z ~ A / 2 ; R  A1 / 3
                         5 4 0 R

                EC ( Z , Z  1)  A2 / 3
                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Liquid Drop Model Nucleus
• Phenomenological model to understand binding energies.
• Consider a liquid drop
       – Ignore gravity and assume no rotation
       – Intermolecular force repulsive at short distances, attractive at intermediate
         distances and negligible at large distances  constant density.
       – n=number of molecules, T=surface tension, B=binding energy
         E=total energy of the drop, a,b=free constants
                    E=-an + 4pR2T                      B=an-bn2/3


                                                                                 surface area ~ n2/3
      Analogy with nucleus
             Nucleus has constant density
             From nucleon-nucleon scattering experiments we know:
                     Nuclear force has short range repulsion and is attractive at intermediate distances.
             Assume charge independence of nuclear force, neutrons and protons have
              same strong interactions check with experiment (Mirror Nuclei!)
                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Coulomb Term
• The nucleus is electrically charged with total charge Ze
• Assume that the charge distribution is spherical and compute the
  reduction in binding energy due to the Coulomb interaction
                      Ze
                           Q(r )
    ECoulomb                      dQ             Q (r )  Ze(r / R )3 dQ  3Zer 2 / R 3 dr
                      0
                          4 0 r
               to change the integral to dr ; R=outer radius of nucleus

                       R
                            3( Ze) 2 r 5              ( Ze) 2
   ECoulomb                            dr  (3 / 5)
                                                                                                 includes self interaction of last
                                       6
                            4 0 r R                 4 0 R
                                                                                                 proton with itself. To correct this
                       0                                                                         replace Z2 with Z*(Z-1)
              … and remember R=R0A-1/3
                                                                                 in principle you could take d from this calculation
                       Z *( Z  1)
BCoulomb ( Z , A)  d
                                                                                 but it is more accurate to take it from the overall
                            1/ 3
                          A
                                                                                 fit of the SEMF to data (nuclei not totally
                                                pdfMachine
                                                                                 spherical or homogeneous)
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Mirror Nuclei
 • Does the assumption of the drop model of constant binding energy for every
   constituent of the drop acatually hold for nuclei?
 • Compare binding energies of mirror nuclei (nuclei with np). Eg 73Li and
   7 Be.
    4
 • If the assumption holds the mass difference should be due to n/p mass
   difference and Coulomb energy alone.
 • Let’s compute the Coulomb energy correction from results on previous page
                              3 e2                                         3 e2
     Ecoulomb ( Z , Z  1)            [ Z ( Z  1)  ( Z  1)( Z  2)]            2( Z  1)
                              5 4 0 R                                    5 4 0 R
             Z ~ A / 2 ; R  R0 A1/ 3 to find that EC ( Z , Z  1)  A2 / 3
        Now lets measure mirror nuclei masse, assume that the model holds and
         derive DECoulomb from the measurement.
        This should show an A2/3 dependence
        And the scaling factor should yield the correct R0 of 1.2 fm
  
                                                pdfMachine
         if the assumptions were right
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
“Charge
        symmetry”


   nn and pp
   interaction same
   (apart from
   Coulomb)




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
More charge symmetry
• Energy Levels of two mirror nuclei for a number of excited states
• Corrected for n/p mass difference and Coulomb Energy

                                                                   DEcorrected




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
From Charge Symmetry to Charge
                               Independence
• Mirror nuclei showed that strong interaction is the same for nn
  and pp.
• What about np ?
• Compare energy levels in “triplets” with same A, different
  number of n and p. e.g.
                22                      22                       22
                10 Ne                   11 Na                    12 Mg
• If we find the same energy levels for the same spin states 
  Strong interaction is the same for np as nn and pp.



                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Charge Independence
                                                                                                                              DEcorrected
• Same spin/parity states
  should have the same
  energy.
• Yes: np=nn=pp
• Note: Far more states in
  22 Na. Why?
    11
• Because it has more np pairs
  then the others
• np pairs can be in any Spin-
  Space configuration
• pp or nn pairs are excluded
  from the totally symmetric
  ones by Herr Pauli
                                                                    22
                                                                         10Ne
• Note also that 2211Na has the
                                                                                                                       22
  lowest (most bound) state,                                                                                                12Mg
  remember for the deuteron
                                                                                                         22
                                                                                                                11Na
  on next page

                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Charge Independence
      • We have shown by measurement that:
               – If we correct for n/p mass difference and Coulomb interaction, then
                 energy levels in nuclei are unchanged under n  p
               – and we must change nothing else! I.e. spin and space wavefunctions
                 must remain the same!
      • Conclusion: strong two-body interaction same for pp, pn and
        nn if nucleons are in the same quantum state.
      • Beware of the Pauli exclusion principle! eg why do we have
        bound state of pn but not pp or nn?
               – because the strong force is spin dependent and the most strongly
                 bound spin-space configurations (deuteron) are not available to nn or
                 pp. It’s Herr Pauli again!
               – Just like 2211Na on the previous triplet level schema

                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Volume and Surface Term
• We now have all we need to trust that we can apply the
  liquid drop model to a nucleus
        – constant density
        – same binding energy for all constituents
• Volume term:                                          BVolume ( A)   aA
                                                                            2/3
• Surface term:                                         BSurface ( A)  bA
• Since we are building a phenomenological model in which
  the coefficients a and b will be determined by a fit to
  measured nuclear binding energies we must inlcude any
  further terms we may find with the same A dependence
  together with the above
                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Asymmetry Term
      • Neutrons and protons are spin ½ fermions  obey
        Pauli exclusion principle.
      • If all other factors were equal nuclear ground state
        would have equal numbers of n & p.
    neutrons                        protons                 Illustration
                                                               n and p states with same spacing .
                                                               Crosses represent initially occupied states in ground
                                                                state.
                                                               If three protons were turned into neutrons
                                                               the extra energy required would be 3×3 .
                                                               In general if there are Z-N excess protons over
                                                                neutrons the extra energy is ((Z-N)/2)2 . relative
                                                                to Z=N.
                                                               But how big is D ?
                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Asymmetry Term
      • Assume:
               – p and n form two independent, non-interacting
                 gases occupying their own square Fermi wells
               – kT << D
               – so we can neglect kT and assume T=0
               – This ought to be obvious as nuclei don’t suddenly
                 change state on a warm summers day!
               – Nucleons move non-relativistically (check later if
                 this makes sense)
                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Asymmetry Term
      • From stat. mech. density of states in 6d phase space = 1/h3
                4 p 2 dpV
           dN particle 
                                     h3
                           here N       could be the number of protons or neutrons
                                                                 particle


      • Integrate up to pf to get total number of protons Z (or Neutrons N), & Fermi
        Energy (all states filled up to this energy level).

                                                   3            3          4   3
                  Z  (4 V / 3h ) pF                               and V   R0 A
                                                                           3
                                                 1/ 3                                                                                  2          2/3
                                h      Z                                     2                                                    h      Z
PF  (3 / 4 )           2/3
                                                        and E  p                          EF  (3 / 4 )                   4/3
                                R0      A                                        2m                                              2mR02    A
                                                                                                                                          

                                                                                                                EF
      • Change variables p  E to find avg. E
                                                                                                                     E 3/ 2 dE
                       dN / dp
             dN / dE           const  E1/ 2                                               E               0
                                                                                                                                  (3 / 5) EF
                                                                                                                
                                                                                                                EF
                       dp / dE
                                                                                                                     E1/ 2 dE
                                                                                                                0
                                                                                                                
                                                pdfMachine
           These are all standard stat. mech. results!
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Asymmetry Term
        Compute total energy of all protons by Z*<E>                                                                 call this K
                                                                                       2                        2/3
               P                         P      3          4/3  h    Z
            E  Total     Z E                   (3 / 4 )        2
                                                                    Z 
                                                5              2mR0  A 
        Use the above to compute total energy of Z protons and N neutrons
                  K
          ETotal        Z 5/ 3  N 5/ 3  change variables from (Z,N,A)
                 A2 / 3                      to (y,A) with y=N-Z
                KA5/ 3
       ETotal  2 / 3 5 3  (1  y / A)5/ 3  (1  y / A)5/ 3  where y/A is a small number (e)
               A 2 
                KA
                                                              
