Inelastic hadronic cross section appears to include elastic processes

Hi all,

While looking at the secondaries from inelastic hadronic interactions, I noticed that certain events seem to be displaying the characteristics of elastic rather than inelastic collisions.

To illustrate this point, I’ve created an example starting from /extended/hadronic/Hadr03. In this example, I have modified the code so that it also stores

  • the energy of the most energetic secondary
  • the energy of the most energetic secondary IF the most energetic secondary is of the same type as the primary

Running this setup with the macro inelastic.mac, I obtain the following distribution for the collision of 1 TeV antiproton on Bismuth-209 (simulated 1 million events)

Blue: Energy distribution of most energetic secondary
Orange: Same but only for events in which the most energetic secondary is also an anti-proton

What’s striking is that 2.3% of events fall in the last bin. I.e. these are events in which the most energetic secondary is also an anti-proton with almost the exact same energy as the primary. Repeating this setup for other primaries it gives:

  • Proton: similar result, 4.0% in last bin
  • Neutron: similar result, 3.9% in last bin
  • Alpha: No issue, no events in last bin
  • Carbon-12: No issue, no events in last bin

Context: I am currently working on an analysis to perform a measurement of the inelastic hadronic cross section of proton and helium. As simulation framework we consider Geant4 and FLUKA. Our measurement for helium is consistent between Geant4 and FLUKA. Our measurement for proton from Geant4 is inconsistent with FLUKA. However, if we apply an add-hoc correction to account for the fraction of elastic collisions that Geant4 considers as inelastic, the results are consistent.
Ideally, I would prefer to have a more solid solution than this add-hoc correction. My questions are:

  • Has anyone come across this effect before?
  • Do people agree that these are elastic events?
  • If so, is there a way to set up the physics model in such a way that these events do not contribute to the inelastic processes?

Geant4 Version: 11.2.0
Operating System: CentOS7
Compiler/Version: gcc (GCC) 11.3.0
CMake Version: 3.26.2
Physics list: G4HadronPhysicsFTFP_BERT

Environment was set using:

source /cvmfs/
source /cvmfs/


thanks for reporting this interesting difference between Geant4 and FLUKA, of which we were not aware!
After some checking and discussion with our FLUKA-CERN colleagues, we think to have understood the origin of the “problem”: quasi-elastic interactions.
Quasi-elastic interactions are defined as hadron-nucleus interactions in which there is an elastic interaction between the projectile hadron and one (or more) nucleon(s) of the target nucleus. This type of interaction, is somehow similar to the coherent elastic scattering - in which the projectile hadron has an elastic scattering with the whole target nucleus, leaving the latter in its ground state - except that the target nucleus get excited and therefore some secondaries are produced by the nuclear de-excitation.
Both Geant4 and FLUKA includes quasi-elastic interactions, but in Geant4 these interactions are accounted as inelastic interactions, whereas in FLUKA they are accounted as part of the coherent elastic scattering (and therefore the secondaries are neglected), at least when the projectile hadron has a momentum above 5 GeV/c.
The motivation for the choice of FLUKA is that, experimentally, it can be difficult to separate between elastic and quasi-elastic interactions, at least at relatively high projectile energies.

What should be “equivalent” in Geant4 and FLUKA is the so-called “production cross section”, i.e. the hadron-nucleus inelastic cross section after removing the quasi-elastic cross section.

This quasi-elastic treatment in FLUKA might be changed in the future for FLUKA-CERN, and could be already changed in recent versions of FLUKA-INFN, and becoming therefore consistent with the Geant4 treatment.
No plan instead to change anything in Geant4 related the treatment of quasi-elastic interactions.

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