Monopole Coulomb-deflection factor for heavy-particle inner-shell-ionization cross sections

Abstract

The repulsion between positively charged projectiles and the nucleus of target atoms gives rise to a Coulomb-deflection factor that reduces the inner-shell-ionization cross sections calculated for straight-line particle trajectories. In the monopole approximation to the repulsion, this factor depends on the function ${G}_{0}(x)={[x\frac{d{K}_{\mathrm{ix}}(y)}{\mathrm{dy}{|}_{y=x}}]}^{2}$, where ${K}_{\mathrm{ix}}$ is the Bessel function of imaginary order. Through identities between Bessel functions of complex order and argument we have, in this addendum to an earlier paper [W. Brandt and G. Lapicki, Phys. Rev. A 20, 465 (1979)], reduced the evaluation of ${G}_{0}(x)$ to computed functions. Values of ${G}_{0}(x)$ and its integrals as they appear in the theory of $K$- and $L$-shell ionizations are tabulated. The monopole approximation is compared with results based on the standard approximation $G(x)=1$ which describes the experimental data.