This entry is the continuation of the cascade effects on the pg peak shape entry:

https://exp-astro.physik.uni-frankfurt.de:8080/E108/475

The main point is that having more cascade makes the impulse carried by one photon smaller --> recoil cone is
smaller --> pg peak gets more centered

When one wants to make an "all-inklusive" simulation the problem comes, that there are too many populated states
after CN* decay (many are just theoretical), also many cascades afterwards as well.
Instead, one can make a "statistical approach":
 1, take an average 1st populated state after the gamma emission of the CN*.
 2, take an average of the gamma energies after the p-capture. (it includes also the photons from the CM* to the
1st state after g emission with energy of [(E_CM - Q) - E_1st_state] --> should these be excluded from the avg.
gamma energy calculation?)
 3, the excited compound nucleus first decays to 1, then cascading down with the avg energy of 2,

    number_of_cascades = E_1st_state/E_avg_gamma. 

    For the 124Xe at 7AMeV using the TALYS code the above values are:
    E_1st_state = 6.74 MeV
    E_avg_gamma = 2.75 MeV
    number_of_cascades = 2.45

To reproduce the resulting avg. pg peak, I took a 2 and a 3 cascade simulations produced by MOCADI and mixed
them as 55% of the 2-cascade and 45% of the 3-cascade for this naiv, statistical model.
Then, to test the peakshape, I fit this mixed distribution to a part our measurement data at 7AMeV after a
sloppy Rutherford background removal (the background removal can be more improved, I used this as a quick method
for now). The calculated Chi^2/NDF ~ 3, which is not a super good value, but taking into account that this is a
strongly naiv model, and the background removal can be also improved, the chi^2/NDF value can be also
interpreted as promising.