Equivalence of local and non-local potentials and the perey effect

Abstract

Abstract A general discussion of the transformation which relates the wave functions in equivalent non-local and energy dependent local potentials is presented. In general this relation is nonlocal, ψ n l = pψ L , however it is shown that P must contain a local part P 0 = (1−∂V L (E)/t6E) 1 2 . For reasonable potentials P 0 is expected to be the most important contribution to P . This is also shown explicitly by generating by means of an expansion an equivalent non-local potential from a given local potential. If the non-local potential is assumed to have the form V nl (| r − r ′|, | r + r ′|) this allows one to determine P (beyond the first approximation, P ≈ P 0 ) and thus obtain Ψ nl directly from the wave functions used in the usual optical-model analysis of the scattering. Finally this expansion when applied in reverse provides an extension of the effective mass approximation.