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Neutron Energies, Velocity & Thermal
Neutrons
 Abdul Rizwan (Reg# 2007-Mech-2616)

 Waleed Mumtaz (Reg# 2007-Mech-2615)

 Adnan Rasheed (Reg# 2007-Mech-2557)

 Adnan Khan (Reg# 2007-Mech-2620)

 Suhaib Ilyas (Reg# 2007-Mech-2595)
Neutron

 Sub atomic particle
 No charge and greater mass
 Free neutrons are unstable
 High penetrating power
 Essential in Fission process
Neutron Source
    Different sources of neutrons are:

   Radioisotopes which undergo spontaneous fission
   Radioisotopes which decay with alpha particles 
   Radioisotopes which decay with high energy photons
    co-located with beryllium or deuterium
   Plasma focus and plasma pinch devices
   Light ion accelerators
Neutron Energies
   Neutron energy indicates a free kinetic energy,
    usually given in electron volts

   En= mnV2/(2*gc) = 5.227*10-13 V2 ( eV)

   Fission neutron energy range is (0.075……..17 ) MeV

   Prompt neutron vs delayed neutron

   Prompt neutrons have average energy of about 2 MeV.
Prompt Neutron Energy Spectrum U235
Classification of Neutrons
• neutrons are classified according to their energy

• thermal neutrons have an energy of about
  ~ 0.025 eV
• epithermal neutrons, resonance neutrons, slow
  neutrons have energies between 0.01 MeV and 0.1
  MeV

• fast neutrons - 0.1 MeV and 20 MeV

• relativistic neutrons
Neutron Energy Distribution
Ranges
   Fast neutrons          > energy approximately 1 MeV
   Slow neutrons          > energy less than or equal 0.4 eV
   Epithermal neutrons   > energy 1 eV to 10 keV
   Hot neutrons          > energy about 0.2 eV
   Thermal neutrons       > energy of about 0.025 eV
   Cold neutrons         > energy 5x10−5 eV to 0.025 eV
   Very cold neutrons    > energy 3x10−7 eV to 5x10−5 eV
   Ultra cold neutrons   > energy less than 3x10−7 eV
   Continuum region      >energy 0.01 MeV to 25 MeV
   Resonance region      >energy 1 eV to 0.01 MeV
   Low energy region     > energy less than 1 eV
Thermal Neutrons
   Slow neutron having energy 0.025 eV

   Results from scattering

   Moderator mediums are H , D , BeO, Be

   Neutrons at a given temp posses wide range of
    energies and corresponding speeds
    Maxwell-Boltzman distribution:
                        2π
            f (E ) =            e − E / kT E 1/2
                     ( πkT )3/2
Most Probable Neutron Velocities
• Most probable neutron velocity is given by
•          Vm=(2kT/m)0.5=128.39 T0.5
    v=most probable velocity of neutron (m/sec)
     k=Boltzman's constant (1.3805*10-23 J/ K)
     T=absolute temperature in degrees Kelvin ( K)
     m =mass of neutron 1.66 x 10-24gram
• The energy corresponding to Vm is given by
         Em= kT = 8.617*10-5 T (eV )
     At T = 20 0C
     Vm = 2200 m/sec
     Em =0.025 eV
Thermal Neutron Speeds & Energies

Temperature 0C   Vm ( m/sec)   Em (eV)

20               2200          0.0252

260              2964          0.0459

537.8            3656          0.0699

1000             4580          0.1097
Velocity Distribution At Two
Temperatures
Interaction of Neutrons
   Neutrons are uncharged and can travel
    appreciable distances in matter without
    interacting




   Neutrons interact mostly by inelastic scattering
    or elastic scattering
Inelastic Scattering

• A part of the kinetic energy that is transferred
  to the target nucleus upon collision

• The nucleus becomes excited and a gamma
  photon/photons are emitted
Elastic scattering

• Interaction between fast neutrons and low atomic
 number Z
• For slowing down neutrons
• Responsible for neutron – slowing in reactors
• Fast neutrons lose K.E. As A result of scattering
 collisions with nuclei which act as moderators
Interaction of Neutrons

   .......E o , M, V → m.......
     (before collision)


.......E, M, V1 → m, ν 1 .......
      (after collision)
Continued…
• total kinetic energy and momentum are
 conserved and we have:
             1
             2
                 MV 2 = 1 MV12 + 1 mv 1
                        2        2
                                      2


             and MV = MV1 + mv 1


•Solving for V1 and substituting into:

                         (M - m)
                    V1 =         V
                         (M + m)
Continued…
           1
      E 0 = MV for incident neutron
              2

           2
        1
 and E = MV12 we get
        2
                          2
             M−m
      E = E0     
             M +m
• The energy transferred to target nucleus is:

                             M - m 2 
             E 0 - E = E 0 1 -      
                            M +m 
                                       
Continued…
            1      2   1     2        4mME
  Emax = MV -
            2          2   MV1   =            2
                                     (M + m )

