Energy threshold for the Bethe formula of proton electronic stopping power

Dear FLUKA experts,

I hope you are all well. I had a quick question regarding proton electronic stopping power. In Battistoni et al. (10.3389/fonc.2016.00116), it is said that it is calculated from the Bethe formula with the appropriate corrections but that at low energies the approach by Ziegler (in several papers) is followed. This is similar to what is done in ICRU Report 49.

I assume that the transition between the two formalisms depends on the material but could you give an approximate energy value? ICRU 49 mentions 1 MeV.

Also, it would be great if you could give further information on what is implemented as Ziegler approach (Am I right to assume that it is the empirical formula in ICRU 49?).

Thank you very much for your time in advance. Any help would be appreciated!

Best regards,

Daniel

Dear Daniel,

The stopping power evaluation currently used in FLUKA follows one and the same approach throughout the energy domain in which charged particles are transported.

It consists of a series of terms (Bethe-Bloch, Barkas, density-effect correction, shell correction - Mott correction and effective charge for ions). With a twist: the shell correction additionally contains any difference between the sum of the rest of terms and experimental data (typically NIST data for e.g. protons), so that (unrestricted) stopping powers match experimental data by construction.

I understand Ziegler et al. fitted their low-energy parametrizations also on experimental data. So in the end both approaches should be essentially equivalent (except for possible differences in the experimental data employed by both).

With kind regards,

Cesc

Dear Cesc,

Thank you very much for your reply! To confirm, the NIST proton data you mention is the one calculated following Stopping-Power & Range Tables for Electrons, Protons, and Helium Ions | NIST and, particularly, Description of PSTAR and ASTAR databases, right?

Best regards,

Daniel

Hi Daniel,

Right, it should generally follow what you find in e.g. PSTAR for protons.

Cheers,

Cesc

Dear Cesc,

Great, thank you for your help.

Best regards,

Daniel