Third-order continuum distorted-wave double-scattering 1s-1s transitions

A non-relativistic description of the differential cross section (DCS) for Thomas double-scattering electron capture at asymptotically high velocity is developed within the third order continuum distorted-wave (CDW) perturbation theory for 1s → 1s transitions in proton-hydrogen collisions. It is shown that at the critical proton scattering angles, namely the forward peak, Thomas maximum, small angles and the interference minimum, the CDW series has converged at second order. Moreover, it is proven that the third-order correction makes no contribution to the velocity-dependent υ-11 and υ-12 behaviour of the Thomas double-scattering total cross sections at the leading angles. The Oppenheimer-Brinkman-Kramers (OBK) travelling atomic orbital plane wave theory is compared to the CDW approximation. It is observed that the second-order OBK (OBK2) theory has not converged. It remains an open question as to whether fourth-order terms or higher in the OBK approximation contribute to the various differential cross sections. It is concluded that the CDW model gives a superior description of the Thomas double-scattering mechanism than the OBK model. (Author)