Scattering in a spherical potential: Motion of complex‐plane poles and zeros

Scattering of spinless nucleons in a spherical potential is examined with the use of a computer graphics simulation VSCAT. The potential is defined stepwise and the Schrödinger equation is solved to obtain wavefunctions, scattering phases, partial‐wave total cross sections, and differential cross sections, which are then displayed graphically. For the particular case of a square well, partial‐wave amplitudes are displayed over the complex momentum plane in a three‐dimensional plot. The well depth is then varied to follow the motion of poles in the complex momentum plane as they become resonances and then are bound states. Also displayed are the partial‐wave zeros, which are required to satisfy Levinson’s theorem for multiple states. The requirement on well depth is developed to produce a specified number of bound states and enumerate the energies which, at a given well depth, create equal scattering phases in adjoining partial waves δ_l−1=δ_l=δ_l+1. This symmetry of scattering phases exists for both repulsive and attractive square potentials. A square repulsive core is also studied, which has the same triple‐point symmetry as the square well.