Radiation Protection and Shielding
Lesson 13 - Gamma ray sources
In this lesson, we will be covering important aspects about gamma ray sources.
The book lists 7 gamma ray source categories:
As in the previous lesson, I expect you to be able to describe the physical mechanism for each of these (as I had you do in the Reading Assignment) and work very simple problems that require basic skills you already have (e.g., atom density determinations for nuclides, time-dependent buildup and decay, reaction rate determination from fluxes and cross sections).
In this lesson, we are going to divide our study of gamma ray sources into four parts:
Fission product gamma rays
We have already studied the spontaneous fission process, in the previous lesson. What remains is to tie in the gamma rays that are produced along with the neutrons that we have already studied. This relationship can be made through Equation 4.9 in the text:
which is shown in Figure 4.5.
As mentioned in the text, this energy distribution can be used reasonably accurately for all of the commonly fission isotopes.
If we are concerned with the yield over a single energy group in a multigroup energy structure, we have:
Similarly, if we are interested in the energy deposited over a finite range (such as a single energy group), this would be:
Note that this distribution integrates to 8.13 over its entire range; this is the approximate number of gamma rays produced per fission event and not per neutron. Comparing this to our determination of the spontaneous fission neutron source in the previous lesson, we must divide by the data in the 4th column of Table 4.2 to get the number of fissions before using this gamma ray distribution.
Gamma rays from radioactive sources
The most common gamma ray source is produced by radioactive material. The procedure for determining the source rates for this situation boils down to two steps:
The difficulty of the first step will vary. The most common situations you will encounter (in increasing order of difficulty) are:
The second step involves use of decay data for radioactive isotopes, like provided to you in Appendix H. Notice that this table gives a series of gamma rays for each radioactive isotope, with the energy and percentage yield [in brackets]. If you are asked to present this data in energy ranges (e.g., sources for each of the groups in a multigroup energy structure, as discussed in the previous lesson), you are only faced with a slight book-keeping problem: just organize the emitted gamma rays by "lumping" all of those within the range.
The procedure used with Appendix H data will cover gamma ray source categories 1, 6, and 7.
Use of the ORIGEN code
The industry standard code for calculating burnup, radioactive decay, and radioactive source terms is the ORIGEN code, which was written at the Oak Ridge National Laboratory, and which has been incorporated into the SCALE system. (We will be learning how to use ORIGEN as part of the SCALE system later in the semester.)
If the user supplies ORIGEN with:
then ORIGEN will provide resulting isotopic atom densities and particle source terms (neutrons and gamma rays) in the desired multigroup energy structure, at user-specified future times.
Therefore, use of ORIGEN (or another code like it) takes care of gamma ray source categories 1, 2, 3, and 6.
Use of coupled multigroup cross section libraries
In the previous lesson (and in the previous example in this lesson), we used the idea of approximating energy-dependent values as histograms within a multigroup energy structure. In the previous lesson, we illustrated the concept using neutron source energy distributions, but the same concept is used to present energy dependent cross section data. For example, the energy-dependent total cross section of a isotope, , can be approximated by the group structure, g:
Likewise, double differential cross sections representing scattering from energy E to energy E' are approximated by group-to-group cross sections:
It is customary to use the multigroup energy treatment for both neutron and gamma ray problems. For problems that involve both neutrons and gamma rays in the same problem, it is possible to combine the neutron cross section (with, say, G groups) and gamma ray cross section data (with G' groups) into a single coupled cross section that contains G + G' groups. (By tradition, the neutron groups are the lower numbered groups and the gamma ray groups are the higher-numbered groups.)
But, the coupled cross section library does not just contain the gamma ray data appended to the neutron data. In addition, the cross sections for neutron events that produce gamma rays are represented as scattering events from the neutron groups to gamma ray groups. These reactions include our Category 4 and 5 events:
Therefore, there is no reason for the analyst to worry about these source categories if she is using a coupled cross section library -- it will be taken care of automatically by the cross sections.
Return to Course Outline © 1998 by Ronald E. Pevey. All rights reserved.