Effective interatomic interaction in a low-density Bose–Einstein condensate

The Gross–Pitaevskii representation for the atom–atom interaction in the nonlinear Schrödinger equation for a trapped dilute Bose–Einstein condensate is shown to not generally satisfy the Hartree self-consistent-field equation. An alternate representation is proposed to satisfy the Hartree equation that takes proper account of both the repulsive and attractive parts of the true atom–atom potential. This is explicitly demonstrated for the cases of dilute Rb and He condensates.