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Lesson 18 - Photon response functions

When we turn our attention from neutron response functions to photon response functions, are job gets more complicated because of two facts:

  1. The notation for photon response functions is traditionally different than for neutrons, so we have to learn it.
  2. We cannot be so sure of what particles are being "covered" by the flux calculation.

 

Photon notation

First, let's deal with the notational difference.  So far, our equation for the local response functions (by which we mean the response function for material that affects the flux) has been the one developed in Lesson 16:

wpe1B7.gif (1845 bytes)

where  wpe1B6.gif (1006 bytes) is the energy transferred to the material medium by secondary charged particles due to neutron reaction type j of isotope i.

We have already seen that photon reaction coefficients are historically expressed in terms of the linear attenuation coefficient:

wpe1E0.gif (1557 bytes)

Well, since the wpe1B6.gif (1006 bytes) are dependent on the i and j summations, it is difficult to provide a direct analog of the first equation using the wpe1D5.gif (871 bytes).  How the traditional photon notation has treated this difficulty has been to define a family "linear deposition coefficients" with the general form of:

wpe1DC.gif (1697 bytes)

which results in the response function being defined as:

wpe1E1.gif (1481 bytes)

Several important points need to be made about the wpe1E2.gif (1053 bytes):

  • Although they look like interaction coefficients and have the same units (1/cm) as macroscopic cross sections, they cannot be multiplied by flux to get any physical reaction rate.

  • Likewise, for the same reason they cannot be used to compute exponential attenuation rates


Note: You should get it firmly in mind that if I ask you for an attenuation rate that involves computing a value wpe1E3.gif (910 bytes), there will NEVER be a subscript on the wpe1D5.gif (871 bytes).


  • The ONLY legitimate use for a wpe1D5.gif (871 bytes) WITH a subscript occurs when it is multiplied by E to get an energy deposition or energy deposition rate.

 

Matching of flux with deposition coefficient

If you look at the tables in Appendix C, you will not find a listing for wpe1EC.gif (905 bytes).  We have been using this symbol as a "stand-in" for linear coefficients that will allow us to approximate the dose rate -- when multiplied by the energy E of the incident photon and by the photon flux.

This last phrase "... and by the photon flux" is where the problem comes in.

The photon reaction mechanisms that we studied earlier -- photoelectric effect, Compton scattering, and pair production -- result in the release of a range of secondary photons.   Some of them have relatively high energies -- especially the pair production photons at 0.511 MeV and the Compton photons, which usually have energies comparable to the incident photon.  Others, however, have very low energies -- especially the photons from Bremsstrahlung and the fluorescent photons from the photoelectric reactions.   The question is: Are each of these categories of photons included in the flux calculation or not?

 

You should become familiar with Figure 5.4 in the book, so that you can properly match up the energy deposition coefficient to use with the details of the flux calculation. In summary, you should use:

  • wpe1ED.gif (1195 bytes) if Compton scatter photons are included in the flux calculation, but not the others.
  • wpe1EE.gif (1200 bytes) if Compton scatter and pair-production photons are included in the flux calculation, but not fluorescence or Bremsstrahlung photons.
  • wpe1EF.gif (1200 bytes) if all sources except Bremsstrahlung photons are included in the flux calculation.  (NOTE: This is the coefficient that most closely corresponds to kerma, since the (intermediate) electrons would be considered to be secondary charged particles.)
  • wpe1F1.gif (1207 bytes) if all four sources of secondary photons are included in the flux calculation.

 


Example: For a flux of 100 particles/s/cm2 of 2 MeV photons in lead of density 11.7 g/cc, what is the (a) kerma rate and (b) the reaction rate in the lead?  (Assume that the proper deposition cross section is the linear energy transport cross section, wpe1E5.gif (907 bytes).

Answer:  Using the value for lead given in Table C.5, the interaction coefficients at 2 MeV are:

wpe1E6.gif (1624 bytes), both in cm2/g

Using the first of these, the reaction rate (in mass units) is found by multiplying the mass interaction coefficient by the flux to get:

wpe1E8.gif (2665 bytes)

The associated kerma is found from:

wpe1EA.gif (3982 bytes)


 

You should closely study the examples in section 5.7.4 of the text.

 

 


Return to Course Outline                                                                                               1998 by Ronald E. Pevey.  All rights reserved.