Theory of electron capture from a hydrogenlike ion by a bare ion: Intermediate-state contributions to the amplitude

Electron capture from a hydrogenlike ion of large nuclear charge ZTe by a bare ion of charge ZPe moving with speed v has been studied using the strong-potential Born approximation to the amplitude. Under the conditions ZPZT and ZPe²v, it is shown that, in comparison with the impulse approximation, the correct weighting of the target spectrum of intermediate states in the strong-potential Born theory significantly alters the 1s→1s cross section and at the same time makes peaking approximations to the amplitude more realistic, even for low v. The specific cases of ZT=6, 10,and 18 are treated over the velocity range ZT3ve²ZT(0.3). 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 strong-potential Born theory is seen to give a good representation of the data. Total cross sections for 1s→1s capture for ZP=ZT=1 are also presented.