Energy-dependent effective interactions for dilute many-body systems

A. Collin, P. Massignan, and C. J. Pethick
Phys. Rev. A 75, 013615 – Published 12 January 2007

Abstract

We address the issue of determining an effective two-body interaction for mean-field calculations of the 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.

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  • Received 11 October 2006

DOI:https://doi.org/10.1103/PhysRevA.75.013615

©2007 American Physical Society

Authors & Affiliations

A. Collin, P. Massignan*, and C. J. Pethick

  • NORDITA, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark

  • *Present address: Institute for Theoretical Physics, University of Utrecht, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands.

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Issue

Vol. 75, Iss. 1 — January 2007

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