Considerations on the Dirac-Hartree-Fock-Bogoliubov applied to asymmetric nuclear matter

The Dirac-Hartree-Fock-Bogoliubov (DHFB) approximation has been used successfully to describe $S=0, T=1$ pairing (proton-proton and neutron-neutron pairing) in both symmetric nuclear matter and in finite nuclei . As proton-neutron pairing of both the $S=0, T=1$ and $S=1, T=0$ types also seems to be important in light nuclei, where protons and neutrons occupy the same shell, we are extending the model to include these. Using the DHFB approximation, we obtain the long-range interaction field, the HF field Σ, as well as the short-range interaction one, the pairing field Δ, as a function of the baryon momenta and of the density. We are including the pn pairing in the model of asymmetric nuclear matter in order to study the relative importance of the two basic types of pairing and to study effects of the asymmetry on the pairing. In this work, we discuss the effect on the states of the system of the broken spatial, spin and isospin symmetries that result when $S=1, T=0 $ pairing is taken into account in asymmetric nuclear matter. (author)