ELECTRON-IMPACT EXCITATION OF ELECTRIC OCTUPOLE TRANSITIONS IN POSITIVE-IONS - ASYMPTOTIC-BEHAVIOR OF THE SUM OVER PARTIAL-COLLISION STRENGTHS

An investigation has been made, for the case of octupole transitions, of the dependence of the partial-collision strength on the orbital angular momentum of the colliding electron. It is shown that, similar to the dipole and quadrupole transitions, the sum over partial-collision strengths is asymptotic to a geometric series of common ratio E(j)/E(i), where E(i) and E(j) are the initial and final energies of the colliding electron, respectively. For large incident energies (E(j)/E(i) approximately 1) the convergence of the sum to the geometric series is rather slow, since the geometric-series method only starts to become valid for large values of angular momentum. This difficulty is overcome by developing an alternative method in which the approximation is made that E(j)/E(i) = 1. An analytic formula is then obtained to estimate the contribution to the total-collision strength from large values of angular momentum. Results of partial- and total-collision strengths are presented for direct electric octupole transitions in Ca+ and Sr+.