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

Abstract

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-HF 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 analyse 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 the isovector pairing is treated by BCS-like models.

Isoscalar-isovector proton-neutron pairing and quartet condensation inN=Znuclei

“…We wish to conclude this paper by emphasizing the striking analogy between the like-particle and proton-neutron pairing pictures which has emerged in this study and which is also supported by our previous works on the same subject [13][14][15][16][17]19]. Thus, if on one side a condensate of collective J = 0 pairs provides a good approximation to the ground state of spherically symmetric like-particle pairing Hamiltonians, on the other side, as shown here, a condensate of J = 0,T = 0 quartets provides a good approximation to the ground state of spherically symmetric proton-neutron pairing Hamiltonians.…”

“…As seen in Table III, the results of the PBCS approximations (14)(15) and (16), which do not conserve the isospin and the angular momentum, respectively, are much less accurate than the ones provided by QCM. We also notice that for all nuclei P BCS1 gives more binding than P BCS iv , while the latter gives more binding than P BCS is , except for sd-shell nuclei.…”

“…Since the states (15) and (16) are condensates, respectively, of T = 1 and T = 0 proton-neutron pairs, one might think that a comparison of their correlation energies could give a clear evidence on what type of proton-neutron pairing is prevailing in N = Z nuclei. However, a conclusion based only on this comparison would be misleading because, as shown in the next section, the PBCS approximation is not accurate enough to describe properly the isovector and isoscalar pairing correlations.…”

“…In Refs. [13][14][15] it was shown that the ground state of realistic isovector pairing Hamiltonians can be described with high precision as a condensate of alpha-like quartets, as suggested by the exactly solvable SO(5) model [8]. However, at variance with the SO(5) model, the quartet condensation model (QCM) for realistic pairing Hamiltonians is based on collective quartets which take properly into account the spin-orbit interaction.…”

Isoscalar and isovector pairing in a formalism of quartets

“…[32], for the treatment of isovector and isoscalar pairing correlations in realistic mean field calculations. The advantage of these mean field calculations compared to the commonly used HFB models is the exact conservation of particle number and isospin in the pairing channel.…”