Uncertainty Propagation Vs USRBIN Energy Deposition

Dear FLUKA Experts,
Sorry for resurrecting this topic (Uncertainty: Overall Value) but after going through the wiki page, I found that I could implement the general formula for uncertainty propagation. That is,

In my case,

For a 20 MeV Monoenergetic proton Beam traversing the target, I got (ignoring the first bin).

E_avg [keV] = 2.86943374 and sigma_E_avg [keV] = 6.49E-03

Now using the USRBIN card as suggested, I got the following results (screen shot).

  1. First, no units are indicated, so I do not understand whether it’s in GeV or what?
  2. Secondly if the propagation method above is correct, shouldn’t theses values coincide?
    Please advise.

DETECT_Card.inp (4.8 KB)

Modified Output
DETECT_Card_17_tab.lis (222.5 KB)

Dear Zavier,

thanks for your question, I am looking into it and I will come back as soon as possible.


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Dear Zavier,

to answer your first question, when scoring ENERGY with a Region mesh, the USRBIN result is reported in GeV/primary and the error, as written in the .lis file, is a percentage error.

Looking at your DETECT file, the first bin has the highest counts comparing it to the others: excluding it from the calcualtion you are performing causes the deviation from the average energy deposited computed with USRBIN .
Simply including the first bin counts in the average, I get 2.48E-07 GeV/primary, closer to the USRBIN result.
In order to obtain an even similar result, you should set more appropriately the DETECT bins since, as it is now, the majority of the bins give 0.
For example, with the following DETECT card, I get, using your formulas, an average energy deposited of 1.38E-07 GeV/primary with uncertainty 6.9E-01 %

I will let you set it accordingly to you needs but in general the USRBIN gives you already the average energy deposited in the region that you are interested with its own error without the need of any post processing.

Finally to point out that, if I understand correctly the structure of your DETECT file, it looks like that you are not considering Ei = LBi + 0.5*(UPi-LBi), rather Ei = UBi.

I hope this helps you in solving your doubts!

Dear Giuseppe,
Thank you very much for your reply. Is there any reason you chose 22.78 keV instead of 500 keV as your E_max for the DETECT card? Or is this based on the readings from my “…tab.lis” file? By checking, I see that the counts reduce to zero beyond this value.


Dear Zavier,

as you correctly understood, I have chosen the Emax for DETECT simply looking at which was the last bin with significant counts in the .lis file, no physic reason behind. From this come also my statement to set this value depending on your needs.


Thank you very much!
…and the USRBIN average also considers zero energy deposition events. Correct?


yes, USRBIN (with selected mesh Region) gives the average energy deposition (in GeV) per primary.
It is done summing, for each primary of a cycle, the energy deposited in the region and finally dividing it by the number of primaries per cycle (ni). If a primary gives 0 as energy deposited, it is taken into account in the sum.


Thank you very much, Giuseppe. I think I understand clearly now.



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