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Semi-analytic Faddeev solution to the $N$-boson problem with zero-range interactions

T. Sogo·O. Sørensen·A. S. Jensen·D. V. Fedorov
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Abstract

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.

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T. Sogo, O. Sørensen, A. S. Jensen, D. V. Fedorov. 2004-07-02. Semi-analytic Faddeev solution to the $N$-boson problem with zero-range interactions. https://doi.org/10.1209/epl%2Fi2004-10405-1

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