On the Application of Faddeev Equations and the Coulomb t Matrix to Asymptotic Electron Capture in Hydrogen
Abstract
Faddeev equations together with the Coulomb t matrix have been used to determine the asymptotic amplitude for electron capture from neutral hydrogen by fast protons. The results show that in the highenergy limit the capture cross section should go down as v^{11}, where v is the velocity of the incident proton. The capture amplitude is identical to Drisko's secondBornapproximation calculation except for a complex energydependent phase factor which ultimately approaches unity with sufficiently high incident energy. The major contribution to the threebody capture amplitude can be shown to come from the onenergyshell twobody t matrix, in agreement with general theorems concerning scattering from complex systems. At high incident energies, the onenergyshell contribution to the capture amplitude (not the cross section) will decrease as v^{5}, while the offenergyshell continuum contribution will decrease as v^{6}. The contributions from the sum of the infinite number of twobody boundstate poles can be shown to converge, and the sum can be explicitly performed at high enough incident energies in all except the forward direction. The boundstate contributions to the capture amplitude go down as v^{11}, which is much less than the continuum contributions.
 Publication:

Physical Review A
 Pub Date:
 November 1970
 DOI:
 10.1103/PhysRevA.2.1811
 Bibcode:
 1970PhRvA...2.1811C