Energy-dependent effective interactions for dilute many-body systems

Details Energy-dependent effective interactions for dilute many-body systems Energy-dependent effective interactions for dilute many-body systems

2006-10-11

arxiv.org/abs/cond-mat/0610314v1

Phys. Rev. A 75, 013615 (2007)

Physics

Condensed Matter

Other Condensed Matter

6 pages, 2 figures

Scientific paper

10.1103/PhysRevA.75.013615

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.

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