Theory of Electron Capture from a Hydrogenlike Ion by a Bare Ion with Extensions to Inner-Shell Capture.
I give a complete systematic derivation of a new approximation. for the calculation of the cross section for electron capture from a. hydrogenlike ion of large nuclear charge Z(,T)e by a bare ion of charge. Z(,P)e moving with speed v. The amplitude in the wave treatment is. obtained through consistent expansion in the small parameters. Z(,P)/Z(,T) and Z(,P)e('2)/(H/2PI)v; however, the ratio Z(,T)e('2)/(H/2PI)v is not assumed. small. Electron-target nucleus interactions are included to all orders. and electron-projectile interactions were included consistently to. first order so that the theory is called the strong potential Born. (SPB). Following a careful analysis of the approach to the energy. shell, an off-shell factor is seen to arise which does not appear in the. impulse approximation (IA). The effects of this factor on the capture. amplitude are explored. It is shown that, in comparison with the IA,. the correct weighting of the target spectrum of intermediate states. in the SPB significantly alters the 1s (--->) ns cross section and at the. same time makes peaking approximations to the amplitude more realistic, even for intermediate velocity Z(,P)e('2)/(H/2PI) << v(, ) Z(,T)e('2)/(H/2PI). The specific cases of Z(,T) = 6, 10, 18 are treated over the velocity range Z(,T)/3(, ) (H/2PI)v/e('2)(, ) Z(,T)/(0.3). I derive the effects of the off-shell factor on excited state capture and justify the derivation of the cross section for asymptotically high v. The result agrees with the third Born cross section when Z(,P)/Z(,T) << 1. Instituting a one-electron model, K-shell capture cross sections and probabilities for protons on carbon, neon, and argon are calculated and compared with experiment. The SPB is seen to give a good representation of the data. Total cross sections for 1s (--->) 1s capture for Z(,P) = Z(,T) = 1 are also presented. Cross sections for all processes listed are tabulated and some possible extensions of the formalism are discussed.
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- Physics: Atomic