Stopping power of hydrogen in hafnium and the importance of relativistic 4f electrons

MONTANARI, C. C.; MIRANDA, P. A.; ALVES, E.; MENDEZ, A. M. P.; MITNIK, D. M.; MIRAGLIA, J. E.; CORREA, R.; WACHTER, J.; AGUILERA, M.; CATARINO, N.; DA SILVA, R. C.

Physical Review A

APS

Lugar: New York; Año: 2020 vol. 101

2469-9926

The stopping power of protons through Hf foil has been studied both experimentally and theoretically. Themeasurements were performed at the Laboratory of Accelerators and X-Ray Diffraction in Lisbon by using thetransmission method on self-supporting stopping material. The overall uncertainty of around 5% was establishedover the protons energy range (0.6-2.5) MeV. The theoretical developments involved fully relativistic atomicstructure calculations for Hf, which required the solution of the Dirac equation. The shell-wise local plasmaapproximation was used to describe the energy transferred to the bound 1s-4 f electrons, and the outer fourelectrons were considered as a free electron gas. We found the relativistic description of the 4 f shell and thescreening between 4 f and 5p electrons to be decisive around the stopping maximum. Present theoretical andexperimental results are in very good agreement in the energy region of the new measurements. However,our theoretical stopping cross sections show substantial differences with the most used semiempirical models(SRIM2013 and ICRU-49) at intermediate to low energies. Our calculations suggest the stopping maximumto be higher and shifted to lower energies than these previous predictions. Future measurements around themaximum and below would be necessary for a better understanding of the stopping power of hafnium.