       ETotal  5 3 (1   )5/ 3  (1   )5/ 3 
               2                                
• Binomial expansion keep lowest term in y/A
                           2 3        21 35 ( N  Z ) 2
          ETotal  2              KA       K
                                                                             note! linear terms cancel

                                        9        A                                               ( N  Z )2
                                                         ETotal ( Fermi  Gas )  const *
 This terms is only proportional to volume                                                                                                A
                                                                                                                comes from a fit of the
 (A). It has already been captured by the
 Volume term of the liquid pdfMachine
                                                                                                                SEMF to measurements
                         A pdf writer that produces quality PDF files with ease!
                            drop model aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
                                                                                                                analytical ≈ 24 MeV
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Asymmetry term
      • From the Fermi Gas model we learn that
               – due to the fermionic nature of p and n we loose in
                 binding energy if the nucleus deviates from N=Z

                                                            ( N  Z )2
      •      The Asymmetry term: B Asymmetry ( N , Z )   c A




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
• Observations:
  • Nuclei with even number of n or                                                                 Pairing Term
    even number of p more tightly
                                                                                                     Neutron separation energy
    bound then with odd numbers.
                                                                                                     [MeV] in Ba isotopes
    See figure
  • Only 4 stable o-o nuclei but 153
    stable e-e nuclei.
  • p energy levels are Coulomb                                                                                                   56+N
                                                                                                                                         56Ba
    shifted wrt n  small overlap of
    wave functions between n and
    p.
  • Two p or two n in same energy
    level with opposite values of jz
    have AS spin state
        forced into sym spatial w.f.
        maximum overlap
        maximum binding energy
                                                                                                                 Neutron number
           because of short range
           attraction.
Note: this only holds for nn and pp, not for
np.  We don’t have a preference for even A
                             pdfMachine
                          A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
 Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
     nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                          “Broadgun pdfMachine printer” and that’s it! Get yours now!
Pairing Term
• Measure that the Pairing effect smaller for larger A
• Phenomenological*) fit to A dependence gives A-1/2

          BPairing ( A)   1/ 2
                            
                           A
                                            d
                                                                                Note: If you want to plot binding energies
          e-e                              +ive                                 versus A it is often best to use odd A only
                                                                                as for these the pairing term does not
          e-o                              0                                    appear

          o-o                              -ive                                                     *) For an even more insightful
                                                                                                    explanation of the A dependence
                                                                                                    read the book by Jelley
                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Semi Empirical Mass Formula

    • Put everything together:
                                                                                                                2         2
                                                               2/3          (N  Z )     Z
   B( N , Z )  aA  bA                                                  c           d 1/ 3  1/ 2
                                                                                                
                                                                               A        A      A
                                  Volume            Surface                       Asymmetry                         Coulomb   Pairing
                                  Term              Term                          Term                              Term      Term

         Lets see how all of these assumptions fit reality
         And find out what the constants are
            Note: we went back to the simpler Z instead of Z*(Z-1)
                                                  2




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Semi Empirical Mass Formula
                                        Binding Energy vs. A for beta-stable odd-A nuclei



                                                                                                                Fit parameters
                                     Iron                                                                       in MeV

                                                                                                                a 15.56
                              Not smooth because Z                                                              b 17.23
                              not smooth function of A
                                                                                                                c 23.285
                                                                                                                d 0.697
                                                                                                                d +12 (o-o)
                                                                                                                d 0 (o-e)
                                                                                                                d -12 (e-e)




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Semi Empirical Mass Formula

    • Conclusions
             –    Only makes sense for A≥20
             –    Good fit for large A (good to <1%) in most places.
             –    Deviations are interesting  shell effects.
             –    Coulomb term constant agrees with calculation.
             –    Explains the valley of stability (see next lecture).
             –    Explains energetics of radioactive decays, fission and fusion.




                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
                                                                     aziz_muhd33@yahoo.co.in
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Nuclear Shell Model
           • Potential between nucleons can be studied by studying
             bound states (pn, ppn, pnn, ppnn) or by scattering cross
             sections:         np -> np pp -> pp nD -> nD pD -> pD
           • If had potential could solve Schrod. Eq. Don’t know
             precise form but can make general approximation
           • 3d Finite Well with little r-dependence (except at edge of
             well)
           • Almost spherically symmetric (fusion can be modeled as
             deformations but we’ll skip)
           • N-N interactions are limited (at high A) due to Pauli
             exclusion. p + n -> p’ + n’ only if state is available



                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Infinite Radial Well
                                                2 d 2u                    2 l ( l  1) 
          • Radial part of Scrod Eq
                                                            V ( r )                    u  Eu
                                                               
                                               2m dr 2                   2m        r2
                                             
                                                                                        
                                             u( r )  rR ( r )   P ( r )  4u 2



          • Easy to solve if l=0
                                                   2 n                                  p2   ( k ) 2   ( hn) 2
      u  sin kr                               k                                    E 
                                                    2a                                   2m     2m       8ma 2
                                                                                                      



          • For L>0, angular momentum term goes to infinity at r=0.
            Reduces effective wavelength, giving higher energy
          • Go to finite well. Wave function extends a bit outside well giving
            longer effective wavelength and lower energy (ala 1D square
            wells)
                                                pdfMachine
          • In nuceli, potential goes to infinity at r=0 (even with L=0) as that
                         A pdf writer that produces quality PDF files with ease!
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
            would be equivalent to nucleon “inside” other nucleon
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Angular part
• If V(r) then can separate variables y(r,q,f) = R(r)Y( q,f) have spherical
  harmonics for angular wave function
• Angular momentum then quantized like in Hydrogen (except that L>0
  for n=1, etc)
                         L2  l (l  1)  2                                      LZ   m
                        l  0,1,2                          m   l l                          n  r  quantum#
• Energy doesn’t depend on m
• Energy increases with increasing n (same l)
• Energy increases with increasing l (same n)
• If both n,l vary then use experimental observation to determine
  lower energy
• Energy will also depend on strong magnetic coupling between
                                                    pdfMachine
  nucleons
                             A pdf writer that produces quality PDF files with ease!
    Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
        nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
• Fill up states separately for p,n
                             “Broadgun pdfMachine printer” and that’s it! Get yours now!
L,S,J Coupling: Atoms vs Nuclei
 •      ATOMS: If 2 or more electrons, Hund’s rules:
 •      Maximise total S for lowest E (S=1 if two)
 •      Maximise total L for lowest E (L=2 if 2 P)
 •      Energy split by total J (J=3,2,1 for S=1,L=2)

 • NUCLEI: large self-coupling. Plus if 2 p (or 2 n) then will anti-align
    giving a state with J=0, S=0, L=0
   leftover “odd” p (or n) will have two possible
        J = L + ½ or J = L – ½
     higher J has lower energy
    if there are both an odd P and an odd n (which is very rare in
    stable) then add up Jn + Jp
 • Atom called LS coupling nuclei called jj
                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
 • Note that magnetic moments add differently as different g-factor
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
    for p,n
Spin Coupling in Nuclei
• All nucleons in valence shell have same J
• Strong pairing causes Jz antiparallel (3 and -3)       spin
  wavefunction = antisymmetric               space wavefunction =
  symmetric
• This causes the N-N to be closer together and increases the
  attractive force between them
• e-e in atoms opposite as repulsive force
• Can also see in scattering of polarized particles
• Even N, even Z nuclei. Total J=S=L=0 as all n,p paired off
• Even N, odd Z or odd N, even Z. nuclear spin and parity
  determined by unpaired nucleon
• Odd N, odd Z. add together unpaired n,p

