An investigation is made of the low temperature behavior of a two-dimensional many-fermion system parameterized to serve as a model of a mono-molecular layer of liquid He3. The calculations are made using the ∧oo 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 six-twelve 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 1.1°K at a density corresponding to ro = 6.1 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.
Anderson, Roger H. and Foster, Theodore C. (1966) "Ground-State Properties of a Model of a Two -Dimensional System of Liquid Helium Three," Journal of the Institute for Research: Ser. A: No. 3, Article 2. Available at: http://digitalcommons.spu.edu/jir/vol5/iss3/2