Excitation and ionization contributions to sum-rule Born cross sections for collisions of one-electron ions with atoms

Abstract

The contributions of bound-state excitations and continuum ionizations to the total inelastic (sum-rule) cross section are examined in Born approximation. The results of an investigation of this problem for the case of one-electron ions colliding with neutral atoms are presented. Emphasis in this work is placed on the general features of these types of cross sections and on the relative contributions of excitation and ionization to the total Born cross section. In addition, extensive numerical results for the parameters which determine the cross sections for electron loss, and for excitation to bound states, are given for one-electron ions having atomic numbers up to 30 colliding with He, N, and Ar target atoms. It is shown that for the asymptotic (high-velocity) Born cross sections, excitation never contributes more than a certain fraction of the total sum-rule inelastic cross section, and this fraction has a bound which is determined by the dipole limit of the transition amplitudes for the incident ion. This bound is given by $\frac{M_{\mathrm{ex}}^2}{M_{\mathrm{tot}}^2}$, where $M_{\mathrm{tot}}^2$ is the -1 energy moment of the dipole-oscillator-strength distribution and $M_{\mathrm{ex}}^2$ is the contribution to this moment from transitions to bound excited states. This result is independent of the target atom involved in the collision. Since $\frac{M_{\mathrm{ex}}^2}{M_{\mathrm{tot}}^2}$ does not depend on the atomic number for one-electron ions, this bound is also independent of the incident-ion atomic number in this case. As a consequence, ionization never contributes less to the sum-rule cross sections than the fraction $(1-\frac{M_{\mathrm{ex}}^2}{M_{\mathrm{tot}}^2})=\frac{M_{\mathrm{ion}}^2}{M_{\mathrm{tot}}^2}$. The more general problem, which involves multielectron ions (or atoms) colliding with atoms, is discussed from several viewpoints, and similar results are suggested for that case. In particular, separate upper bounds on the Born-excitation cross section, and lower bounds on the Born electron-loss cross section, are proposed which are all expressed as fractions of the total inelastic-scattering Born cross section.