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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:
-
Radioactive sources
-
Prompt fission gamma rays
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Fission product gamma rays
-
Neutron capture gamma rays
-
Gamma rays from inelastic neutron scattering events
-
Neutron activation gamma rays
-
Annihilation gamma rays
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:
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An extension of spontaneous fission to include the resulting gamma rays
(Category 2).
-
A discussion of what we can do with radioactive sources using data from
the book (Categories1 and 6).
-
A discussion of what we can do with the help of the ORIGEN code, which
is the Oak Ridge National Laboratory standard code for performing burn-up,
decay, and source determination calculations. This will largely take
care of real world needs for categories 1, 2, 3, and 6.
-
Finally, a discussion of modern coupled multigroup cross section libraries:
how neutron and gamma calculations are done simultaneously with these datasets,
which takes care of categories 4 and 5.
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.
NOTE: I have lowered the lower limit from 0.1 MeV to 0.035
MeV so that the integral better matches the total number of gamma rays
produced, which is given in the text as 8.13.
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.
Example: What is the gamma ray source rate from a 1 microgram
point source of Cf-252?
Answer: This is the same source that was used in an example
problem in the previous lesson. From Table 4.2, the spontaneous fission
yield of  neutrons/sec/gram.
Therefore the neutron source rate is:
From the fourth column of the same Figure, we get that there are 3.73
neutrons produced per fission. Therefore, the gamma ray source rate
must be:
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:
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Find the activity for each radioactive nuclide in disintegrations/sec (possibly
per unit volume, area or length)
-
Multiply by the gamma ray yield per disintegration in each energy range
of interest.
The difficulty of the first step will vary. The most common
situations you will encounter (in increasing order of difficulty) are:
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The activity will be given to you in terms of curies or becquerels of given
radioactive isotopes.
-
The mass will be given to you in terms of grams (or grams/cc) of given
radioactive isotopes. In this case, you have to convert the mass
into a nuclide density, find the decay constant (possibly from the half-lives
given in Appendix H of the text), and multiply the two to get the activity.
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You will be given the mass or density of parent isotopes (i.e., isotopes
that become radioactive when irradiated), plus the flux conditions over
given time intervals. In this case, you will need to find the nuclide
density of the parent (perhaps using natural abundances given in Table
C.2), multiply this by the activiation cross section in Table C.2, and
perform a build-up/decay calculation to get the concentration of the daughter
nuclides. (I assume you learned how to do this from previous courses.)
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.
Example: What is the gamma ray source rate from a 1 curie 
source? Provide the output in the following energy group form:
|
Group number, g
|
Upper limit of group,  ,
MeV |
| 1 |
3 |
| 2 |
2.5 |
| 3 |
2 |
| 4 |
1.5 |
| 5 |
1 |
| 6 |
0.5 |
| Bottom of group 6 |
0 |
Answer: The activity of the sources is 
disintegrations per second (= definition of a curie). Organizing the Appendix
H data according to the requested group structure gives us:
Group 1: No gamma rays above 2500 keV.
Group 2: 3 gamma rays in range 2000-2500
keV with percentages of 1.21+4.99+1.55 = 7.75%
Group 3: 5 gamma rays in range 1500-2000
keV with summed percentages of 24.43%.
Group 4: 7 gamma rays in range 1000-1500
keV with summed percentages of 32.01%.
Group 5: 5 gamma rays in range 500-1000
keV with summed percentages of 56.92%.
Group 6: No gamma rays below 500 keV.
[Note: A careful reading of the footnotes tells us that about 10% of
the energy released per decay is unaccounted for in the discrete list.
It would be conservative, then, to increase each of the contributions by
10% to provide this energy balance. In reality, this energy is usually
physically due to a bunch of very low-energy gamma rays that will not travel
very far -- maybe not even out of the physical source itself.]
Using the above data gives us a group-wise source of:
|
Group number, g
|
Source, #/sec |
| 1 |
0 |
| 2 |
2.87E9* |
| 3 |
9.04E9 |
| 4 |
1.19E10 |
| 5 |
2.11E10 |
| 6 |
0 |
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:
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Initial contents of a sample (i.e., atom densities or masses of all isotopes
in the sample);
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A cross section library (SCALE has several that the user can specify);
and
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The flux conditions in the sample,
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:
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Neutron capture gamma rays
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Gamma rays from inelastic neutron scattering 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.
Example: What would be the coupled scattering cross section corresponding
to the 1-2 MeV gamma ray production from thermal absorption in natural
carbon?
Answer: From Table C.3, the thermal absorption cross section
in natural carbon is 3.37E-3 barns. From the same table, each thermal
absorption produces 0.2953 gamma rays between 1 and 2 MeV. Therefore,
the scattering cross section from thermal neutrons to this energy range
is 0.2953*3.37E-3 barns, or 9.95E-4 barns.
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NE406 Radiation Protection and Shielding