                                                 pdfMachine
• Explains ad hoc pairing term in mass formula
                          A pdf writer that produces quality PDF files with ease!
 Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
     nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                          “Broadgun pdfMachine printer” and that’s it! Get yours now!
Energy Levels in Nuclei
• Levels in ascending order (both p,n)
 State    n L degeneracy(2j+1) sum
  1S1/2 1 0          2               2***
  1P3/2 1 1          4               6
  1P1/2 1 1          2               8***
  1D5/2 1 2          6              14
  2S1/2 2 0          2               16
  1D3/2 1 2          4               20***
  1F7/2 1 3          8               28***
  2P3/2 2 1          4               32
  1F5/2 1 3          6               38
  2P1/2 2 1          2               40
  1G9/2 1 4         10               50***

*** “magic” number is where there is a large energy gap between a
                                                pdfMachine
  filled shell and the next level. More tightly bound nuclei. (all filled
                         A pdf writer that produces quality PDF files with ease!
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
  subshells are slightly “magic”)
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
Magic Numbers
• Large energy gaps between some filled shells and next (unfilled)
  shell give larger dE/A and more made during nucleosnthesis in
  stars
 # protons                 #neutrons
  2 He                       2 He-4
  6 C                        6 C-12
  8 O                        8 O-16
  20 Ca                     20
  28 Ni                      28 Cr-52(24,28)
  50 Sn                      50 Ni-78
  82 Pb                       82
                            126
                            136

• Ni-78 (2005) doubly magic. While it is unstable, it is the much
  neutron rich.
                                                pdfMachine
                         A pdf writer that produces quality PDF files with ease!
• Usually more isotopes if p or n are magic. Sn has 20 isotopes, 10
Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across
    nearly all Windows platforms, simply open the document you want to convert, click “print”, select the
                         “Broadgun pdfMachine printer” and that’s it! Get yours now!
  of which are stable
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]
Advanced nuclear physics [compatibility mode]

Más contenido relacionado

Destacado

4_RenatoCargill_apresentação
4_RenatoCargill_apresentação4_RenatoCargill_apresentação
4_RenatoCargill_apresentaçãoequipeagroplus
 
Nuclear Fusion Reactor - Eco-friendly Atomic Energy
Nuclear Fusion Reactor - Eco-friendly Atomic EnergyNuclear Fusion Reactor - Eco-friendly Atomic Energy
Nuclear Fusion Reactor - Eco-friendly Atomic Energy"Douglas" F. Palte
 
ultra structure of nucleus
ultra structure of nucleusultra structure of nucleus
ultra structure of nucleusSana Khan
 
OBC | String theory and quests for unification of fundamental forces of nature
OBC | String theory and quests for unification of fundamental forces of natureOBC | String theory and quests for unification of fundamental forces of nature
OBC | String theory and quests for unification of fundamental forces of natureOut of The Box Seminar
 
Nuclear physics report
Nuclear physics reportNuclear physics report
Nuclear physics reportHazel Hall
 
JINR seminar on cold nuclear fusion, Dubna, Russia, July 2014 (English)
JINR seminar on cold nuclear fusion, Dubna, Russia, July 2014 (English)JINR seminar on cold nuclear fusion, Dubna, Russia, July 2014 (English)
JINR seminar on cold nuclear fusion, Dubna, Russia, July 2014 (English)ColdFusionPower
 
Neutrino research.docx
Neutrino research.docxNeutrino research.docx
Neutrino research.docxHari Ram
 
Term paper presentation on NUCLEAR COLD FUSION REACTION
Term paper presentation on NUCLEAR COLD FUSION REACTIONTerm paper presentation on NUCLEAR COLD FUSION REACTION
Term paper presentation on NUCLEAR COLD FUSION REACTIONAnurag Bhattacharjee
 
To the standard model - Ion Cotaescu
To the standard model - Ion CotaescuTo the standard model - Ion Cotaescu
To the standard model - Ion CotaescuSEENET-MTP
 
The Standard Model and the LHC in the Higgs Boson Era
The Standard Model and the LHC in the Higgs Boson EraThe Standard Model and the LHC in the Higgs Boson Era
The Standard Model and the LHC in the Higgs Boson Erajuanrojochacon
 
Intro to Coldfusion
Intro to ColdfusionIntro to Coldfusion
Intro to ColdfusionTerry Ryan
 
Nuclear waste management in Germany (compared to Denmark)
Nuclear waste management in Germany (compared to Denmark)Nuclear waste management in Germany (compared to Denmark)
Nuclear waste management in Germany (compared to Denmark)Oeko-Institut
 
Generation of electricity by nuclear fusion
Generation of electricity by nuclear fusionGeneration of electricity by nuclear fusion
Generation of electricity by nuclear fusionSamuel Haspot
 
Satellite RF Communication
Satellite RF CommunicationSatellite RF Communication
Satellite RF CommunicationJim Jenkins
 
Jack Oughton - A Layman's Guide To Nuclear Fusion v1.0
Jack Oughton - A Layman's Guide To Nuclear Fusion v1.0Jack Oughton - A Layman's Guide To Nuclear Fusion v1.0
Jack Oughton - A Layman's Guide To Nuclear Fusion v1.0Jack Oughton
 
Mossbauer spectroscopy
Mossbauer spectroscopyMossbauer spectroscopy
Mossbauer spectroscopyYogesh Chauhan
 
Experimental Searches for Dark Matter
Experimental Searches for Dark MatterExperimental Searches for Dark Matter
Experimental Searches for Dark MatterMorgan Catha
 

Destacado (20)

4_RenatoCargill_apresentação
4_RenatoCargill_apresentação4_RenatoCargill_apresentação
4_RenatoCargill_apresentação
 
Nuclear Fusion Reactor - Eco-friendly Atomic Energy
Nuclear Fusion Reactor - Eco-friendly Atomic EnergyNuclear Fusion Reactor - Eco-friendly Atomic Energy
Nuclear Fusion Reactor - Eco-friendly Atomic Energy
 
Nuclear world
Nuclear worldNuclear world
Nuclear world
 
ultra structure of nucleus
ultra structure of nucleusultra structure of nucleus
ultra structure of nucleus
 
In The Beginning
In The BeginningIn The Beginning
In The Beginning
 
OBC | String theory and quests for unification of fundamental forces of nature
OBC | String theory and quests for unification of fundamental forces of natureOBC | String theory and quests for unification of fundamental forces of nature
OBC | String theory and quests for unification of fundamental forces of nature
 
Nuclear physics report
Nuclear physics reportNuclear physics report
Nuclear physics report
 
JINR seminar on cold nuclear fusion, Dubna, Russia, July 2014 (English)
JINR seminar on cold nuclear fusion, Dubna, Russia, July 2014 (English)JINR seminar on cold nuclear fusion, Dubna, Russia, July 2014 (English)
JINR seminar on cold nuclear fusion, Dubna, Russia, July 2014 (English)
 
Neutrino research.docx
Neutrino research.docxNeutrino research.docx
Neutrino research.docx
 
Term paper presentation on NUCLEAR COLD FUSION REACTION
Term paper presentation on NUCLEAR COLD FUSION REACTIONTerm paper presentation on NUCLEAR COLD FUSION REACTION
Term paper presentation on NUCLEAR COLD FUSION REACTION
 
To the standard model - Ion Cotaescu
To the standard model - Ion CotaescuTo the standard model - Ion Cotaescu
To the standard model - Ion Cotaescu
 
The Standard Model and the LHC in the Higgs Boson Era
The Standard Model and the LHC in the Higgs Boson EraThe Standard Model and the LHC in the Higgs Boson Era
The Standard Model and the LHC in the Higgs Boson Era
 
Intro to Coldfusion
Intro to ColdfusionIntro to Coldfusion
Intro to Coldfusion
 
Nuclear waste management in Germany (compared to Denmark)
Nuclear waste management in Germany (compared to Denmark)Nuclear waste management in Germany (compared to Denmark)
Nuclear waste management in Germany (compared to Denmark)
 
Generation of electricity by nuclear fusion
Generation of electricity by nuclear fusionGeneration of electricity by nuclear fusion
Generation of electricity by nuclear fusion
 
cold fusion ppt
cold fusion pptcold fusion ppt
cold fusion ppt
 
Satellite RF Communication
Satellite RF CommunicationSatellite RF Communication
Satellite RF Communication
 
