Four-body corrected first Born approximation for single-electron capture into arbitrary states of energetic projectiles

Abstract

Single charge exchange in collisions between fast bare projectiles and heliumlike atomic systems is investigated by means of the four-body boundary-corrected first Born approximation. An extensive analytical study of the general transition amplitude for electron capture into the arbitrary ${n}^{f}{l}^{f}{m}^{f}$ final states of the projectile is carried out. The quantum-mechanical transition amplitude for both symmetric and asymmetric collisions is derived in terms of a two-dimensional numerical quadrature over real variables. An illustrative computation is performed involving state-selective and total single-capture cross sections for $p$-He and ${\mathrm{Li}}^{3+}$-He collisions at intermediate and high impact energies. Detailed comparisons with the available measurements are reported with the purpose of further assessing the validity and utility of the four-body corrected first Born method in various applications ranging from fusion research to radiotherapy.