Generalized pseudopotentials for higher partial wave scattering.
We derive a generalized zero-range pseudopotential applicable to all partial wave solutions to the Schrödinger equation based on a delta-shell potential in the limit that the shell radius approaches zero. This properly models all higher order multipole moments not accounted for with a monopolar delta function at the origin, as used in the familiar Fermi pseudopotential for s-wave scattering. By making the strength of the potential energy dependent, we derive self-consistent solutions for the entire energy spectrum of the realistic potential. We apply this to study two particles in an isotropic harmonic trap, interacting through a central potential, and derive analytic expressions for the energy eigenstates and eigenvalues.
Stock
René
R
Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA.
Silberfarb
Andrew
A
Bolda
Eric L
EL
Deutsch
Ivan H
IH