Energy-dependent effective interactions for dilute many-body systems
Abstract
We address the issue of determining an effective two-body interaction for mean-field calculations of energies of many-body systems. We show that the effective interaction is proportional to the phase shift, and demonstrate this result in the quasiclassical approximation when there is a trapping potential in addition to the short-range interaction between a pair of particles. We calculate numerically energy levels for the case of an interaction with a short-range square-well and a harmonic trapping potential and show that the numerical results agree well with the analytical expression. We derive a generalized Gross--Pitaevskii equation which includes effective range corrections and discuss the form of the electron--atom effective interaction to be used in calculations of Rydberg atoms and molecules.
Cite
@article{arxiv.cond-mat/0610314,
title = {Energy-dependent effective interactions for dilute many-body systems},
author = {A. Collin and P. Massignan and C. J. Pethick},
journal= {arXiv preprint arXiv:cond-mat/0610314},
year = {2007}
}
Comments
6 pages, 2 figures