A pseudo-potential analog for zero-range photoassociation and Feshbach resonance
M. G. Moore
TL;DR
This paper introduces a zero-range pseudo-potential method for atom-molecule interactions, analogous to Fermi-Huang's approach, providing analytical solutions for Feshbach resonances in trapped two-atom systems.
Contribution
It develops a novel zero-range pseudo-potential framework for atom-molecule coupling, enabling analytical solutions for Feshbach resonances in confined geometries.
Findings
The zero-range approach accurately reproduces the scattering amplitude in the long-wavelength limit.
An analytical solution for two-atom Feshbach resonance in a harmonic trap is derived.
The method simplifies the analysis of atom-molecule interactions in confined systems.
Abstract
A zero-range approach to atom-molecule coupling is developed in analogy to the Fermi-Huang pseudo-potential treatment of atom-atom interactions. It is shown by explicit comparison to an exactly-solvable finite-range model that replacing the molecular bound-state wavefunction with a regularized delta-function can reproduce the exact scattering amplitude in the long-wavelength limit. Using this approach we find an analytical solution to the two-channel Feshbach resonance problem for two atoms in a spherical harmonic trap.
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