Bose Condensation and Momentum Distribution in a Simplified Liquid-He4Ground State

Bose-Einstein condensation and the atomic momentum distribution are investigated for a simplified liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ground state obtained by antisymmetrization, with respect to the electron variables, of a product of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$-atom wave functions, each in its individual electronic and translational ground state. The momentum distribution is defined and evaluated by the method of redundant modes and generalized Tani transformation. Bose-Einstein condensation is found, with a condensate depletion of 6% owing to the purely kinematical repulsion arising from the Pauli exclusion principle. The noncondensed atoms are spread in momentum space by an amount of a few inverse Bohr radii. Dynamical correlations would increase the depletion in a more realistic ground state.