Charge-transfer equations for completely stripped positive ions in helium

Abstract

Coupled-channel equations which include the momentum-transfer terms and which are intended for application over proton energy range 1-1000 keV are derived for completely stripped positive ions in helium. In particular, a realistic nine-parameter wave function is employed to obtain from the general equations direct and exchange matrix elements for the specific reaction $X^{i+}+\mathrm{He}\left(1\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)\to X^{\mathrm{}(i-1\mathrm{})+}\mathrm{}\left(\mathrm{nl}\right)+{\mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}$ in which four target states are incorporated. The resulting simple expressions for the elements are calculable via the standard Gauss-Legendre and Gauss-Laguerre quadratures. In presenting the final expressions for the elements, the ease of directly programming them for a computer has been a primary consideration. The limitation of the calculation is discussed.