The validity of the shape-independent approximation is studied for three trapped atoms. By comparing the total ground-state energy calculated using pseudopotentials in the Hartree-Fock approximation to the exact ground-state energy, the shape-independent approximation is shown to agree quantitatively only in the low-density limit. It is also shown using configuration interaction that a Dirac δ function is not suitable as a replacement for the two-body interaction in exact theories.
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Esry et al. (1999) studied this question.
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