Ground-State Energy of Neutron Gas

In the calculation of the energy per neutron in the zeroth cluster and first perturbative order at different neutron densities, a complete set of correlated basic functions has been used to represent the ground-state wave function for a system of neutron gas. Three potentials, all fitting two-nucleon data, were used. They are the Hamada-Johnston (HJ), Breit, and Brueckner-Gammel-Thaler (BGT) potentials. The results show that the energy decreases monotonically, as neutron density decreases and that the energy values at low densities are nearly the same for all three potentials. But at high densities, the BGT result departs quite markedly from those for HJ and Breit potentials. The results also indicate that a bound state due to the nuclear $n-n$ force alone does not exist for a system of neutron gas.