Quartet condensation and isovector pairing correlations inN=Znuclei

Abstract

We propose a simple quartet condensation model (QCM) which describes with very high accuracy the isovector pairing correlations in self-conjugate nuclei. The quartets have an alpha-like structure and are formed by collective isovector pairs. The accuracy of the QCM is tested for N=Z nuclei for which exact shell model diagonalizations can be performed. The calculations are done with two isovector pairing forces, one extracted from standard shell model interactions and the other of seniority type, acting, respectively, upon spherical and axially-deformed single-particle states. It is shown that for all calculated nuclei the QCM gives very accurate values for the pairing correlations energies, with errors which do not exceed 1%. These results show clearly that the correlations induced by the isovector pairing in self-conjugate nuclei are of quartet type and also indicate that QCM is the proper tool to calculate the isovector proton-neutron correlations in mean field pairing 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.…”

“…This is not anymore possible in the presence of the spin-orbit interaction. The question we address in this study is whether the ground state of the Hamiltonian (1) as well as of the most general isovector-isoscalar pairing Hamiltonian (17) (see below), can be well approximated by a condensate of alphalike quartets, as in the case of isovector pairing [13]. Thus, as in Ref.…”

“…Thus, with the isovector pairs (12) can be formed the following PBCS states with well-defined numbers of protons and neutrons [13]:…”

“…[13], the QCM state was further simplified by factorizing the mixing amplitudes which define the quartets. Due to this factorization it was possible to express the quartet condensate in terms of collective pairs and to use the recurrence relations method for the evaluation of the expectation value of the Hamiltonian.…”

“…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.…”