Augustine C. Chen

Nonrelativistic off-shell two-body Coulomb amplitudes

Publisher Summary The off-shell T-matrix of a two-body interacting system provides, in principle, all the necessary information about the system. On very general grounds, it can be shown that the simple poles of the off-shell T-matrix correspond to the bound states of the system and the residues at these poles are related to the wavefunctions of corresponding bound states. The separable series representation together with partial wave decomposition permits the reduction of the Faddeev equations from a five-variable to a single-variable integral equation. The Coulomb branch-point singularities are actually part of the distortion factors to account for the long range Coulomb effects, which are absent in the plane-wave momentum representation for the incident wave and the propagation of the colliding particles. There are arguments concerning whether the Coulomb branch-point singularities on the initial and final half of the energy shell are physical, because in all cases of physical interest, the scattering of charged particles is caused by an interaction that is somewhat screened at very large distances. Consequently, these singularities should be removed by introducing appropriate screening in actual applications. Because physical results should not depend on the screening, it is therefore expected that correct results can be obtained by allowing the screening to approach zero.