# Re: [fluka-discuss]: nucleus mass

From: Alfredo Ferrari <alfredo.ferrari_at_cern.ch>
Date: Fri, 27 Apr 2018 08:43:41 +0200

Dear Shirley

the Fluka interaction models assures energy and momentum conservation
down to (almost) the computer precision. Typically the "errors" on
energy/momentum conservation are of the order of 1E-13 or less wrt the
initial state (total) energy (including target mass).

In order to properly cross check energy conservation you should consider
the "exact" mass of each individual isotope (initial and final state),
which are in general different from A x atomic mass unit.

Two things to be careful about:

a) "nuclear" masses must be considered and not atomic ones, that is
atomic electron masses and their binding must be undone from the
atomic mass
b) as already mentioned above, the individual mass excess of each given
isotope (that is the difference wrt A x amu) must be considered,
this is important because generally speaking nuclear reactions tend
to produce residuals which are less stable than the original target
nucleus therefore implying an apparent energy loss (that is energy
going into residual nucleus mass)

Fluka has detailed tables with the experimental excess masses for some
4000 isotopes and those are the basis for the energy balance.

Considering your example, the Fluka "nuclear" mass of 40-Ar is 37.21554
GeV and its "nuclear" excess mass (that is the difference wrt 1/12 of
the 12-C "nuclear" mass) is -0.03401 GeV, the "nuclear" mass of
38-Ar is 35.35288 GeV and it excess mass is -0.03419 GeV, and the
(lab) threshold for pi+ + 40-Ar -> pi+ + n + n + 38-Ar is
0.01653 GeV (the reaction Q is -0.01647) as you can calculate from
the numbers above (and the pion and neutron masses), which is somewhat
larger than 2 x neutron excess mass which is 0.01614, exactly by those
~400 keV that you (correctly) found apparently missing.

Hope this helps!
Alfredo

+----------------------------------------------------------------------+
| Alfredo Ferrari || Tel.: +41.22.76.76119 |
| CERN-EN/STI || Fax.: +41.22.76.69474 |
| 1211 Geneva 23 || e-mail: Alfredo.Ferrari_at_cern.ch |
| Switzerland || |
+----------------------------------------------------------------------+

On Thu, 26 Apr 2018, Shirley Li wrote:

> Dear FLUKA users,
>
> I'm looking at pion inelastic interaction in argon and trying to understand
> the energy balance.  I'm wondering how are nucleus masses calculated or what
> database are they taken from?  In mgdraw, I record all secondary particles
> out of an inelastic interaction, including the residual nuclei, to look at
> the energy balance.
>
> For example, in the attached output file, the first reaction is pi +40Ar ->
> pi + 2n + 2 gamma + 38Ar.  If I include nucleus mass, i.e, m_40ar = 39.96u &
> u = 0.9315 GeV, the total energy before reaction is 38.0575 GeV.  The total
> energy after reaction is 38.0571 GeV, not an exact match.  And the
> difference becomes larger when the residual nucleus has a smaller A.   I'm
> not sure if the difference is because I used wrong nucleus masses.
>
> Thank you very much!
>
> Shirley
>
>

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Received on Fri Apr 27 2018 - 10:13:08 CEST

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