Electron capture at relativistic energies

Abstract

The theory of electron capture into the ground state from ground-state hydrogen atoms by high-energy incident protons is generalised to allow for relativistic effects arising from the high velocity of relative motion of the particles involved in the collision and from the use of Dirac wavefunctions for the atomic electron. The Oppenheimer-Brinkman-Kramers approximation is employed to obtain scattering amplitudes for capture without and with change of electron spin. Simple but accurate analytical expressions for the OBK capture cross sections are derived by expanding in powers of the fine-structure constant. At extremely high energies the capture cross sections are found to decay slowly as E_kin^-1, where E_kin is the kinetic energy of the incident proton, in accordance with the result previously obtained by Mittleman (1964).