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 δl−1=δl=δl+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.
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March 1989
Research Article|
March 01 1989
Scattering in a spherical potential: Motion of complex‐plane poles and zeros
Richard A. Arndt;
Richard A. Arndt
Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
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L. David Roper
L. David Roper
Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
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Computers in Physics and IEEE Computational Science & Engineering 3, 65–72 (1989)
Article history
Received:
July 15 1987
Accepted:
September 12 1988
Citation
Richard A. Arndt, L. David Roper; Scattering in a spherical potential: Motion of complex‐plane poles and zeros. Computers in Physics and IEEE Computational Science & Engineering 1 March 1989; 3 (2): 65–72. https://doi.org/10.1063/1.168318
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