Isovector proton-neutron pairing and Wigner energy in Hartree-Fock mean field calculations

We propose a new approach for the treatment of isovector pairing in self-consistent mean field calculations which conserves exactly the isospin and the particle number in the pairing channel. The mean field is generated by a Skyrme--Hartree-Fock functional while the isovector pairing correlations are described in terms of quartets formed by two neutrons and two protons coupled to the total isospin $T=0$. In this framework we analyze the contribution of isovector pairing to the symmetry and Wigner energies. It is shown that the isovector pairing provides a good description of the Wigner energy, which is not the case for the mean field calculations in which pairing is treated by BCS-like models.