RE: [fluka-discuss]: Interpretation of cross section and yield from USRYIELD

From: Anton Lechner <Anton.Lechner_at_cern.ch>
Date: Tue, 3 Dec 2013 18:56:25 +0000

Dear Lee,

I would like to mention one important point first: avoid setting the atomic weight on the MATERIAL card (FLUKA determines this internally). For hydrogen you put 1.000 amu instead of the actual 1.00794 amu which alters results by some 10 percent due to the different number of atoms/unit volume assumed in the simulation.

Now to the cross section calculation. The interpretation of the calculated result is indeed a bit tricky.

When you request "plain cross section" for neutron production on the USRYIELD card and you specify as reference material your "Water18", you get following quantity (for simplicity, I assume our result is already integrated over both x1 and x2): yield * sigma_av, where:
   *) yield = number of neutrons produced per incident proton
   *) sigma_av = average inelastic cross section per nucleus in "Water18"=(2/3*sigma_H + 1/3*sigma_O18)=(2/3 * 1.8920E-02mb + 1/3 * 896.55 mb) = 298.86 mb

To get now the actual neutron production cross section you have to do the following:

1) you have to get the yield per inelastic nuclear interaction instead of incident proton: yield_per_interaction = yield / (d/lambda), where:
   *) d = thickness of your target
   *) lambda = inelastic nuclear scattering length of your target material (= 33.67 cm, you can find this number the output file)

2) you have to use the total inelastic cross section of your target material, not the average: sigma = sigma_av * N_at, where:
   *) N_at = number of atoms in your compound (2H + 1O = 3)

Putting all this together, your actual neutron production cross section in your target is: (yield * sigma_av)/(d/lambda)*N_at

Of course, this descriptions only applies for a thin target. Apart from this, the above estimate gives you the neutron production cross section due to any nuclear interaction in your geometry, not only due to p + O18 -> F18 + n. A quick calculation I did by myself shows that the FLUKA neutron production cross section for 15 MeV p on O18 is ~550 mb, while for the mentioned channel with F18 production I get something like 125 mb (note the statistical error for these estimates is still large). I got these results using a 50 um pure O18 target and the code I sent in my last Email.

Cheers, Anton







________________________________
From: Chenyen Lee [chenyenlee_at_gmail.com]
Sent: 30 November 2013 03:33
To: Anton Lechner
Cc: fluka-discuss_at_fluka.org
Subject: Re: [fluka-discuss]: Interpretation of cross section and yield from USRYIELD

Dear Anton and Forum :


2013/11/30 Anton Lechner <Anton.Lechner_at_cern.ch<mailto:Anton.Lechner_at_cern.ch>>
Dear Lee,

You can interpret the values you specify (from the summary file created with USYSUW) as follows: for example, the differential yield of 0.1 GeV^-1 you get in the energy interval 0-0.01 GeV simply means that 0.1 GeV^-1*0.01GeV=1E-03 neutrons with E<10 MeV were produced in inelastic hadronic interactions within your entire geometry (also in the surrounding air). Of course this is consistent with the value you got for the larger energy interval, since most neutrons are below 10 MeV.
From the link you included in your file, I guess that you are only interested in neutrons produced in following reaction:
p + O18 -> F18 + n
If this is the case, you should not forget that a non-negligible fraction of neutrons also emerge from other processes, e.g.:
p + O18 -> O17 + n + p
p + O18 -> N14 + n + alpha
USRYIELD will count all neutrons, also those from the latter interactions.
If you are only interested in the first reaction, you could for example use USDRAW in the MGDRAW user routine. By including
'(RESNUC)', you have access to the atomic and mass number of the residual nucleus and you can filter neutrons accordingly. I included some sample code below.

Thank for your reply, I do not even know there is non-negligible fraction of neutrons from other processes.
I will try the function when I'm more familiar with it.

The output of yield from USRYIELD makes much more sense to me now.
However, it seems to me that I can not interpret the cross section part as yield.

The XS0-0.01, 61 bin scores the neutron binning from 0 to 10MeV.
The results of cross section give around 30mb/GeV.
Is cross section (with E<10MeV were produced) 30mb/GeV * 10MeV = 0.3mb ?

0.3mb is consistent with the results from XS0-1, 65 bin from 0 to 1GeV.
But It deviates too much from the recommended cross section which gives 87mb.


Thank in advance


Lee
Received on Tue Dec 03 2013 - 19:56:25 CET

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