Local Density Approximation for proton-neutron pairing correlations. I. Formalism

In the present study we generalize the self-consistent Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate space to the case which incorporates an arbitrary mixing between protons and neutrons in the particle-hole (p-h) and particle-particle (p-p or pairing) channels. We define the HFB density matrices, discuss their spin-isospin structure, and construct the most general energy density functional that is quadratic in local densities. The consequences of the local gauge invariance are discussed and the particular case of the Skyrme energy density functional is studied. By varying the total energy with respect to the density matrices the self-consistent one-body HFB Hamiltonian is obtained and the structure of the resulting mean fields is shown. The consequences of the time-reversal symmetry, charge invariance, and proton-neutron symmetry are summarized. The complete list of expressions required to calculate total energy is presented.Comment: 22 RevTeX page

Deuteron formation in expanding nuclear matter from a strong coupling BCS approcah

The process of deuteron formation in intermediate heavy ion reactions is approached within the strong coupling BCS theory assuming that the final stage of the reaction can be described as an adiabatic expansion of a piece of nuclear matter. Since the gap equation in the 3S1-3D1 channel goes over into the deuteron Schrödinger equation in the low density limit, a smooth transition from the superfluid Cooper pair phase to a Bose deuteron gas is found. For a fixed entropy ranging from 0.5 to 2 units per particle the deuteron fraction, the chemical potential and temperature are reported as a function of density. For densities down to ρ=0.1 fm-3 and lower, the deuteron-to-nucleon ratio rapidly increases from a density threshold strongly depending on the entropy. Decreasing further the density this ratio tends logarithmically to one. The possible relevance of these results for heavy ion collisions and the shortcomings of the present approach are briefly discussed