Ground-State Properties of a Model of a Two-Dimensional System of Liquid Helium-3

An investigation is made of the low-temperature behavior of a two-dimensional many-fermion system parametrized to serve as a model of a monomolecular layer of liquid ${\mathrm{He}}^3$. The calculations are made using the ${\Lambda }_{00}$ approximation of the Martin-Schwinger thermodynamic Green's function theory. A Herzfeld potential is used for the two-body interaction in order that the resulting $T$-matrix equation can be solved exactly. Three sets of the three parameters of this potential are chosen by requiring that they reproduce either the experimental and theoretical low-temperature second virial coefficient, the phase shifts calculated from the 6-12 potential, or the experimental binding energy and density of the three-dimensional system. The chemical potential, energy per particle, density, and specific heat are calculated. Of the three sets of parameters the maximum binding energy for the two-dimensional system results from the potential which predicts the correct three-dimensional experimental energy and density. The maximum binding in this case is 0.68°K at a density corresponding to $r_0=2.9\mathrm{}$ Å. Three-dimensional calculations were made with the several sets of parameters, with the result that the virial-coefficient and phase-shift sets predict too little attraction.