Multiple outer-shell ionization effect in inner-shell x-ray production by light ions

L-shell x-ray production cross sections by 0.25–2.5-MeV ${}_2{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$ ions in ${}_{28}{}^{}{}_{}{}^{}\mathrm{Ni}$, ${}_{29}{}^{}{}_{}{}^{}\mathrm{Cu}$, ${}_{32}{}^{}{}_{}{}^{}\mathrm{Ge}$, ${}_{33}{}^{}{}_{}{}^{}\mathrm{As}$, ${}_{37}{}^{}{}_{}{}^{}\mathrm{Rb}$, ${}_{38}{}^{}{}_{}{}^{}\mathrm{Sr}$, ${}_{39}{}^{}{}_{}{}^{}\mathrm{Y}$, ${}_{40}{}^{}{}_{}{}^{}\mathrm{Zr}$, and ${}_{46}{}^{}{}_{}{}^{}\mathrm{Pd}$ are reported. The data are compared to the first Born approximation and the ECPSSR theory that accounts for the projectile energy loss (E) and Coulomb deflection (C) as well as the perturbed-stationary-state (PSS) and relativistic (R) effects in the treatment of the target L-shell electron. Surprisingly, the first Born approximation appears to converge to the data while the ECPSSR predictions underestimate them in the low-velocity limit. This is explained as the result of improper use of single-hole fluorescence yields. A heuristic formula is proposed to account for multiple ionizations in terms of a classical probability for these phenomena and, after it is applied, the ECPSSR theory of L-shell ionization is found to be in good agreement with the data.