title: Generalized pseudopotentials for higher partial wave scattering.
abstract: 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.
authors.affiliation: Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA.
authors.forename: René
authors.initials: R
authors.lastname: Stock
authors.forename: Andrew
authors.initials: A
authors.lastname: Silberfarb
authors.forename: Eric L
authors.initials: EL
authors.lastname: Bolda
authors.forename: Ivan H
authors.initials: IH
authors.lastname: Deutsch