Semi-analytic solution to the N-boson problem with zero-range interactionsT. Sogo1, O. Sørensen2, A. S. Jensen1 and D. V. Fedorov1
1 Department of Physics and Astronomy, University of Aarhus DK-8000 Aarhus C, Denmark
2 Max-Planck-Institute for the Physics of Complex Systems Nöthnitzer Straße 38, D-01187 Dresden, Germany
received 6 October 2004; accepted in final form 22 December 2004
published online 2 February 2005
We study two-body correlations for N identical bosons by use of the hyperspherical adiabatic-expansion method. We use the zero-range interaction and derive a transcendental equation determining the key ingredient of the hyperradial potential. The necessary renormalization is for both repulsive and attractive interactions achieved with an effective range expansion of the two-body phase shifts. Our solutions including correlations provide the properties of Bose-Einstein condensates exemplified by stability conditions as established by mean-field Gross-Pitaevskii calculations. The many-body Efimov states are unavoidable for large scattering lengths.
31.15.Ja - Hyperspherical methods.
21.45.+v - Few-body systems.
05.30.Jp - Boson systems.
© EDP Sciences 2005