Jack Oughton - A Layman's Guide To Nuclear Fusion v1.0
Jack Oughton - A Layman's Guide To Nuclear Fusion v1.0Jack Oughton - A Layman's Guide To Nuclear Fusion v1.0
Jack Oughton - A Layman's Guide To Nuclear Fusion v1.0
 
Mossbauer spectroscopy
Mossbauer spectroscopyMossbauer spectroscopy
Mossbauer spectroscopy
 
Experimental Searches for Dark Matter
Experimental Searches for Dark MatterExperimental Searches for Dark Matter
Experimental Searches for Dark Matter
 

Más de Dr.imran aziz

Plasma physics by Dr. imran aziz
Plasma physics by Dr. imran azizPlasma physics by Dr. imran aziz
Plasma physics by Dr. imran azizDr.imran aziz
 
Nanotechnology,ppt by dr.imran aziz [compatibility mode]
Nanotechnology,ppt by dr.imran aziz [compatibility mode]Nanotechnology,ppt by dr.imran aziz [compatibility mode]
Nanotechnology,ppt by dr.imran aziz [compatibility mode]Dr.imran aziz
 
Crystal physics by imran aziz
Crystal physics  by imran azizCrystal physics  by imran aziz
Crystal physics by imran azizDr.imran aziz
 
Fundamentals of modern physics by imran aziz
Fundamentals of modern physics  by imran azizFundamentals of modern physics  by imran aziz
Fundamentals of modern physics by imran azizDr.imran aziz
 
Technical Schedule Seems2010
Technical Schedule Seems2010Technical Schedule Seems2010
Technical Schedule Seems2010Dr.imran aziz
 
Effect Of Many Body Interactions On Indices Of Refraction Of Alkali Halides
Effect Of Many Body Interactions On Indices Of Refraction Of Alkali HalidesEffect Of Many Body Interactions On Indices Of Refraction Of Alkali Halides
Effect Of Many Body Interactions On Indices Of Refraction Of Alkali HalidesDr.imran aziz
 
Effect Of Many Body Interactions On Indices Of Refraction Of Alkali Halides
Effect Of Many Body Interactions On Indices Of Refraction Of Alkali HalidesEffect Of Many Body Interactions On Indices Of Refraction Of Alkali Halides
Effect Of Many Body Interactions On Indices Of Refraction Of Alkali HalidesDr.imran aziz
 
Conducting Polymer By Imran Aziz
Conducting Polymer By Imran AzizConducting Polymer By Imran Aziz
Conducting Polymer By Imran AzizDr.imran aziz
 
Conducting Polymer By Imran Aziz
Conducting Polymer By Imran AzizConducting Polymer By Imran Aziz
Conducting Polymer By Imran AzizDr.imran aziz
 
Introduction To Luminescence
Introduction To LuminescenceIntroduction To Luminescence
Introduction To LuminescenceDr.imran aziz
 

Más de Dr.imran aziz (10)

Plasma physics by Dr. imran aziz
Plasma physics by Dr. imran azizPlasma physics by Dr. imran aziz
Plasma physics by Dr. imran aziz
 
Nanotechnology,ppt by dr.imran aziz [compatibility mode]
Nanotechnology,ppt by dr.imran aziz [compatibility mode]Nanotechnology,ppt by dr.imran aziz [compatibility mode]
Nanotechnology,ppt by dr.imran aziz [compatibility mode]
 
Crystal physics by imran aziz
Crystal physics  by imran azizCrystal physics  by imran aziz
Crystal physics by imran aziz
 
Fundamentals of modern physics by imran aziz
Fundamentals of modern physics  by imran azizFundamentals of modern physics  by imran aziz
Fundamentals of modern physics by imran aziz
 
Technical Schedule Seems2010
Technical Schedule Seems2010Technical Schedule Seems2010
Technical Schedule Seems2010
 
Effect Of Many Body Interactions On Indices Of Refraction Of Alkali Halides
Effect Of Many Body Interactions On Indices Of Refraction Of Alkali HalidesEffect Of Many Body Interactions On Indices Of Refraction Of Alkali Halides
Effect Of Many Body Interactions On Indices Of Refraction Of Alkali Halides
 
Effect Of Many Body Interactions On Indices Of Refraction Of Alkali Halides
Effect Of Many Body Interactions On Indices Of Refraction Of Alkali HalidesEffect Of Many Body Interactions On Indices Of Refraction Of Alkali Halides
Effect Of Many Body Interactions On Indices Of Refraction Of Alkali Halides
 
Conducting Polymer By Imran Aziz
Conducting Polymer By Imran AzizConducting Polymer By Imran Aziz
Conducting Polymer By Imran Aziz
 
Conducting Polymer By Imran Aziz
Conducting Polymer By Imran AzizConducting Polymer By Imran Aziz
Conducting Polymer By Imran Aziz
 
Introduction To Luminescence
Introduction To LuminescenceIntroduction To Luminescence
Introduction To Luminescence
 

Último

CapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapitolTechU
 
How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17Celine George
 
What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?TechSoup
 
3.21.24 The Origins of Black Power.pptx
3.21.24  The Origins of Black Power.pptx3.21.24  The Origins of Black Power.pptx
3.21.24 The Origins of Black Power.pptxmary850239
 
Practical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxPractical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxKatherine Villaluna
 
How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17Celine George
 
AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxAUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxiammrhaywood
 
Patterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptxPatterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptxMYDA ANGELICA SUAN
 
M-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxM-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxDr. Santhosh Kumar. N
 
The Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsThe Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsEugene Lysak
 
How to Solve Singleton Error in the Odoo 17
How to Solve Singleton Error in the  Odoo 17How to Solve Singleton Error in the  Odoo 17
How to Solve Singleton Error in the Odoo 17Celine George
 
PISA-VET launch_El Iza Mohamedou_19 March 2024.pptx
PISA-VET launch_El Iza Mohamedou_19 March 2024.pptxPISA-VET launch_El Iza Mohamedou_19 March 2024.pptx
PISA-VET launch_El Iza Mohamedou_19 March 2024.pptxEduSkills OECD
 
5 charts on South Africa as a source country for international student recrui...
5 charts on South Africa as a source country for international student recrui...5 charts on South Africa as a source country for international student recrui...
5 charts on South Africa as a source country for international student recrui...CaraSkikne1
 
How to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesHow to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesCeline George
 
CAULIFLOWER BREEDING 1 Parmar pptx
CAULIFLOWER BREEDING 1 Parmar pptxCAULIFLOWER BREEDING 1 Parmar pptx
CAULIFLOWER BREEDING 1 Parmar pptxSaurabhParmar42
 
DUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRA
DUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRADUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRA
DUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRATanmoy Mishra
 
Benefits & Challenges of Inclusive Education
Benefits & Challenges of Inclusive EducationBenefits & Challenges of Inclusive Education
Benefits & Challenges of Inclusive EducationMJDuyan
 
Presentation on the Basics of Writing. Writing a Paragraph
Presentation on the Basics of Writing. Writing a ParagraphPresentation on the Basics of Writing. Writing a Paragraph
Presentation on the Basics of Writing. Writing a ParagraphNetziValdelomar1
 
How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17Celine George
 
The basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxThe basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxheathfieldcps1
 

Último (20)

CapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptx
 
How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17
 
What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?What is the Future of QuickBooks DeskTop?
What is the Future of QuickBooks DeskTop?
 
3.21.24 The Origins of Black Power.pptx
3.21.24  The Origins of Black Power.pptx3.21.24  The Origins of Black Power.pptx
3.21.24 The Origins of Black Power.pptx
 
Practical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxPractical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptx
 
How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17
 
AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxAUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
 
Patterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptxPatterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptx
 
M-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxM-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptx
 
The Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsThe Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George Wells
 
How to Solve Singleton Error in the Odoo 17
How to Solve Singleton Error in the  Odoo 17How to Solve Singleton Error in the  Odoo 17
How to Solve Singleton Error in the Odoo 17
 
PISA-VET launch_El Iza Mohamedou_19 March 2024.pptx
PISA-VET launch_El Iza Mohamedou_19 March 2024.pptxPISA-VET launch_El Iza Mohamedou_19 March 2024.pptx
PISA-VET launch_El Iza Mohamedou_19 March 2024.pptx
 
5 charts on South Africa as a source country for international student recrui...
5 charts on South Africa as a source country for international student recrui...5 charts on South Africa as a source country for international student recrui...
5 charts on South Africa as a source country for international student recrui...
 
