Nonlocal potentials, isolated states, and Levinson's theorem

A compact expression for the calculation of phase shifts is derived for a p otential which is the sum of local and nonlocal parts. Nonlocal potentials can support positive energy bound states, that is, states embedded in the c ontinuous energy spectrum. These states, sometimes referred to as "isolated " states, are not associated with any poles of the S matrix. Some controver sy exists in the literature on how such bound states are included in Levins on's theorem; it is found that the phase shift should be taken continuous a t the energy of the bound state rather than taken to have a discontinuity o f pi. For simplicity, the analysis is restricted to the radial s wave Schro dinger equation and separable nonlocal potentials. (C) 1999 American Instit ute of Physics. [S0022-2488(99)03601-4].