Alpha-like quartet condensation and isovector pairing correlations in N=Z nuclei

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.Comment: 11 pages, two table

Proton-neutron pairing in N=Z nuclei: quartetting versus pair condensation

The isoscalar proton-neutron pairing and isovector pairing, including both isovector proton-neutron pairing and like-particle pairing, are treated in a formalism which conserves exactly the particle number and the isospin. The formalism is designed for self-conjugate (N=Z) systems of nucleons moving in axially deformed mean fields and interacting through the most general isovector and isoscalar pairing interactions. The ground state of these systems is described by a superposition of two types of condensates, i.e., condensates of isovector quartets, built by two isovector pairs coupled to the total isospin T=0, and condensates of isoscalar proton-neutron pairs. The comparison with the exact solutions of realistic isovector-isoscalar pairing Hamiltonians shows that this ansatz for the ground state is able to describe with high precision the pairing correlation energies. It is also shown that, at variance with the majority of Hartree-Fock-Bogoliubov calculations, in the present formalism the isovector and isoscalar pairing correlations coexist for any pairing interactions. The competition between the isovector and isoscalar proton-neutron pairing correlations is studied for N=Z nuclei with the valence nucleons moving in the $sd$ and $pf$ shells and in the major shell above $^{100}$Sn. We find that in these nuclei the isovector pairing prevail over the isoscalar pairing, especially for heavier nuclei. However, the isoscalar proton-neutron correlations are significant in all nuclei and they always coexist with the isovector pairing correlations.Comment: 12 pages, 1 figur

Density Matrix Renormalization Group and the Nuclear Shell Model

We describe the use of the Density Matrix Renormalization Group method as a means of approximately solving large-scale nuclear shell-model problems. We focus on an angular-momentum-conserving variant of the method and report test results for the nucleus $^{48}Cr$. The calculation is able to reproduce both the ground state energy and the energy of the first excited state, by diagonalizing matrices much smaller than those of the full shell model.Comment: 7 pages, 3 figures; To appears in Phys. Rev.