How to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesHow to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 Sales
 
CAULIFLOWER BREEDING 1 Parmar pptx
CAULIFLOWER BREEDING 1 Parmar pptxCAULIFLOWER BREEDING 1 Parmar pptx
CAULIFLOWER BREEDING 1 Parmar pptx
 
DUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRA
DUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRADUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRA
DUST OF SNOW_BY ROBERT FROST_EDITED BY_ TANMOY MISHRA
 
Benefits & Challenges of Inclusive Education
Benefits & Challenges of Inclusive EducationBenefits & Challenges of Inclusive Education
Benefits & Challenges of Inclusive Education
 
Presentation on the Basics of Writing. Writing a Paragraph
Presentation on the Basics of Writing. Writing a ParagraphPresentation on the Basics of Writing. Writing a Paragraph
Presentation on the Basics of Writing. Writing a Paragraph
 
How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17How to Show Error_Warning Messages in Odoo 17
How to Show Error_Warning Messages in Odoo 17
 
The basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptxThe basics of sentences session 10pptx.pptx
The basics of sentences session 10pptx.pptx
 

Advanced nuclear physics [compatibility mode]

  • 1. Advanced Nuclear Physics MOHAMMAD IMRAN AZIZ Assistant Professor PHYSICS DEPARTMENT SHIBLI NATIONAL COLLEGE, AZAMGARH (India). pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 2. Nuclides The total number of protons in the nucleus of an atom is called the atomic number of the atom and is given the symbol Z. The number of electrons in an electrically-neutral atom is the same as the number of protons in the nucleus. The number of neutrons in a nucleus is known as the neutron number and is given the symbol N. The mass number of the nucleus is the total number of nucleons, that is, protons and neutrons in the nucleus. The mass number is given the symbol A and can be found by the equation Z + N = A. . pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 3. why electrons cannot exist inside a nucleus: Nuclear constituents and their properties This can be explained mathematically also using Heisenberg's uncertainty principle as follows pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 4. Confinement Calculation Electtron is not found in the nucleus, it means we are talking about free electron. That is free electron does not exist.n ....> p + e, here this is beta deacy and electron that becomes free is emitted out of the nucleus as free electron as can not exist due to Heisenberg uncertainty. pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 5. It is common practice to represent the total angular momentum of a Nuclear Spin nucleus by the symbol I and to call it "nuclear spin". For electrons in atoms we make a clear distinction between electron spin and electron orbital angular momentum, and then combine them to give the total angular momentum. But nuclei often act as if they are a single entity with intrinsic angular momentum I. Associated with each nuclear spin is a nuclear magnetic moment which produces magnetic interactions with its environment. The nuclear spins for individual protons and neutrons parallels the treatment of electron spin, with spin 1/2 and an associated magnetic moment. The magnetic moment is much smaller than that of the electron. For the combination neutrons and protons into nuclei, the situation is more complicated. pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 6. • A characteristic of the collection of protons and neutrons (which are fermions) is that a nucleus of odd mass number A will have a half-integer spin and a nucleus of even A will have integer spin. The suggestion that the angular momenta of nucleons tend to form pairs is supported by the fact that all nuclei with even Z and even N have nuclear spin I=0. The half-integer spins of the odd-A nuclides suggests that this is the nuclear spin contributed by the odd neutron pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 7. Nuclear Magnetic Moments • Associated with each nuclear spin is a magnetic moment which is associated with the angular momentum of the nucleus. It is common practice to express these magnetic moments in terms of the nuclear spin in a manner parallel to the treatment of the magnetic moments of electron spin and electron orbital angular momentum. • For the electron spin and orbital cases, the magnetic moments are expressed in terms of a unit called a Bohr magneton which arises naturally in the treatment of quantized angular momentum pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 8. Electric Quadrupole Moments of Nuclei The nuclear electric quadrupole moment is a parameter which describes the effective shape of the ellipsoid of nuclear charge distribution. A non-zero quadrupole moment Q indicates that the charge distribution is not spherically symmetric. By convention, the value of Q is taken to be positive if the ellipsoid is prolate and negative if it is oblate. The quantity Q0 is the classical form of the calculation represents the departure from spherical symmetry in the rest frame of the nucleus. pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 9. Generally, the measured quantity is proportional to the z-component of the magnetic moment (the component along the experimentally determined direction such as the direction of an applied magnetic field, etc. ). In this treatment, the use of a "gyromagnetic ratio" or "g-factor" is introduced. The g- factor for orbital is just gL = 1, but the electron spin g-factor is approximately gS = 2 pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 10. For free protons and neutrons with spin I =1/2, the magnetic moments are of the form where Proton: g = 5.5856912 +/- 0.0000022 Neutron: g = -3.8260837 +/- 0.0000018 The proton g-factor is far from the gS = 2 for the electron, and even the uncharged neutron has a sizable magnetic moment! For the neutron, this suggests that there is internal structure involving the movement of charged particles, even though the net charge of the neutron is zero. If g=2 were an expected value for the proton and g=0 were expected for the neutron, then it was noted by early researchers that the the proton g-factor is 3.6 units above its expected value and the neutron value is 3.8 units below its expected value. This approximate symmetry was used in trial models of the magnetic moment, and in retrospect is taken as an indication of the internal structure of quarks in the standard model of the proton and neutron pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 11. Note that the maximum effective magnetic moment of a nucleus in nuclear magnetons will be the g-factor multiplied by the nuclear spin. For a proton with g = 5.5857 the quoted magnetic moment is m = 2.7928 nuclear magnetons. Nuclear Magnetic moment Nuclide spin I m in mN n 1/2 -1.9130418 p 1/2 +2.7928456 2H(D) 1 +0.8574376 17O 5/2 -1.89279 57Fe 1/2 +0.09062293 57Co 7/2 +4.733 93Nb 9/2 +6.1705 pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 12. Nuclei • Parameters of nuclei • Strong Interaction • Binding Energy • Stable and Unstable Nuclei • Liquid-Drop Model Numerous Applications: • nuclear power • applications in medicine, biology and chemistry • evolution of stars and the Universe • nuclear weapons pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 13. Size of Nuclei and Rutherford Scattering 1/3 R  R0 A - depends weakly on A (number of nucleons in the nucleus) R0  1.2 1015 m  1.2 fm Geiger, Marsden, 238 1/3 Rutherford,1910 R 92 U   1.2 fm   238   7.4 fm Scattering pattern was consistent with that expected for -particles: bare He nuclei scattering of  particles by pointlike objects having a charge of +79e (the charge of the gold nucleus). This allowed Rutherford to put an upper limit on the size of the nucleus (<310-14m for gold). Calculations were strictly classical. However, because of the Coulomb interaction between alpha-particles and nucleus, the result miraculously coincides with the exact quantum-mechanical one (recall the success of the Bohr model for atoms). To measure the size of a nucleus, one has to use more energetic  particles (or electrons, which are more R – the fitting commonly used these days) that get parameter pdfMachine close enough to get inside the nucleus. A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 14. Nuclear Mass A 12 X C number of nucleons in the nucleus chemical symbol 6 Z (mass number of the nucleus) for the element number of protons in the nucleus 6 protons + 6 neutrons N  A Z (atomic number of the element) The neutron number: Atomic Mass (the mass of a neutral atom): M  Z  m p  N  mn  U nucleus / c 2  Z  me  U el .nucl . / c 2 U nucleus ,U el .nucl .  