Theory of the Fermion Liquid

The ground-state wave function generated by a system of interacting bosons is used as the correlation factor in a trial function describing the interacting fermion system. Expectation values are computed by the technique of the generalized normalization integral. The resulting cluster integrals are evaluated by introducing simple approximate forms for the $n$-particle distribution functions defined by the boson wave function. To illustrate the method, it is applied to establish a connection between known results for fermion and boson forms of a hard-sphere system at low density. As a second illustration experimental information on liquid ${\mathrm{He}}^4$ is used to work out properties of a hypothetical fermion-type system of mass 4. Results are given for the energy, effective mass, and magnetic behavior. The application to ${\mathrm{He}}^3$ waits on the evaluation of the radial distribution function and liquid structure factor for the corresponding artificial boson system of mass 3.