Relativistic second-order OBK approximation for electron capture

Abstract

The capture of an electron from a target hydrogenic ion T by a fully stripped projectile ion P, having atomic numbers ZT and ZP respectively, is investigated using the relativistic second-order Oppenheimer-Brinkman-Kramers (ROBK2) approximation. By expanding in powers of alpha ZT and alpha ZP and retaining the leading terms, alpha being the fine-structure constant, approximate formulae are derived for the scattering amplitude which are used to obtain approximate closed analytical expressions for the differential and total cross sections for electron capture between ground states. These differ from the author's previous formulae in that second-order terms in alpha are retained in the denominator leading to considerable improvement in the capture cross sections. Total cross sections for 1s-1s electron capture by incident protons from target hydrogen atoms calculated using the ROBK2 approximation are in good agreement with the relativistic continuum distorted-wave calculations of Deco and Rivarola (1987) over a wide range of projectile energies. Also the ROBK2 total cross sections for 1s-1s electron capture by incident bare neon ions from target atoms with ZT=13, 30, 47, 73, 92 are in satisfactory accordance with the relativistic eikonal and first Born approximation calculations of Eichler. Moreover reasonably satisfactory agreement is obtained between the ROBK2 total cross sections and the experimental data for incident bare C, Ne and Ar ions on various atomic targets.