Pairing theory of the symmetry energy

Abstract

As a model which displays a picture of the symmetry energy as an energy of rotation in isospace of a Cooper pair condensate, a Hamiltonian with a pairing force and an interaction of isospins is analyzed in the Hartree-Bogolyubov (HB) plus Random Phase (RPA) approximation. The HB energy minus Lagrangian multiplier terms is shown to be locally minimized by a product of neutron and proton Bardeen-Cooper-Schrieffer states. Nambu-Goldstone RPA solutions appear due to global gauge invariance and isobaric invariance. In an idealized case of infinitely many equidistant single-nucleon levels, the symmetry energy is composed of contributions from the single-nucleon and isospin interaction energies and the RPA correlation energy. The contribution of the latter is dominated by a neutron-proton Nambu-Goldstone solution, which makes the total symmetry energy nearly proportional to T(T+1). Observations reported from Skyrme force calculations are discussed in the light of these results. Calculations with deformed Woods-Saxon single-nucleon levels give results similar to those of the idealized case, whereas a somewhat different behavior is found with spherical Woods-Saxon levels. The calculations with Woods-Saxon single-nucleon levels reproduce surprisingly well the empirical symmetry energy.

arXiv commentMinor formal corrections. To be published in Physical Review C

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Cited by in corpus (14)

• Overview of Neutron-Proton Pairing
• Four-nucleon alpha-type correlations and proton-neutron pairing away of N=Z line
• Relation between Wigner energy and proton-neutron pairing
• Collective inertia of Nambu-Goldstone mode from linear response theory
• Isovector proton-neutron pairing and Wigner energy in Hartree-Fock mean field calculations
• Nuclear masses near N = Z from Nilsson-Strutinsky calculations with pairing corrections beyond BCS from an isospin-conserving pairing force
• Isospin effects in N~Z nuclei in extended Density Functional Theory
• Isoscalar and isovector neutron-proton pairing
• Effect of Wigner energy on the symmetry energy coefficient in nuclei
• Effects of pairing correlations on the neutron skin thickness and the symmetry energy
• Role of pair-vibrational correlations in forming the odd-even mass difference
• Iso-scalar liquid drop model
• Closed expression for the pair vibrational correlation energy of a uniform distribution of single-nucleon levels
• Collective model with isovector pair and alpha-particle type correlations