# 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:

where  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:

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

which results in the response function being defined as:

• 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 , there will NEVER be a subscript on the .

• The ONLY legitimate use for a 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 .  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:

• if Compton scatter photons are included in the flux calculation, but not the others.
• if Compton scatter and pair-production photons are included in the flux calculation, but not fluorescence or Bremsstrahlung photons.
• 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.)
• 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, .

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

, 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:

The associated kerma is found from:

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