0 - attraction between nucleons in the nucleus and between electrons and the nucleus U el .nucl .  U nucleus  mp c 2 - we can neglect Uel.-nucl. and introduce a convenient mass unit: M 12 C 1u  6  1.66054 1027 kg  931.49MeV / c 2 12 Mass Unit m p  proton mass  1.007277u mn  neutron mass  1.008665u m  electron mass  0.000549u pdfMachine e A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 15. Nuclear Density MA  1au  1au 3 3 3 3 3 3    R  R0 A  R0 4 4 4 1.66 1027 kg  2.4 1017 kg / m3 3 15 3   1.2 10 m  4 ! The density of neutron stars is comparable with that of nuclei. (Unstable) isotopes of tin and zinc. pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 16. The Need for a “Strong Force” Which interaction controls the size of nucleons? This cannot be electromagnetic interaction: protons have the same electric charge (they would repel each other) and also there are attractive forces between protons and electrically neutral neutrons. Strong Interaction: binds protons to protons, neutrons to neutrons, and protons to neutrons with roughly the same force does not affect certain other kinds of particles (specifically electrons) is short-ranged (the range ~ 2 fm). Nucleons separated by a larger distance exert no strong forces on each other. These observations are explained by the quark model of nucleons. g Nucleons are the combination of quarks that are strong-interaction- u neutral (like an electrically-neutral atom). Two nucleons interact only if they are close enough that the distances between various pairs of d quarks are significantly different. u quarks and gluons ~ 10-15 m pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 17. Structure of Matter g u El.-mag. interaction u d determines the size of quarks atoms and gluons ~ 10-15 m ~ 10-10 - 10-9 m Protons & Neutrons (nucleons) are almost an empty space (the Atom is almost an quark size is <10-18 m) empty space (the nuclear volume is ~10- 15 of the atomic volume) Strong interaction determines the size of nuclei and nucleons pdfMachine A pdf writer that produces quality PDF files with -15 ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across ~ 10 - 10 -14m nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 18. Binding Energy Binding energy: Esys  EB  E parts EB  E parts  Esys -the binding energy is positive for a bound system Recall a H atom: the binding energy is 13.6 eV (the ground state energy with sign “minus”). n n p p add EB n n E parts   mi  c 2 Esys p We can compute the binding energy if we know masses of a system and its constituents: EB   mass of all particles consituting the atom    mass of the atom    c 2     Z  m1 H  N  mn  M A X   c 2 EB  M  c 2  1 Z  mass deficit pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 19. Binding Energy curve Because of the short-range character of strong interaction (basically, between nearest and next-to- nearest neighbors), the interaction energy per nucleon with increasing Z saturates at the level ~ (Z/2)(# of neighbors). Binding energy per nucleon (EB/A), MeV increasing Z is caused by the long-range Coulomb B   Z 2 The decrease of the binding energy with repulsion of protons: Mass number, A The binding energy ~ 10MeV/nucleon is ~1% of the nucleon’s rest energy: we can pdfMachine consider the nucleus as a system of individual nucleons A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 20. Liquid-Drop Model 2 2 A “semi-classical” model of the EB  aV A  as A2/3  ac Z  aa  A  2Z  A1/3 A nucleus: describes reasonably well the dependence EB(A): dq  r  q r  - charge density q r dq  r   4 3 2     r    4 r  dr R0 3 U  R0      0 4 0 r pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 21. Liquid-Drop Model (cont’d) pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 22. Limitations of Liquid-Drop Model Maria Goeppert-Mayer, J.H.D.Jensen pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 23. Stable Nuclei Isotopes: all nuclei that have the same number of protons (Z) but different number of neutrons (N). Since the chemical properties of an atom are determined by the number of its electrons, isotopes of the same element have almost identical chemical properties. Example: naturally occurring isotopes of oxygen 16 17 19 8 0 8 0 8 0 Related questions: - What makes unstable nuclei unstable? - What are the mechanisms by which they transform themselves into stable nuclei? -Why do light stable nuclei tend to have N  Z? - Why do heavier nuclei tend to have more neutrons than protons? - Why are there no stable nuclei with Z>83? pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 24. What makes unstable nuclei unstable? Both protons - and neutrons are energy fermions (they obey the exclusion principle). Nuclei are two- 0 r component Fermi systems. Each nuclear energy level can contain four particles: two protons (s=½) 12 and two neutrons (s=½). 6 C The potential experienced by nucleons is a 3D potential well. The ground-state configuration of the carbon-16 nucleus : If a nucleus is allowed to decrease its energy by transforming “excessive” protons (neutrons) into neutrons (protons), it will do it! protons neutrons The processes responsible for these transformations are driven by weak interaction (the fourth fundamental interaction): The weak interaction (unlike the strong interaction) affects both quarks and leptons, (unlike the el.-mag. interaction) can affect electrically neutral particles, and (unlike gravity) does not affect photons. The effective range of the weak interaction is ~ 10-18m. Some important transformation processes driven by weak interaction: n  e  p   pdfMachine p   n  e  A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in p   e  n  Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 25. Why N  Z for light nuclei 13 13 8 O energy 7 N energy If the electrostatic repulsion t1/2  8.9ms of protons can be neglected (this is the case of light nuclei: recall that the positive electrostatic energy Z2), the nucleus tends to keep approximately equal numbers of protons and neutrons. protons neutrons protons neutrons 14 14 6 C energy 7 N energy Even in this case, the nucleus t1/2  5730 y can still lower its total energy: the rest energy of neutron is slightly more than the rest energy of a proton and an electron. pdfMachine A pdf writer that produces quality PDF files with ease! protons neutrons protons aziz_muhd33@yahoo.co.in neutrons Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 26. Why N > Z for heavy nuclei 44 44 22 Ti energy 20 Ca energy In the heavy nuclei, the electrostatic energy cannot be neglected. As a result, the protons’ energy levels are “pushed up” with respect to the neutrons’ levels. In the “otherwise stable” 44Ti, two protons undergo the transformation into neutrons, the end product is stable 44Ca. . . . . . . . . . . protons neutrons protons neutrons The proton-neutron disbalance becomes more pronounced with increasing Z. pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 27. Nuclear Masses and Sizes • Masses and binding energies – Absolute values measured with mass spectrometers. – Relative values from reactions and decays. • Nuclear Sizes – Measured with scattering experiments (leave discussion until after we have looked at Rutherford scattering). – Isotope shifts pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 28. Nuclear Mass Measurements • Measure relative masses by energy released in decays or reactions. – X  Y +Z + DE – Mass difference between X and Y+Z is DE/c2. • Absolute mass by mass spectrometers (next transparency). • Mass and Binding energy: • B = [Z MH + N Mn – M(A,Z)]/c2 pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 29. Mass Spectrometer • Ion Source • Velocity selector  Detector electric and magnetic forces equal and opposite Velocity – qE=qvB  v=E/B Ion Source selector • Momentum selector, circular orbit satisfies: – Mv=qBr – Measurement r gives M. pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 30. Binding Energy vs A • B increases with A up to 56Fe and then slowly decreases. Why? • Lower values and not smooth at small A. pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 31. Nuclear Sizes & Isotope Shift • Coulomb field modified by finite size of nucleus. • Assume a uniform charge distribution in the nucleus. Gauss’s law  r 3Ze integrate and apply boundary conditions E ( ) 2 R 4 0 r • Difference between actual potential and Coulomb Zer 2 3Ze V (r )   3 8 0 R 8 0 R  • Use 1st order perturbation theory