A Practical Method of Solving Cutoff Coulomb Problems in Momentum Space: Application to the Lippmann-Schwinger Resonating-Group Method and the pd Elastic Scattering

Abstract

A practical method of solving cutoff Coulomb problems of two-cluster systems in momentum space is given. When a sharply cut-off Coulomb force with a cutoff radius ρ is introduced at the level of constituent particles, the two-cluster direct potential of the Coulomb force becomes in general a local screened Coulomb potential. The asymptotic Hamiltonian yields two types of asymptotic waves; one is an approximate Coulomb wave with ρ in the middle-range region, and the other a free (no-Coulomb) wave in the longest-range region. The constant Wronskians of this Hamiltonian can be calculated in either region. We can evaluate the Coulomb-modified nuclear phase shifts for the screened Coulomb problem using the matching condition proposed by Vincent and Phatak for the sharply cut-off Coulomb problem. We apply this method first to an exactly solvable model of the αα scattering with the Ali-Bodmer potential and confirm that a complete solution is obtained with a finite ρ. The stability of nuclear phase shifts with respect to the change in ρ within some appropriate range is demonstrated in the αα resonating-group method (RGM) calculation using the Minnesota three-range force. An application to the pd elastic scattering is also discussed.