Note on the perturbation calculation of phase shifts for central and non-central interactions

Abstract

It is shown that the calculation of the phase-shifts can be reduced to an ordinary eigen-value problem (for a closed state). By applying the usual perturbation theory to the latter, one obtains readily the phase shifts as series in powers of the interaction potential. The procedure, it is shown, is applicable to non-central as well as centrally symmetric interactions. Explicit expressions for phase shifts upto second order are given for both kinds of potentials.