Levinson's Theorem and the Nodes of Zero-Energy Wave Functions for Potentials with Repulsive Coulomb Tails

Levinson's theorem relation phase shifts and bound states, developed for a short-range potential Vₛₕ, is extended to scattering by Vₛₕ+VC, where VC is a repulsive Coulomb potential. The subtleties associated with $L=0$, $E=0$ bound states for Vₛₕ alone are not present for Vₛₕ+VC. Information is also obtained on the relation between the nodal structure of the zero-incident-energy wave function and the number of bound states; some extensions to scattering by a compound target are possible.