Validity of the shape-independent approximation for Bose-Einstein condensates

Abstract
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.