Generalized Pseudopotentials for Higher Partial Wave Scattering

Abstract

We derive a generalized zero-range pseudopotential applicable to all partial wave solutions to the Schroedinger 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.

RevTeX 4 pages, 1 figure, final published version

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• p-Wave Optical Feshbach Resonances in Yb-171
• Universal Two-Body Spectra of Ultracold Harmonically Trapped Atoms in Two and Three Dimensions
• Three-body interaction near a narrow two-body zero crossing
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• Multichannel Molecular State and Rectified Short-range Boundary Condition for Spin-orbit Coupled Ultracold Fermions Near p-wave Resonances
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• Efficient determination of eigenenergies and eigenstates of $N$ ($N=3$--$4$) identical 1D bosons and fermions under external harmonic confinement