Re: Energy deposited greater that incident energy for neutron?

From: Alfredo Ferrari <>
Date: Thu, 27 Oct 2011 18:18:26 +0200


I believe you miss a very important point about energy and energy
conservation. Obviously energy conservation must be computed taking into
account mass energy (of both projectile and all target nuclei involved
in interactions) as well as kinetic energy as we all know. To rely on
initial kinetic energy is very naive and deeply wrong. You cannot estimate
energy conservation in the way you report, since you are disregarding all
mass/binding energy losses or gains, which is obviously pretty wrong.

Let me make an "extreme" case: suppose you input a beam of neutrons at
thermal energies in a large target of whichever material. Sooner or later
all neutrons will get captured emitting a few MeV worth of gammas, despite
the neutron energy being just a small fraction of eV. Hence the ratio of
deposited energy versus initial energy will be a few 10^7 in every event.
Is this violating energy conservation or wrong? Obviously not, is it
perfectly ok, the energy of the photons come from binding energies, that
is the reaction

         n + M(A,Z) -> M(A+1,Z) + neutron_binding_energy_of_A+1,Z

is exoenergetic, or in naive words, your target is now "lighter" by a few

Another obvious example is an antiproton beam. Even at "zero" kinetic
energy the antiproton annihilation will give you roughly two GeV of
deposited energy. Where they come from? Obviously from the masses of both
the projectile and a nucleon from the target which are no longer there

Last but not least: fission and nuclear reactors or bombs. In this case a
"beam" of essentially thermal neutrons (-> kinetic energies in the sub-eV
range) is producing huge amount of energy thru nuclear fission which is
obviously conserving energy when the masses of the intial target and final
fragments are correctly accounted for. Obviously fusion reactors in the
sun are another obvious example

In your naive view reactors and bombs will never work (maybe this is a
plus) and the sun could not shine (this is a major minus)

So far for the physics. Now what FLUKA does?

FLUKA conserves energy TAKING INTO ACCOUNT binding energies and mass
energies *perfectly* on average. For all interactions, neutrons below
20 MeV excluded, the code conserves energy down to the machine
accuracy (1E-15) event-by-event at each interaction, obviously again
accounting for mass/binding energy losses and gains. There is no error
in the code and nothing to be corrected, and I do not know where/if you
ever saw statements contrary to this.

Event-by-event there could be some slight over/under-conservation because
of neutrons below 20 MeV which deposit energy thru kerma factors (see the
manual, it is important to understand how the group transport mechanics
works). Kerma factors are "exact" on average but since they are "average"
energy depositions for a given neutron energy in a given material
event-by-event there could be some spread around the exact conservation
value. There is no simple way to ensure exact conservation event-by-event
below 20 MeV since neutron cross sections and interactions in this energy
regime are based (for all codes) on evaluated datafiles which typically
contain only inclusive informations and not exclusive ones.

I do not know if you intend "event-by-event" or "on average".
In both cases obviously it is possible and physically correct for the
physical reasons explained above to have deposited "visible" energy
larger (smaller) than initial kinetic energy. On top of the physical
effects which alone could produce event-by-event (and on average) energy
deposition larger than the initial kinetic energy, in the "event-by-event"
deposition there could be a further effect due to the use of kerma factors
(or more properly to the lack of correlated data in the neutron evaluated

I would be surprised you see more deposited energy than initial energy "on
average" with a 600 MeV neutron beam, since at that energy binding energy
losses (eg for (n,2n) or more complex reactions) tend to dominate over
gains thru capture. While in event-by-event scoring it could well be, both
because of physical reasons or for the kerma business.


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

On Wed, 26 Oct 2011, denis wrote:

> Dear Fluka experts,
> Summing up all energy deposited by a incident neutron of 600 MeV inside a
> cube of 3*3*3 m made of pure
> Plastic Scintillator (BC408) , i get counts in the final E_deposit/E_initial
> spectrum greater than 1. .
> I would like to understand how can it be that FLUKA gives in some cases
> E_deposited > E_initial (neutron).
> Could this be linked to wrong Energy threshold defintion for secondary
> particles,
> wrong physic model ( i used CALORIMETRY and DELTARAYS card ). I have seen
> many reports using FLUKA showing
> the same problem with incident neutron particle. It seems to be a known
> problem but i can not figure out why ?
> I will be very thankful for any explanation here.
> Best regards,
> Denis Bertini
Received on Fri Oct 28 2011 - 11:11:43 CEST

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