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.

arXiv comment10 pages, 2 figures

References in corpus (12)

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Cited by in corpus (12)

• Symmetry restoration in the mean-field description of proton-neutron pairing
• Gamow-Teller excitations at finite temperature: Competition between pairing and temperature effects
• A quartet BCS-like theory
• Analytical approach for the Quartet Condensation Model
• $\alpha$-like quartetting in the excited states of proton-neutron pairing Hamiltonians
• Disentangling the pair and quartet condensates
• Spin-Triplet Pairing in Heavy Nuclei is Stable Against Deformation
• Unified description of pairing and quarteting correlations within the particle-hole-boson approach
• Collective treatment of the isovector pair correlations. Boson representation
• Coexistence of quartets and pairs in even-even $N>Z$ nuclei
• Proton-neutron pairing and binding energies of nuclei close to N=Z line
• Structure of the quartetting ground state of $N=Z$ nuclei