Spatial structure of neutron Cooper pair in low density uniform matter

Abstract

The spatial structure of the neutron Cooper pair in superfluid low-density uniform matter is analyzed by means of BCS calculations employing a bare force and the effective Gogny interaction. It is shown that the Cooper pair exhibits a strong spatial dineutron correlation over a wide range of neutron densities $\ensuremath{\rho}/{\ensuremath{\rho}}_{0}\ensuremath{\approx}{10}^{\ensuremath{-}4}\ensuremath{-}0.5$. This feature is related to the crossover behavior between the pairing of the weak coupling BCS type and the Bose-Einstein condensation of bound neutron pairs. It is also shown that the zero-range \ensuremath{\delta} interaction can describe the spatial structure of the neutron Cooper pair if the density-dependent interaction strength and the cutoff energy are appropriately chosen. Parametrizations of the density-dependent \ensuremath{\delta} interaction satisfying this condition are discussed.