${}_1{}^1{}_{}{}^{}\mathrm{H}_{}^{+}{}_{}{}^{}$- and ${}_2{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$-induced $M$-shell x-ray-production cross sections for selected elements in the rare-earth region

The measurements of $M$-shell x-ray-production cross sections induced by ${}_1{}^1{}_{}{}^{}\mathrm{H}_{}^{+}{}_{}{}^{} \mathrm{and} {}_2{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$ ions are compared to the first-Born-approximation and ECPSSR (energy loss, Coulomb-deflection effects; perturbed-stationary-state approximation, with relativistic corrections) theories. Most of the reported experimental data were measured in our laboratory and the other measurements were taken from the literature. The data from our laboratory were for incident ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ ions in the energy range from 0.25 to 2.5 MeV. The $M$-shell x-ray-production cross sections were measured for the following thin targets: ${}_{59}{}^{}{}_{}{}^{}\mathrm{Pr}$, ${}_{60}{}^{}{}_{}{}^{}\mathrm{Nd}$, ${}_{63}{}^{}{}_{}{}^{}\mathrm{Eu}$, ${}_{64}{}^{}{}_{}{}^{}\mathrm{Gd}$, ${}_{66}{}^{}{}_{}{}^{}\mathrm{Dy}$, ${}_{67}{}^{}{}_{}{}^{}\mathrm{Ho}$, ${}_{68}{}^{}{}_{}{}^{}\mathrm{Er}$, ${}_{70}{}^{}{}_{}{}^{}\mathrm{Yb}$, and ${}_{72}{}^{}{}_{}{}^{}\mathrm{Hf}$. The data from the literature were for protons and ${\mathrm{He}}^{+}$ ions in the energy range from 30 keV to 40 MeV. These data were for the following elements: ${}_{54}{}^{}{}_{}{}^{}\mathrm{Xe}$, ${}_{59}{}^{}{}_{}{}^{}\mathrm{Pr}$, ${}_{60}{}^{}{}_{}{}^{}\mathrm{Nd}$, ${}_{62}{}^{}{}_{}{}^{}\mathrm{Sm}$, ${}_{63}{}^{}{}_{}{}^{}\mathrm{Eu}$, ${}_{64}{}^{}{}_{}{}^{}\mathrm{Gd}$, ${}_{65}{}^{}{}_{}{}^{}\mathrm{Tb}$, ${}_{66}{}^{}{}_{}{}^{}\mathrm{Dy}$, ${}_{67}{}^{}{}_{}{}^{}\mathrm{Ho}$, ${}_{68}{}^{}{}_{}{}^{}\mathrm{Er}$, ${}_{70}{}^{}{}_{}{}^{}\mathrm{Yb}$, ${}_{72}{}^{}{}_{}{}^{}\mathrm{Hf}$, ${}_{73}{}^{}{}_{}{}^{}\mathrm{Ta}$, ${}_{74}{}^{}{}_{}{}^{}\mathrm{W}$, ${}_{78}{}^{}{}_{}{}^{}\mathrm{Pt}$, ${}_{79}{}^{}{}_{}{}^{}\mathrm{Au}$, ${}_{80}{}^{}{}_{}{}^{}\mathrm{Hg}$, ${}_{82}{}^{}{}_{}{}^{}\mathrm{Pb}$, ${}_{83}{}^{}{}_{}{}^{}\mathrm{Bi}$, and ${}_{92}{}^{}{}_{}{}^{}\mathrm{U}$. The first-Born-approximation calculations of the ionization cross section were made using the plane-wave Born approximation for direct ionization and the Oppenheimer-Brinkman-Kramers approximation of Nikolaev for electron capture. The ECPSSR theory of Brandt and Lapicki [Phys. Rev. A 23, 1717 (1981)] goes beyond the first Born approximation and accounts for the energy loss, Coulomb deflection, and relativistic effects in the perturbed-stationary-state theory. The first Born approximation overpredicts all measurements. The ECPSSR theory predicts the $M$-shell production cross sections correctly for $Z_2>70\mathrm{}$ and energies per $\mu >0.25\mathrm{}$ MeV/μ. In the rare-earth region the ECPSSR results lie above the data at higher projectile energies and fall off below the data at lower energies.