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

Abstract

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., ${v}_{1}\ensuremath{\ll}{v}_{2K}$, is extended to intermediate velocities ${v}_{1}\ensuremath{\simeq}{v}_{2K}$. 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 ${v}_{1}\ensuremath{\gg}{v}_{2K}$, 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 $\frac{{Z}_{1}}{{Z}_{2}}<0.5$ 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.