Properties of Liquid Helium-3 in the Two-Body Correlation Approximation. I

This is the first of two papers in which the low-temperature properties of liquid ${\mathrm{He}}^3$ are to be calculated in the thermodynamically consistent "$T$-matrix" approximation. The set of coupled integral equations which are to be solved is exhibited in Sec. I of this paper. Section II is devoted to a preliminary, zero-temperature calculation which employs the additional approximations of using separable potentials and a non-interacting spectral function to define the interaction of two particles in the medium: the ${〈T〉}_0$ approximation. In this approximation we obtain a spectral function for the quasiparticles which we expect to display general features in common with those of the actual spectral function. Using this spectral function, we calculate the thermodynamic properties of the system and find that they compare favorably with those obtained in other calculations.