Universal cross sections forK-shell ionization by heavy charged particles. II. Intermediate particle velocities

Experimental $K$-shell ionization cross sections of ${}_{13}{}^{}{}_{}{}^{}\mathrm{Al}$ and ${}_{28}{}^{}{}_{}{}^{}\mathrm{Ni}$ are reported for ions of ${}_1{}^1{}_{}{}^{}\mathrm{H}$, ${}_1{}^2{}_{}{}^{}\mathrm{H}$, ${}_2{}^4{}_{}{}^{}\mathrm{He}$, ${}_3{}^6{}_{}{}^{}\mathrm{Li}$, and ${}_3{}^7{}_{}{}^{}\mathrm{Li}$ with kinetic energies in the range from 2 to 36 MeV, and of ${}_{28}{}^{}{}_{}{}^{}\mathrm{Ni}$ for ions of ${}_6{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_8{}^{16}{}_{}{}^{}\mathrm{O}$, and ${}_9{}^{19}{}_{}{}^{}\mathrm{F}$ in the range from 4 to 90 MeV. The theory of direct Coulomb $K$-shell ionization, as developed in an earlier paper [Phys. Rev. A 7, 983 (1973)] for projectiles of atomic number $Z_1$, small compared to the target atomic number $Z_2$, and of velocities $v_1$ small compared to the target $K$-shell electron velocity $v_{2K}$, i.e., $v_1\ll v_{2K}$, is extended to intermediate velocities $v_1\simeq v_{2K}$. New effects appear. They add to the $Z_1^2$-proportional cross sections one derives from linear-response theories for direct ionizations. They are attributed to the polarization of the target $K$ shell in the field of the projectile, and to electron capture by the projectile. Guided by the perturbed stationary-state theory of atomic collisions, the polarization effects are incorporated so that the theory retains the unifying aspects of the cross sections derived in the plane-wave Born approximation, but the variables now contain the nonlinear effects as scaling factors. Electron-capture cross sections are added. When $v_1\gg v_{2K}$, such contributions subside, and one retrieves the cross sections of the linear-response approximation. The theory predicts $K$-shell ionization cross sections for projectiles with $\frac{Z_1}{Z_2}<0.5\mathrm{}$ at all velocities in a comprehensive manner. It agrees with experimental data covering six orders of magnitude for collisions partners with $\frac{Z_1}{Z_2}$ ranging from 0.03 to 0.3 and $\frac{v_1}{v_{2K}}$ from 0.07 to 2.