Electron-impact-excitation cross sections of hydrogenlike ions

Abstract

Convergent close-coupling (CCC) and Coulomb-Born with exchange and normalization (CBE) methods are used to study electron-impact excitation of hydrogenlike ions. The nl\ensuremath{\rightarrow}${\mathrm{n}}^{|\mathrm{I}\mathrm{H}}$${\mathrm{l}}^{|\mathrm{I}\mathrm{H}}$ cross sections demonstrate (i) good agreement between the CCC and CBE results, (ii) a scaling over ion nuclear charge z, (iii) a domination of the dipole (${\mathrm{l}}^{|\mathrm{I}\mathrm{H}}$=l\ifmmode\pm\else\textpm\fi{}1) contributions in total n\ensuremath{\rightarrow}${\mathrm{n}}^{|\mathrm{I}\mathrm{H}}$ cross sections, and (iv) significant effect of electron exchange in the energy range x3 (here x is the ratio of the incident electron kinetic energy \ensuremath{\varepsilon} to the transition energy ${\mathrm{E}}_{\mathrm{n},{\mathrm{n}}^{|\mathrm{I}\mathrm{H}}}$). For ions with z>5 the n\ensuremath{\rightarrow}${\mathrm{n}}^{|\mathrm{I}\mathrm{H}}$ cross sections obtained in the CCC and CBE approximations agree with each other to better than 10% for any x. An accuracy of the cross sections scaling over ${\mathrm{z}}^{4}$ depends on z: for z=6--18 the scaling is accurate to better than 10% (quantitative analysis is done for ${\mathrm{n}}^{|\mathrm{I}\mathrm{H}}$7), for ions with z6 the cross sections deviate from the ${\mathrm{z}}^{4}$ scaling more significantly (at x about unity). The n\ensuremath{\rightarrow}${\mathrm{n}}^{|\mathrm{I}\mathrm{H}}$ cross sections are presented by a formula which fits our CCC and CBE results with an accuracy to better than 10% (for transitions with n${\mathrm{n}}^{|\mathrm{I}\mathrm{H}}$7 in ions with z>5). The new Gaunt factor G(x) suggested for the widely used Van Regemorter formula [Astrophys. J. 136, 906 (1962)] makes this formula accurate to better than 50% in the x>3 range and to better than 20% in the x>100 range. It is shown that the semiempirical formula by Vainshtein, Sobelman, and Yukov [Electron-Impact Excitation Cross Sections of Atoms and Ions (Nauka, Moscow, 1973)] provides an accuracy to better than 50% for any incident electron energy. For x2 this formula is accurate to better than 30%. These accuracy assessments are based on a comparison with our CCC and CBE results.