Studying the scattering length by varying the depth of the potential well

Abstract

Discussions of the scattering length frequently focus on the special case of the deuteron, and sometimes statements that are not true in general are made. To obtain a deeper understanding, we study the scattering length as a function of the depth V0 of a square well and an exponential well and show how the scattering length becomes infinite at values of V0 for which new bound states appear at zero energy.