Isovector and isoscalar proton-neutron pairing in N>Z nuclei

Abstract

We propose a particle number conserving formalism for the treatment of isovector-isoscalar pairing in nuclei with N > Z. The ground state of the pairing Hamiltonian is described by a quartet condensate to which is appended a pair condensate formed by the neutrons in excess.The quartets are built by two isovector pairs coupled to the total isospin T = 0 and two collective isoscalar proton-neutron pairs. To probe this ansatz for the ground state we performed calculations for N > Z nuclei with the valence nucleons moving above the cores 16 O, 40 Ca and 100 Sn. The calculations are done with two pairing interactions, one state-independent and the other of zero range, which are supposed to scatter pairs in time-revered orbits. It is proven that the ground state correlation energies calculated within this approach are very close to the exact results provided by the diagonalization of the pairing Hamiltonian. Based on this formalism we have shown that moving away of N=Z line, both the isoscalar and the isovector proton-neutron pairing correlations remain significant and that they cannot be treated accurately by models based on a proton-neutron pair condensate.

Quartet correlations in N = Z nuclei induced by realistic two-body interactions

“…that, (1), it has been proven that the isovector pairing acting on self-consistent Skyrme-HF mean fields can reproduce rather well the mass dependence of Wigner energy [12] and, (2), it has shown that the isovector and isoscalar pairing correlations coexist for any isovector and isoscalar pairing forces [14,15]. This result is in agreement with the exactly solvable models but at variance with the predictions of standard HFB calculations [17,18].…”

Quartetting in odd–odd self-conjugate nuclei

“…Reproducing the basic features of the complex spectra of these odd-odd nuclei in such reduced spaces provides a strong support to the validity of the present approximation scheme. Besides allowing a comprehension of these nuclei that is much simpler and more intuitive than that provided by the shell model, these calculations confirm the central role of quartetting in N = Z nuclei that had already been evidenced in our previous studies of the even-even systems [7,8,9,10,11,12,22]. With respect to these previous works, it appears even more clearly the role of T = 0, J > 0 quartets.…”

“…This has been verified in a recent analysis of even-even nuclei in the sd shell which has evidenced a significant role of T = 0, J = 2, 4 quartets in the low-lying states of 24 Mg and 28 Si [22]. The quartets employed in this analysis have not been constructed variationally, as in the quoted works on pn pairing [7,8,9,10,11,12], owing to the difficulty in applying this procedure in the presence of quartets of various nature. T = 0 quartets have been instead simply assumed to represent the lowest states of 20 Ne (two protons and two neutrons outside the 16 O core).…”

“…We have recently carried out an analysis of the pn pairing in even-even N = Z nuclei both in the isovector and in the isoscalar channels [7,8,9,10,11,12]. This analysis has evidenced, on the one hand, that a description of the ground state correlations induced by this interaction in terms of a condensate of collective pairs (of various form [12]) is not satisfactory and, on the other hand, that these correlations can be accounted for to a high degree of precision by approximating the ground state as a product of identical T = 0 quartets.…”

Disentangling the pair and quartet condensates

“…212 Po= 208 Pb+α [6]. On the other hand, configuration space approaches based on correlated quartet structures were recently proven to describe very precisely the four body correlations induced by the residual nuclear interaction [9][10][11][12][13][14][15][16][17][18][19], in both N = Z and N > Z nuclei. A unified microscopic description of real space α clustering and configuration (shell model) space quartet correlations is an open problem in theoretical nuclear physics.Moreover, in N > Z nuclei, it is necessary to consider the interplay of quartet and neutron pair correla- * Email address: virgil.baran@theory.nipne.ro tions.…”