Review of Hubbell's paper 학부 수업을 위해 만든 Hubbell 논문 리뷰 자료입니다. Photon interaction cross section 과 관련된 내용을 잘 정리해준 논문입니다. :) [Link] http://iopscience.iop.org/article/10.1088/0031-9155/44/1/001/meta

1. 1 7 O c t . 2 0 1 7
Review of photon interaction
cross section data in the
medical and biological context
Jimin Lee
Radiological Physics Laboratory,
Seoul National University

2. Contents
2
1. Introduction
2. History
3. The individual photon interaction processes
4. The mass energy-absorption coefficient
5. Current status and future tasks, particularly for medical and biological applications

3. 1. Introduction

4. 1. Introduction
4
• The discovery of x-rays by R ሷ𝑜ntgen (1895)
• The transmission of a narrow (parallel) beam of x-rays was measured and quantified.
- Barkla (1907), Sadler (1909)
• Mass attenuation coefficient
 𝑡 : Mass thickness (𝑔 𝑐𝑚−2
)
 𝐼0 : Intensity of the incident beam
 𝐼(𝑡) : Intensity of the transmitted beam

5. 1. Introduction
5
• The discovery of x-rays by R ሷ𝑜ntgen (1895)
• The transmission of a narrow (parallel) beam of x-rays was measured and quantified.
- Barkla (1907), Sadler (1909)
• Mass attenuation coefficient
(for homogeneous medium)

6. 1. Introduction
6
• Mass attenuation coefficient
 𝜎𝑡𝑜𝑡 : Total atomic cross section
 𝑢 𝑔 : Atomic mass unit
 1.6605402 × 10−24
𝑔
 𝑢 𝑔 = 1/𝑁𝐴 (𝑁𝐴 : Avogadro’s number, 6.0221367 × 1023
𝑎𝑡𝑜𝑚𝑠/𝑚𝑜𝑙 )
 1/12 of the mass of an atom of the nuclide 12 𝐶
 A : Relative atomic mass of the target element
 1 𝑏𝑎𝑟𝑛 = 10−24
𝑐𝑚2

7. 1. Introduction
7
• Mass attenuation coefficient

8. 1. Introduction
8
• Mass attenuation coefficient
• Nuclear photoeffect (= Photonuclear reaction) is not readily amenable to systematic
calculation and tabulation.
• Hence, 𝜎 𝑝ℎ.𝑛. has been omitted from 𝜇/𝜌 compilations up to the present.

9. 2. History

10. 2. History
10
• Allen (1935) : The first major compilation of 𝜇/𝜌 data
 30 eV – 2.5 MeV, 32 elements (Z = 1 – 92)
 No theory & Only the widely scattered measurements were found in the literature.
 There were wide gaps, requiring extensive interpolation and extrapolation across Z and
photon energy.
• Victoreen (1949) : Semiempirical 𝜇/𝜌 compilation
 Klein-Nishina formula for total Compton scattering
• Davisson and Evans (1952)
 102.2 keV – 6.13 MeV (up to 25.54 MeV for Z = 13 , 82), 24 elements (Z = 1 - 83)
 They obtained pair production cross sections by graphical integration over the Bethe–
Heitler (1934) Born approximation expression.

11. 2. History
11
︙
• Chantler(1995) : Extensive new calculations and theoretical tabulations of scattering cross
sections and quantities related to 𝜇/𝜌
 a few eV up to 1 MeV, Z = 1–92
• However, it is not yet clear how to incorporate this new source of data into 𝜇/𝜌 tables for
medical, biological and other practical applications.

12. 3. The individual
photon interaction
process
• The atomic photoeffect cross section
• Incoherent and Coherent scattering
• Pair and Triplet production

13. 3. The individual photon interaction process | The atomic photoeffect cross section
13
• A photon disappears and an electron is ejected from an atom.
• Absorption-edge fine structure
K edge
Ti (Z= 22)
𝐸 𝐾−𝑒𝑑𝑔𝑒 = 4.79 𝑘𝑒𝑉

14. 3. The individual photon interaction process | Incoherent and Coherent scattering
14
• Incoherent (Compton) scattering cross section
 Berger-Hubbell (1987) XCOM PC program
 Hubbell-Seltzer (1995) tabulation
 Cullen et al (1997) LLNL data base
https://www.nist.gov/pml/xcom-photon-cross-sections-database
• Database Search Form

15. 3. The individual photon interaction process | Incoherent and Coherent scattering
15
• Coherent (Rayleigh) scattering
 Photons are scattered by bound electrons.
 The atom is neither ionized nor excited.
• Currently, 𝜎𝑐𝑜ℎ are focused on use of the second-order relativistic S-matrix formalism.
(Kissel 1995)

16. 3. The individual photon interaction process | Pair and Triplet production
16
• Electron-positron pair production
 A photon disappears in the field of a charged particle.
 An electron-positron pair appears.
• Biological materials except for bone are primarily low Z. → 𝜎𝑡𝑟𝑖𝑝 can be a minor but
significant contribution for high-energy photon applications (above 10 MeV).
• Hubbell et al (1980) : Tabulations of 𝜎 𝑝𝑎𝑖𝑟, 𝜎𝑡𝑟𝑖𝑝 (Z = 1–100 & 1 MeV - 100 GeV)
 Still used in current 𝜇/𝜌 compilations. (i.e. XCOM)

17. 4. The mass energy-
absorption coefficient
• The mass absorption coefficient
• The mass energy-transfer coefficient
• The mass energy-absorption coefficient

18. 4. The mass energy-absorption coefficient
18
• Mass absorption coefficient 𝝁 𝒂/𝝆
 Only scattered photons (both coherent and
incoherent) leave the volume of interest.
• Mass energy-transfer coefficient 𝝁 𝒕𝒓/𝝆
 All secondary photons (fluorescence and
scattered photons) are lost to the volume of
interest.
Photoelectric effect
Pair productionAbsorption
Scattering

19. 4. The mass energy-absorption coefficient
19
• Mass energy-absorption coefficient 𝝁 𝒆𝒏/𝝆
 Computing the energy deposition (ionization,
excitation, heat, etc) at a site (a ‘volume of
interest’)
Photoelectric effect
Pair productionAbsorption
Scattering

20. 5. Current status
and future tasks

21. 5. Current status and future tasks
21
• Uncertainty of cross section data

22. 5. Current status and future tasks
22
• Theoretical calculations
 Atomic photoeffect absorption edge structure
 Accurate scattering results from the relativistic S-matrix theoretical model
 photonuclear data 𝜎 𝑝ℎ.𝑛.
• Experimental capabilities
 More intense and higher-energy synchrotron light sources
 New detectors with better resolution and higher efficiencies
 To provide more accurate measured values of 𝜇/𝜌
 To test and undergird the above theoretical advances

23. (Extra) Triplet production
23
http://slideplayer.com/slide/5246079/16/images/15/Pair+Production+in+the+Electric+Field+(Triplet+Production).jpg
𝑚 𝑒 𝑐2 + ℎ𝜈 = 𝑚 𝛽+ 𝑐2 + 𝑚 𝛽− 𝑐2 + 𝐸
𝑚 0 𝑐2
+ ℎ𝜈 = 3𝑚𝑐2
ℎ𝜈
𝑐
= 3𝑚𝜐 = 3𝑚𝛽𝑐 (𝛽 =
4
5
)
𝑚 =
𝑚0
1 − 𝛽2
=
5
3
𝑚0
ℎ𝜈 = 3𝑚𝛽𝑐2
= 3 ×
5
3
𝑚0 ×
4
5
𝑐2
= 4𝑚0 𝑐2

24. Thank you 