W-Matrix: A New Method for Solving the Two-Body Problem

摘要

We present a new momentum space approach to the two-body problem in partial waves. The method allows one to solve both the bound state and the scattering problems in terms of one single inhomogeneous integral equation and thus unifies the descriptions of both energy regimes. This integral equation is real and manifestly non-singular also at scattering energies; for uncoupled partial waves it can even be solved by iteration under only very global constraints on the potential, regardless of the potential strength. Moreover, its solution (called W-matrix) leads to a very simple and practical integral representation of the Jost function in terms of momentum space quantities only. We demonstrate the applicability of our method by calculating bound state and scattering data for the two-nucleon system with the s-wave Malfliet-Tjon III and the sup 3 S sub 1 - sup 3 D sub 1 Reid soft-core potentials. We find that both the bound state and the scattering problems can be solved reliably with equal ease by our method. (ERA citation 10:045752)