Systematic study of the stopping power of the lanthanides

In the last decade, lanthanides have become the subject of multiple studies due to their importance in technological applications. This paper aims to systematically study the energy loss per unit length of protons on the 15 lanthanides, from lanthanum to lutetium. We investigate the stopping power cross sections by considering the influence of the relativistic atomic structure, namely the description of the $4f$ electrons, the number of electrons in the valence shells, and the electronic screening of the same or close subshells. The electronic stopping model considers separate contributions from bound and valence electrons. We employ a many-electron model for the former and a combination of perturbative and nonperturbative free-electron gas approaches for the latter. Our stopping results for the lanthanide series cover an extended energy range from very low to the MeV region. We compare them with measurements and other theoretical (dpass, casp) and semiempirical (srim) methods. Our results agree with most experimental data, even the recent values around the maximum for gadolinium. We implement Lindhard's scaling for the stopping number for all the data available of the 15 targets. Lindhard scaling for the stopping number includes all the data for the 15 targets. The present paper cast doubts on certain data sets, which should affect srim's description of lanthanides, such as La, Nd, Dy, and Tb. We call attention to the scarcity of measurements in the low and intermediate ranges, and we suggest experimental efforts to shed light on the stopping power of these relevant targets.