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.

Figure 1

Even-even to odd-odd mass difference along the $N=Z$ line calculated by Eq. (10) as a function of mass number. The experimental values, including the ones calculated from extrapolated masses, are from Ref. [4].

Figure 2

The quantity $1/\Phi$ [see Eq. (9)], expressing the strength of the symmetry energy term proportional to $T^2$, as a function of mass number. The experimental values, obtained by removing the contribution of the Coulomb energy, are from Ref. [4].

Figure 3

The quantity $X$ [see Eq. (9)], which gives the contribution of the Wigner energy relative to the standard symmetry energy, as a function of mass number. The experimental values, obtained by removing the contribution of the Coulomb energy, are from Ref. [4].