A Variational Principle for Scattering

A variational principle is presented for the phase shifts ${\delta }_l$ of a central force scattering problem. This generalizes the principles of Schwinger and Hulthèn for $S$-state scattering in that (a) it is applicable to states of higher angular momentum, and (b) it depends explicitly on the "inside" wave function only. The Born approximation may be obtained with the choice of an appropriate trial function. Illustrative calculations have been made for the $S$- and $P$-state scattering states for an exponential well nucleon-nucleon interaction potential. A simple one-parameter trial function was utilized. The results are in excellent agreement with previously given exact calculations.