Properties of liquid and solid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

A Monte Carlo method is used to compute the properties of the fluid and crystal phases of the Lennard-Jones model of $^{4}\mathrm{He}$ at absolute zero. The method yields exact results subject only to statistical sampling errors. The energy, structure factor, and momentum distribution are calculated at several densitites in both phases. In addition, in the crystal phase we have carried out a detailed study of the single-particle distribution function. The densities at which melting and freezing occurs are determined. In both phases perturbative estimates of the three-body Axilrod-Teller potential are computed. Overall the agreement with experiment is good to excellent. However there are significant discrepancies between the computed and experimental equations of state. We believe this is due to the inadequacy of the Lennard-Jones potential.

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