Abstract
We clarify the relation in interacting systems, and in particular ultracold atomic gases, between energy shifts arising from interparticle interactions and scattering phase shifts. A principle result of this paper is an expression for the energy levels of an atom in a container of arbitrary shape in the presence of a short-range scatterer, generalizing the result of Lüscher to containers of shapes other than cubic. We show that, while the energy shifts for a spherical container are under many conditions proportional to the phase shift, those for a cubic container have a more complicated structure. The general relation is extended to problems of particles in traps with smoothly varying potentials, including, e.g., the interaction of a small neutral atom with a Rydberg atom. Finally, we discuss why, even though individual energy levels are very sensitive to boundary conditions, the energies of many-body systems are not.
| Original language | English |
|---|---|
| Journal | Journal of Physics B: Atomic, Molecular and Optical Physics |
| Volume | 44 |
| Issue number | 19 |
| Pages (from-to) | 195207 |
| ISSN | 0953-4075 |
| DOIs | |
| Publication status | Published - 14 Nov 2011 |