Non-partial-wave Coulomb-Born theory for the excitation of many-electron atomic ions

Abstract

A formal theory for the evaluation of the cross section for the excitation of many-electron atomic ion within the framework of the Coulomb-Born approximation is formulated in non-partial-wave version, in which the multiple expansion of the transition matrix element is decomposed into two parts: the target form factor and the projectile distortion form factor. These are the matrix elements of the tensor operators between quantum states, so that any complicated wave function for the target ion can be employed. Thus it becomes possible to apply Coulomb-Born theory to treat the excitation of many-electron atomic ions for impact by charged particles, especially heavy particles. As an illustration, the $1s$-$2s$ and $1s$-$2p$ excitation cross sections of hydrogenlike ions by electron impact are calculated for a wide range of energies using the Coulomb-Born formal analysis.