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THEORY OF ELECTRON CAPTURE FROM A HYDROGENLIKE ION BY A BARE ION WITH EXTENSIONS TO INNER-SHELL CAPTURE
Abstract
I give a complete systematic derivation of a new approximationfor the calculation of the cross section for electron capture from ahydrogenlike ion of large nuclear charge Z(,T)e by a bare ion of chargeZ(,P)e moving with speed v. The amplitude in the wave treatment isobtained through consistent expansion in the small parametersZ(,P)/Z(,T) and Z(,P)e('2)/(H/2PI)v; however, the ratio Z(,T)e('2)/(H/2PI)v is not assumedsmall. Electron-target nucleus interactions are included to all ordersand electron-projectile interactions were included consistently tofirst order so that the theory is called the strong potential Born(SPB). Following a careful analysis of the approach to the energyshell, an off-shell factor is seen to arise which does not appear in theimpulse approximation (IA). The effects of this factor on the captureamplitude are explored. It is shown that, in comparison with the IA,the correct weighting of the target spectrum of intermediate statesin the SPB significantly alters the 1s (--->) ns cross section and at thesame 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.
Subject Area
Atomic physics
Recommended Citation
ALSTON, STEVEN GAIL, "THEORY OF ELECTRON CAPTURE FROM A HYDROGENLIKE ION BY A BARE ION WITH EXTENSIONS TO INNER-SHELL CAPTURE" (1982). ETD collection for University of Nebraska-Lincoln. AAI8306466.
https://digitalcommons.unl.edu/dissertations/AAI8306466