Zer 2 3Ze Ze V ( r )   3 (r  R ) 8 0 R 8 0 R 4 0r   R Z 3/ 2 Z 2 * E   4r  ( r )[ eV ( r )] ( r )dr  ( r )  2( ) exp( Zr / a0 )  2( )3 / 2 0 a0 a0 pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 32. Isotope Shifts R 2 3Ze 3 Ze Zer 2 E   4r 4( Z / a ) (  e)[ 3 ] dr 8 0R 8 0 R 4 0r   0 R 4R 5 R 4R 3 R 1 4 r 2 r 2dr  2  4 r dr  2  4 r dr  2R 2 0 5 0 3 0 r  Ze 2 4  4  3  3 E  ( 4e)( Z / a ) R [        2 ] 4 0 10  3  2  2 2 2 Ze R 3 E  ( Z / a0 ) 5 0 pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 33. Isotope Shifts • Isotope shift for optical spectra • Isotope shift for X-ray spectra (bigger effect because electrons closer to nucleus) • Isotope shift for X-ray spectra for muonic atoms. Effect greatly enhanced because mm~ 207 me and a0~1/m. • All data consistent with R=R0 A1/3 with R0=1.25fm. pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 34. Liquid Drop Model Nucleus • Phenomenological model to understand binding energies. • Consider a liquid drop – Ignore gravity and assume no rotation – Intermolecular force repulsive at short distances, attractive at intermediate distances and negligible at large distances  constant density. E=-an + 4pR2T B=an-bn2/3 • Analogy with nucleus – Nucleus has constant density – From nucleon nucleon scattering experiments: Nuclear force has short range repulsion and attractive at intermediate distances. – Assume charge independence of nuclear force, neutrons and protons have same strong interactions check with experiment! pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 35. Mirror Nuclei • Compare binding energies of mirror nuclei (nuclei n p). Eg 73Li and 74Be. • Mass difference due to n/p mass and Coulomb R energy. Q( r ) E dQ 0 4 0 r Q( r )  Ze( r / R ) 3 dQ  3 Zer 2 / R 3 3( Ze ) 2 r 5 R ( Ze ) 2 E 6 dr  ( 3 / 5) 0 4 0 r R 4 0 R 3 e2 E c ( Z , Z  1)  [ Z ( Z  1)  ( Z  1)( Z  2)] ; Z ~ A / 2 ; R  A1 / 3 5 4 0 R EC ( Z , Z  1)  A2 / 3 pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 36. Liquid Drop Model Nucleus • Phenomenological model to understand binding energies. • Consider a liquid drop – Ignore gravity and assume no rotation – Intermolecular force repulsive at short distances, attractive at intermediate distances and negligible at large distances  constant density. – n=number of molecules, T=surface tension, B=binding energy E=total energy of the drop, a,b=free constants E=-an + 4pR2T  B=an-bn2/3 surface area ~ n2/3  Analogy with nucleus  Nucleus has constant density  From nucleon-nucleon scattering experiments we know:  Nuclear force has short range repulsion and is attractive at intermediate distances.  Assume charge independence of nuclear force, neutrons and protons have same strong interactions check with experiment (Mirror Nuclei!) pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 37. Coulomb Term • The nucleus is electrically charged with total charge Ze • Assume that the charge distribution is spherical and compute the reduction in binding energy due to the Coulomb interaction Ze Q(r ) ECoulomb  dQ Q (r )  Ze(r / R )3 dQ  3Zer 2 / R 3 dr 0  4 0 r to change the integral to dr ; R=outer radius of nucleus R 3( Ze) 2 r 5 ( Ze) 2 ECoulomb   dr  (3 / 5) includes self interaction of last 6 4 0 r R 4 0 R proton with itself. To correct this 0 replace Z2 with Z*(Z-1) … and remember R=R0A-1/3 in principle you could take d from this calculation Z *( Z  1) BCoulomb ( Z , A)  d but it is more accurate to take it from the overall 1/ 3 A fit of the SEMF to data (nuclei not totally pdfMachine spherical or homogeneous) A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 38. Mirror Nuclei • Does the assumption of the drop model of constant binding energy for every constituent of the drop acatually hold for nuclei? • Compare binding energies of mirror nuclei (nuclei with np). Eg 73Li and 7 Be. 4 • If the assumption holds the mass difference should be due to n/p mass difference and Coulomb energy alone. • Let’s compute the Coulomb energy correction from results on previous page 3 e2 3 e2 Ecoulomb ( Z , Z  1)  [ Z ( Z  1)  ( Z  1)( Z  2)]  2( Z  1) 5 4 0 R 5 4 0 R Z ~ A / 2 ; R  R0 A1/ 3 to find that EC ( Z , Z  1)  A2 / 3  Now lets measure mirror nuclei masse, assume that the model holds and derive DECoulomb from the measurement.  This should show an A2/3 dependence  And the scaling factor should yield the correct R0 of 1.2 fm  pdfMachine if the assumptions were right A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 39. “Charge symmetry” nn and pp interaction same (apart from Coulomb) pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 40. More charge symmetry • Energy Levels of two mirror nuclei for a number of excited states • Corrected for n/p mass difference and Coulomb Energy DEcorrected pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 41. From Charge Symmetry to Charge Independence • Mirror nuclei showed that strong interaction is the same for nn and pp. • What about np ? • Compare energy levels in “triplets” with same A, different number of n and p. e.g. 22 22 22 10 Ne 11 Na 12 Mg • If we find the same energy levels for the same spin states  Strong interaction is the same for np as nn and pp. pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 42. Charge Independence DEcorrected • Same spin/parity states should have the same energy. • Yes: np=nn=pp • Note: Far more states in 22 Na. Why? 11 • Because it has more np pairs then the others • np pairs can be in any Spin- Space configuration • pp or nn pairs are excluded from the totally symmetric ones by Herr Pauli 22 10Ne • Note also that 2211Na has the 22 lowest (most bound) state, 12Mg remember for the deuteron 22 11Na on next page pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 43. Charge Independence • We have shown by measurement that: – If we correct for n/p mass difference and Coulomb interaction, then energy levels in nuclei are unchanged under n  p – and we must change nothing else! I.e. spin and space wavefunctions must remain the same! • Conclusion: strong two-body interaction same for pp, pn and nn if nucleons are in the same quantum state. • Beware of the Pauli exclusion principle! eg why do we have bound state of pn but not pp or nn? – because the strong force is spin dependent and the most strongly bound spin-space configurations (deuteron) are not available to nn or pp. It’s Herr Pauli again! – Just like 2211Na on the previous triplet level schema pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 44. Volume and Surface Term • We now have all we need to trust that we can apply the liquid drop model to a nucleus – constant density – same binding energy for all constituents • Volume term: BVolume ( A)   aA 2/3 • Surface term: BSurface ( A)  bA • Since we are building a phenomenological model in which the coefficients a and b will be determined by a fit to measured nuclear binding energies we must inlcude any further terms we may find with the same A dependence together with the above pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 45. Asymmetry Term • Neutrons and protons are spin ½ fermions  obey Pauli exclusion principle. • If all other factors were equal nuclear ground state would have equal numbers of n & p. neutrons protons Illustration  n and p states with same spacing .  Crosses represent initially occupied states in ground state.  If three protons were turned into neutrons  the extra energy required would be 3×3 .  In general if there are Z-N excess protons over neutrons the extra energy is ((Z-N)/2)2 . relative to Z=N.  But how big is D ? pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 46. Asymmetry Term • Assume: – p and n form two independent, non-interacting gases occupying their own square Fermi wells – kT << D – so we can neglect kT and assume T=0 – This ought to be obvious as nuclei don’t suddenly change state on a warm summers day! – Nucleons move non-relativistically (check later if this makes sense) pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 47. Asymmetry Term • From stat. mech. density of states in 6d phase space = 1/h3 4 p 2 dpV dN particle  h3 here N could be the number of protons or neutrons particle • Integrate up to pf to get total number of protons Z (or Neutrons N), & Fermi Energy (all states filled up to this energy level). 