The Ground State Energy of a Fermion Hard Sphere Fluid

Mark Dewing, David M. Ceperley

V.N. Efimov

V Efimov

George Allen Baker Jr., L. P. Benofy, Mauricio Fortes +3 more

Based on the well-known low-density expansion for the ground-state energy per particle of a many-fermion system interacting pairwise via a central potential we develop a perturbation scheme in which the zero-order state is that of the purely-repulsive-spheres fluid. For the hard-core plus square-well pair-interaction case we have deduced, for two-species fermion matter, perturbation formulas up to sixth order in the attractive coupling parameter. We explicitly report results up to fourth order here. Pad\'e-approximant analyses in the density are carried out in each order with the intent of providing the basis necessary for extensive equation-of-state calculations of various many-fermion systems. In particular, for zero order (the fermion hard-sphere fluid) we predict an uncertainty-principle divergence in the energy, and hence pressure, corresponding to the random close packing of spheres, at a density of about 0.5 times the recently obtained value for boson hard spheres and about 0.2 times the well-known empirical value for classical hard spheres.

George Allen Baker Jr., L. P. Benofy, Mauricio Fortes +1 more

A new method of computing the ground state energy of a Fermi fluid is developed and applied to the hard-sphere Fermi fluids of two and four components. We find the results to be highly accurate for low densities. In this paper we compute and report the perturbation series for the ground state energy for the soft, repulsive, square-well problem at a number of densities for a four-component Fermi system as well as the ladder approximation energies for a hard-sphere potential at the same densities.

Judit Németh