Phase shift effective range expansion from supersymmetric quantum mechanics

Abstract

Supersymmetric or Darboux transformations are used to construct local phase equivalent deep and shallow potentials for $\ell \ne 0$ partial waves. We associate the value of the orbital angular momentum with the asymptotic form of the potential at infinity which allows us to introduce adequate long-distance transformations. The approach is shown to be effective in getting the correct phase shift effective range expansion. Applications are considered for the ${}^1{P}_1$ and ${}^1{D}_2$ partial waves of the neutron-proton scattering.

6 pages, 3 figures, Revtex4, version to be publised in Physical Review C