Total ionisation cross section

I’m calculating total cross section of heavy ion interacting with hydrogen atoms or molecules. There is a work of Voitkiv:
title={Hydrogen and helium ionization by relativistic projectiles in collisions with small momentum transfer},
author={A. B. Voitkiv and others},
journal={J.Phys.B: At.Mol.Opt.Phys},
equation 41-43 but when I use it I get 35x more cross section then by running TestEm0 example for hydrogen. My test projectile is 40Ar18+ ion at 600 MeV/u. What am I missing?


please, check dimensions in the paper and in TestEm0.


Hi, for Geant4 is is quite straightforward, I get this line at the output:
processes : ionIoni nuclearStopping total
cross section per atom : 826054 barn 0 pbarn 826054 barn

826054 barns = 8.26e-19 cm**2

The formula from Voitkiv is more tricky, because it is in atomic units. I went through is several times and I belive I don’t have mistakes. But my result is 1.82e-16 cm**2. Could it be that Voitkiv formula, which was developed taking into account very soft electrons, is more precise?

Best, Mariusz

All the low energy Physics models start at about 10 eV, while Voitkiv model does not have any cutoff. Could it be that Geant4 cannot simulate total ionization cross section in very low density media?


I found another paper which calculates and shows measurements of a total ionization cross section for hydorogen:
In Table 1 the ionization cross section for protons at 100 keV is ~1.5E-16 cm2.
When I run electromagnetic/TestEm0 example, modifies to include hydrogen, using various physics list (eg. emlivermore) I get no more than 6.5 Mbarn, which is 6.5E-18 cm2. There is a factor 20 difference. What is the explanation for this discrepancy?


sorry for the late answer. Geant4 has two types of physics, 1st of all, condensed history approach for ionisation and multiple scattering. In this approach all models have a low-energy threshold for delta-electron production. Ionisation cross section is a restricted cross section above this threshold. It should be significantly lower than the the total ionisation cross section.

The alternative approach is developed in low-energy and DNA models where each ionisation collisions are simulation. These models are available for limited number of projectile and target materials, for example, for liquid water and silicon.


Thanks a lot. I would like to calculate cross section (total but also differential ones as a function of energy and emitted electron angle) for very low-density gas, for example hydrogen (ie. no screening effect). For total cross-section the Voitkiv calculation gives 1e-20 m2 what is very similar to a typical dEdx cross section. Does this make sense? I thought dEdx cross section must be higher than ionization.