Particle scattering by harmonically trapped Bose and Fermi gases

TL;DR

This paper analytically investigates particle scattering by harmonically trapped Bose and Fermi gases with short-range interactions, predicting temperature-dependent differential cross-sections and proposing experimental tests for various BEC configurations.

Contribution

It provides the first analytical predictions of scattering cross-sections in trapped quantum gases, linking scattering properties to energy eigenstates and experimental setups.

Findings

Predicted differential scattering cross-sections and their temperature dependence.

Identified coherent scattering as a tool to determine energy eigenstates.

Proposed experimental tests in current Bose-Einstein condensate setups.

Abstract

We have analytically explored the quantum phenomenon of particle scattering by harmonically trapped Bose and Fermi gases with the short ranged (Fermi-Huang $\delta^3_p$ [1]) interactions among the incident particle and the scatterers. We have predicted differential scattering cross-sections and their temperature dependence in this regard. Coherent scattering even by a single boson or fermion in the finite geometry gives rise to new tool of determining energy eigenstate of the scatterer. Our predictions on the differential scattering cross-sections, can be tested within the present day experimental setups, specially, for (i) 3-D harmonically trapped interacting Bose-Einstein condensate (BEC), (ii) BECs in a double well, and (iii) BECs in an optical lattice.