High-energy Born collision strengths for optically forbidden transitions

Collision strengths for optically forbidden transitions in positive ions excited by electron impact tend to finite limits as the energy of the colliding electron becomes infinitely great. This statement applies to theoretical data obtained by means of approximations which ignore relativistic effects. The high-energy limiting values are given by the Born approximation, which Bethe showed can be reduced to a closed expression requiring integration over momentum transfer and the radial distance of the atomic orbital. In the appendix we describe an accurate numerical procedure for evaluating this double integral and also show how to perform the Racah algebra which arises when mixed configurations are used to describe the target. We make applications to several isoelectronic sequences taking configuration interaction into account.