Scattering phase shift for relativistic separable potential with Laguerre-type form factors

TL;DR

This paper derives analytic formulas for relativistic scattering phase shifts using separable potentials with Laguerre form factors, extending previous work to higher angular momenta and multiple potential terms.

Contribution

It provides a generalization of earlier results by including higher angular momentum states and multiple potential terms in the relativistic J-matrix scattering framework.

Findings

Analytic expressions for phase shifts with M=1,2,3 potential terms.

Extension to arbitrary angular momentum states.

Simple numerical evaluation method for M >= 4.

Abstract

As an extension of earlier work [J. Phys. A: Math. Gen. 34 (2001) 11273] we obtain analytic expressions for the scattering phase shift of M-term relativistic separable potential with Laguerre-type form factors and for M = 1, 2, and 3. We take the Dirac Hamiltonian as the reference Hamiltonian. Just like in the cited article, the tools of the relativistic J-matrix method of scattering will be used. However, the results obtained here are for a general angular momentum, which is in contrast to the previous work where only S-wave scattering could be calculated. An exact numerical evaluation for higher order potentials (M >= 4) can be obtained in a simple and straightforward way.