3 3 4 3 Z  (4 V / 3h ) pF and V   R0 A 3 1/ 3 2 2/3 h Z 2 h Z PF  (3 / 4 ) 2/3 and E  p  EF  (3 / 4 ) 4/3 R0  A 2m 2mR02  A     EF • Change variables p  E to find avg. E E 3/ 2 dE dN / dp dN / dE   const  E1/ 2  E  0  (3 / 5) EF  EF dp / dE E1/ 2 dE 0  pdfMachine These are all standard stat. mech. results! A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 48. Asymmetry Term  Compute total energy of all protons by Z*<E> call this K 2 2/3 P P 3 4/3 h Z E Total Z E  (3 / 4 ) 2 Z  5 2mR0  A   Use the above to compute total energy of Z protons and N neutrons K ETotal   Z 5/ 3  N 5/ 3  change variables from (Z,N,A) A2 / 3   to (y,A) with y=N-Z KA5/ 3 ETotal  2 / 3 5 3  (1  y / A)5/ 3  (1  y / A)5/ 3  where y/A is a small number (e) A 2  KA  ETotal  5 3 (1   )5/ 3  (1   )5/ 3  2   • Binomial expansion keep lowest term in y/A 2 3 21 35 ( N  Z ) 2 ETotal  2 KA  K note! linear terms cancel 9 A ( N  Z )2 ETotal ( Fermi  Gas )  const * This terms is only proportional to volume A comes from a fit of the (A). It has already been captured by the Volume term of the liquid pdfMachine SEMF to measurements A pdf writer that produces quality PDF files with ease! drop model aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across analytical ≈ 24 MeV nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 49. Asymmetry term • From the Fermi Gas model we learn that – due to the fermionic nature of p and n we loose in binding energy if the nucleus deviates from N=Z ( N  Z )2 • The Asymmetry term: B Asymmetry ( N , Z )   c A pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 50. • Observations: • Nuclei with even number of n or Pairing Term even number of p more tightly Neutron separation energy bound then with odd numbers. [MeV] in Ba isotopes See figure • Only 4 stable o-o nuclei but 153 stable e-e nuclei. • p energy levels are Coulomb 56+N 56Ba shifted wrt n  small overlap of wave functions between n and p. • Two p or two n in same energy level with opposite values of jz have AS spin state  forced into sym spatial w.f.  maximum overlap  maximum binding energy Neutron number because of short range attraction. Note: this only holds for nn and pp, not for np.  We don’t have a preference for even A pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 51. Pairing Term • Measure that the Pairing effect smaller for larger A • Phenomenological*) fit to A dependence gives A-1/2 BPairing ( A)   1/ 2  A d Note: If you want to plot binding energies e-e +ive versus A it is often best to use odd A only as for these the pairing term does not e-o 0 appear o-o -ive *) For an even more insightful explanation of the A dependence read the book by Jelley pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 52. Semi Empirical Mass Formula • Put everything together: 2 2 2/3 (N  Z ) Z B( N , Z )  aA  bA c  d 1/ 3  1/ 2  A A A Volume Surface Asymmetry Coulomb Pairing Term Term Term Term Term  Lets see how all of these assumptions fit reality  And find out what the constants are  Note: we went back to the simpler Z instead of Z*(Z-1) 2 pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 53. Semi Empirical Mass Formula Binding Energy vs. A for beta-stable odd-A nuclei Fit parameters Iron in MeV a 15.56 Not smooth because Z b 17.23 not smooth function of A c 23.285 d 0.697 d +12 (o-o) d 0 (o-e) d -12 (e-e) pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 54. Semi Empirical Mass Formula • Conclusions – Only makes sense for A≥20 – Good fit for large A (good to <1%) in most places. – Deviations are interesting  shell effects. – Coulomb term constant agrees with calculation. – Explains the valley of stability (see next lecture). – Explains energetics of radioactive decays, fission and fusion. pdfMachine A pdf writer that produces quality PDF files with ease! aziz_muhd33@yahoo.co.in Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 55. Nuclear Shell Model • Potential between nucleons can be studied by studying bound states (pn, ppn, pnn, ppnn) or by scattering cross sections: np -> np pp -> pp nD -> nD pD -> pD • If had potential could solve Schrod. Eq. Don’t know precise form but can make general approximation • 3d Finite Well with little r-dependence (except at edge of well) • Almost spherically symmetric (fusion can be modeled as deformations but we’ll skip) • N-N interactions are limited (at high A) due to Pauli exclusion. p + n -> p’ + n’ only if state is available pdfMachine A pdf writer that produces quality PDF files with ease! Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 56. Infinite Radial Well 2 d 2u  2 l ( l  1)  • Radial part of Scrod Eq  V ( r )   u  Eu  2m dr 2 2m r2    u( r )  rR ( r ) P ( r )  4u 2 • Easy to solve if l=0 2 n p2 ( k ) 2 ( hn) 2 u  sin kr k  E  2a 2m 2m 8ma 2   • For L>0, angular momentum term goes to infinity at r=0. Reduces effective wavelength, giving higher energy • Go to finite well. Wave function extends a bit outside well giving longer effective wavelength and lower energy (ala 1D square wells) pdfMachine • In nuceli, potential goes to infinity at r=0 (even with L=0) as that A pdf writer that produces quality PDF files with ease! Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the would be equivalent to nucleon “inside” other nucleon “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 57. Angular part • If V(r) then can separate variables y(r,q,f) = R(r)Y( q,f) have spherical harmonics for angular wave function • Angular momentum then quantized like in Hydrogen (except that L>0 for n=1, etc) L2  l (l  1)  2 LZ   m l  0,1,2 m   l l n  r  quantum# • Energy doesn’t depend on m • Energy increases with increasing n (same l) • Energy increases with increasing l (same n) • If both n,l vary then use experimental observation to determine lower energy • Energy will also depend on strong magnetic coupling between pdfMachine nucleons A pdf writer that produces quality PDF files with ease! Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the • Fill up states separately for p,n “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 58. L,S,J Coupling: Atoms vs Nuclei • ATOMS: If 2 or more electrons, Hund’s rules: • Maximise total S for lowest E (S=1 if two) • Maximise total L for lowest E (L=2 if 2 P) • Energy split by total J (J=3,2,1 for S=1,L=2) • NUCLEI: large self-coupling. Plus if 2 p (or 2 n) then will anti-align giving a state with J=0, S=0, L=0 leftover “odd” p (or n) will have two possible J = L + ½ or J = L – ½ higher J has lower energy if there are both an odd P and an odd n (which is very rare in stable) then add up Jn + Jp • Atom called LS coupling nuclei called jj pdfMachine A pdf writer that produces quality PDF files with ease! • Note that magnetic moments add differently as different g-factor Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now! for p,n
  • 59. Spin Coupling in Nuclei • All nucleons in valence shell have same J • Strong pairing causes Jz antiparallel (3 and -3) spin wavefunction = antisymmetric space wavefunction = symmetric • This causes the N-N to be closer together and increases the attractive force between them • e-e in atoms opposite as repulsive force • Can also see in scattering of polarized particles • Even N, even Z nuclei. Total J=S=L=0 as all n,p paired off • Even N, odd Z or odd N, even Z. nuclear spin and parity determined by unpaired nucleon • Odd N, odd Z. add together unpaired n,p pdfMachine • Explains ad hoc pairing term in mass formula A pdf writer that produces quality PDF files with ease! Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 60. Energy Levels in Nuclei • Levels in ascending order (both p,n) State n L degeneracy(2j+1) sum 1S1/2 1 0 2 2*** 1P3/2 1 1 4 6 1P1/2 1 1 2 8*** 1D5/2 1 2 6 14 2S1/2 2 0 2 16 1D3/2 1 2 4 20*** 1F7/2 1 3 8 28*** 2P3/2 2 1 4 32 1F5/2 1 3 6 38 2P1/2 2 1 2 40 1G9/2 1 4 10 50*** *** “magic” number is where there is a large energy gap between a pdfMachine filled shell and the next level. More tightly bound nuclei. (all filled A pdf writer that produces quality PDF files with ease! Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across subshells are slightly “magic”) nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now!
  • 61. Magic Numbers • Large energy gaps between some filled shells and next (unfilled) shell give larger dE/A and more made during nucleosnthesis in stars # protons #neutrons 2 He 2 He-4 6 C 6 C-12 8 O 8 O-16 20 Ca 20 28 Ni 28 Cr-52(24,28) 50 Sn 50 Ni-78 82 Pb 82 126 136 • Ni-78 (2005) doubly magic. While it is unstable, it is the much neutron rich. pdfMachine A pdf writer that produces quality PDF files with ease! • Usually more isotopes if p or n are magic. Sn has 20 isotopes, 10 Produce quality PDF files in seconds and preserve the integrity of your original documents. Compatible across nearly all Windows platforms, simply open the document you want to convert, click “print”, select the “Broadgun pdfMachine printer” and that’s it! Get yours now! of which are stable