Weight spectrum / weight function for MG gamma cross sections

[Willem van Rooijen]

Does anybody know of a theoretical derivation or discussion of the proper weight function / weight spectrum in the calculation of multi-group gamma cross sections?

For MG neutron cross sections, there are various theoretical approaches to obtain an "adequate" neutron flux spectrum that can be used for the generation of MG neutron cross sections.

I am looking for something similar for gamma cross sections, but I have not yet been able to find any relevant theory. If anybody can provide a hint I would appreciate it.

Some background:

- SCALE 6.3.1 manual section 10.1.2.4 states that a "flat spectrum" is used to generate the MG gamma cross sections in SCALE

- the JERGENS module (AMPX) has an option for a "1/E spectrum will roll-off"; the same kind of spectrum is provided in the NJOY GAMINR module - but I could not find any theoretical support for this choice

- in the manual of the NJOY GROUPR module the various choices of the weight function for MG neutron cross sections are discussed

Regards,

Namizono

[Jeffrey Ryman]

I am not aware of any derivation in the literature. However, here is what I remember from looking at this question in the late 1970s when I was working on my dissertation research and when I was performing some transport calculations for EPA Federal Guidance Report No. 12 working with the ORNL Health and Safety Research Division in the early 1990s.

The flat spectrum discussed in the SCALE manual is typical of what has been used to produce multi-group gamma cross sections. A flat spectrum has generally been used for cross sections developed at ORNL since the development of the AMPX cross section processing system and probably before that.

If you look at the definition of a group cross section you can see that the effect of the spectrum depends only on the shape of the spectrum within that single group. From a little experimenting that I performed during my dissertation research, I found that small changes in the general shape within the group have little effect on the group cross section. In my experience the spectrum within a group has less effect for narrower energy groups. However, narrower groups can produce more peaked distributions of the double differential scattering cross section as a function of the cosine of the scattering angle, making group-to-group scattering cross sections more difficult to represent by Legendre expansions of only a few terms.

From discussions with other transport practitioners at ORNL and particularly with N. M. Greene (my supervisor) and the principal developer of the AMPX cross section processing system prior to the 2000s, I was advised that the effect of the gamma flux spectrum was not much worried about.

BIG CAVEAT: I have not worked on multigroup photon transport calculations since the early 1990s so I am not current on the literature. All my transport work after I left ORNL and before retirement as well as a little consulting since retirement has used continuous energy Monte Carlo.

[Willem van Rooijen]

Hello Jeffrey,

Thank you for your message.

Mmm... I will review the theory of the interaction between gamma rays and matter (photo-electric effect, Compton scattering, etc). IIRC the energy dependence of the gamma cross sections is quite strong. If that is true, then the energy dependence of the weight flux might not be very relevant. BTW I contacted the SCALE Helpdesk - an automatic reply but nothing more. I contacted the NJOY developers - no reply. A bit disappointing thus far.

Regards

2025年6月1日日曜日 7:04:00 UTC+9 Jeffrey Ryman:

[Willem van Rooijen]

I have studied a bit more. 

First of all, the spectrum that is advertised as "1/E" is not only 1/E. From low energy the spectrum increases as E^2, then 1/E from 100 keV to 10 MeV, and then back to almost zero at 30 MeV. This appears to be a reasonable approximation for the gamma flux in a nuclear reactor.

For the energy range of approx. 100 keV to 10 MeV the Compton effect is dominant. This is basically a scattering reaction where the gamma photon looses energy. It is thus similar to elastic scatter of neutrons, and I guess one can make a theory that the gamma flux is "mostly 1/E" in the energy range where Compton scattering is dominant.

I have been trying to derive some expressions based on the Klein-Nishina formula (which gives the probability of a scattering angle theta) and the Compton-formula, which gives the energy of the gamma photon after a scattering reaction over angle theta. I am not yet very far (and this is really not what my boss is paying me for) so I will continue if I have some free time at work.

Regards,

Namizono

2025年6月2日月曜日 8:15:18 UTC+9 Willem van Rooijen: