Projectile charge-state dependence of $K$-shell ionization by silicon ions: A comparison of Coulomb ionization theories for direct ionization and electron capture with x-ray production data

X-ray-production cross sections measured in $K$-shell ionization of ${}_{21}{}^{}{}_{}{}^{}\mathrm{Sc}$, ${}_{22}{}^{}{}_{}{}^{}\mathrm{Ti}$, ${}_{29}{}^{}{}_{}{}^{}\mathrm{Cu}$, and ${}_{32}{}^{}{}_{}{}^{}\mathrm{Ge}$ by 52-MeV ${}_{14}{}^{28}{}_{}{}^{}\mathrm{Si}_{}^{+q}{}_{}{}^{}$ projectiles with $q=7\mathrm{} \mathrm{to} 14$ are reported, which demonstrate, through their charge-state dependence, the validity of a recently developed electron-capture theory with a reduced binding effect. Furthermore, the data provide evidence for the applicability of the perturbed stationary-state theory of direct ionization for values of $0.44\le \frac{Z_1}{Z_2}\le 0.67$.