• when: M = m; E = Emax

•for neutrons in a head on collision with hydrogen all
    the kinetic energy can be transferred in one
collision since the mass of neutrons and protons
are almost equal.
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presentation uploaded by anwershifa

  • 1. Neutron Energies, Velocity & Thermal Neutrons Abdul Rizwan (Reg# 2007-Mech-2616) Waleed Mumtaz (Reg# 2007-Mech-2615) Adnan Rasheed (Reg# 2007-Mech-2557) Adnan Khan (Reg# 2007-Mech-2620) Suhaib Ilyas (Reg# 2007-Mech-2595)
  • 2. Neutron  Sub atomic particle  No charge and greater mass  Free neutrons are unstable  High penetrating power  Essential in Fission process
  • 3.
  • 4. Neutron Source Different sources of neutrons are:  Radioisotopes which undergo spontaneous fission  Radioisotopes which decay with alpha particles   Radioisotopes which decay with high energy photons co-located with beryllium or deuterium  Plasma focus and plasma pinch devices  Light ion accelerators
  • 5. Neutron Energies  Neutron energy indicates a free kinetic energy, usually given in electron volts  En= mnV2/(2*gc) = 5.227*10-13 V2 ( eV)  Fission neutron energy range is (0.075……..17 ) MeV  Prompt neutron vs delayed neutron  Prompt neutrons have average energy of about 2 MeV.
  • 6. Prompt Neutron Energy Spectrum U235
  • 7. Classification of Neutrons • neutrons are classified according to their energy • thermal neutrons have an energy of about ~ 0.025 eV • epithermal neutrons, resonance neutrons, slow neutrons have energies between 0.01 MeV and 0.1 MeV • fast neutrons - 0.1 MeV and 20 MeV • relativistic neutrons
  • 8. Neutron Energy Distribution Ranges  Fast neutrons > energy approximately 1 MeV  Slow neutrons > energy less than or equal 0.4 eV  Epithermal neutrons > energy 1 eV to 10 keV  Hot neutrons > energy about 0.2 eV  Thermal neutrons > energy of about 0.025 eV  Cold neutrons > energy 5x10−5 eV to 0.025 eV  Very cold neutrons > energy 3x10−7 eV to 5x10−5 eV  Ultra cold neutrons > energy less than 3x10−7 eV  Continuum region >energy 0.01 MeV to 25 MeV  Resonance region >energy 1 eV to 0.01 MeV  Low energy region > energy less than 1 eV
  • 9. Thermal Neutrons  Slow neutron having energy 0.025 eV  Results from scattering  Moderator mediums are H , D , BeO, Be  Neutrons at a given temp posses wide range of energies and corresponding speeds  Maxwell-Boltzman distribution: 2π f (E ) = e − E / kT E 1/2 ( πkT )3/2
  • 10. Most Probable Neutron Velocities • Most probable neutron velocity is given by • Vm=(2kT/m)0.5=128.39 T0.5 v=most probable velocity of neutron (m/sec) k=Boltzman's constant (1.3805*10-23 J/ K) T=absolute temperature in degrees Kelvin ( K) m =mass of neutron 1.66 x 10-24gram • The energy corresponding to Vm is given by Em= kT = 8.617*10-5 T (eV ) At T = 20 0C Vm = 2200 m/sec Em =0.025 eV
  • 11. Thermal Neutron Speeds & Energies Temperature 0C Vm ( m/sec) Em (eV) 20 2200 0.0252 260 2964 0.0459 537.8 3656 0.0699 1000 4580 0.1097
  • 12. Velocity Distribution At Two Temperatures
  • 13. Interaction of Neutrons  Neutrons are uncharged and can travel appreciable distances in matter without interacting  Neutrons interact mostly by inelastic scattering or elastic scattering
  • 14. Inelastic Scattering • A part of the kinetic energy that is transferred to the target nucleus upon collision • The nucleus becomes excited and a gamma photon/photons are emitted
  • 15. Elastic scattering • Interaction between fast neutrons and low atomic number Z • For slowing down neutrons • Responsible for neutron – slowing in reactors • Fast neutrons lose K.E. As A result of scattering collisions with nuclei which act as moderators
  • 16.
  • 17. Interaction of Neutrons .......E o , M, V → m....... (before collision) .......E, M, V1 → m, ν 1 ....... (after collision)
  • 18. Continued… • total kinetic energy and momentum are conserved and we have: 1 2 MV 2 = 1 MV12 + 1 mv 1 2 2 2 and MV = MV1 + mv 1 •Solving for V1 and substituting into: (M - m) V1 = V (M + m)
  • 19. Continued… 1 E 0 = MV for incident neutron 2 2 1 and E = MV12 we get 2 2 M−m E = E0   M +m • The energy transferred to target nucleus is:   M - m 2  E 0 - E = E 0 1 -     M +m   
  • 20. Continued… 1 2 1 2 4mME Emax = MV - 2 2 MV1 = 2 (M + m ) • when: M = m; E = Emax •for neutrons in a head on collision with hydrogen all the kinetic energy can be transferred in one collision since the mass of neutrons and protons are almost equal.