Relation between Wigner energy and proton-neutron pairing

Abstract

The linear term proportional to $|N-Z|$ in the nuclear symmetry energy (Wigner energy)is obtained in a model that uses isovector pairing on single particle levels from a deformed potential combined with a ${\vec{T}}^2$ interaction. The pairing correlations are calculated by numerical diagonalization of the pairing Hamiltonian acting on the six or seven levels nearest the $N=Z$ Fermi surface. The experimental binding energies of nuclei with $N\approx Z$ are well reproduced. The Wigner energy emerges as a consequence of restoring isospin symmetry. We have found the Wigner energy to be insensitive to the presence of moderate isoscalar pair correlations.

(10 pages, 10 figures)

References in corpus (4)

• Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XII: Stiffness and stability of neutron-star matter
• Isospin mixing in nuclei within the nuclear density functional theory
• Microscopic Calculation of IBM Parameters by Potential Energy Surface Mapping
• Pairing theory of the symmetry energy

Cited by in corpus (22)

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• Lightweight self-conjugate nucleus ${}^{80}$Zr
• No-core configuration-interaction model for the isospin- and angular-momentum-projected states
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• A quartet BCS-like theory
• Deformation effects on the coexistence between neutron-proton and particle like pairing in N=Z medium mass nuclei
• Nuclear masses near N = Z from Nilsson-Strutinsky calculations with pairing corrections beyond BCS from an isospin-conserving pairing force
• Isovector and isoscalar proton-neutron pairing in $N>Z$ nuclei
• Isospin effects in N~Z nuclei in extended Density Functional Theory
• Shell structure from nuclear observables
• High Precision Binding Energies from Physics Informed Machine Learning
• Isoscalar and isovector neutron-proton pairing
• Empirical pairing gaps and neutron-proton correlations
• Low-lying states in near-magic odd-odd nuclei and the effective interaction
• Effect of Wigner energy on the symmetry energy coefficient in nuclei
• Role of pair-vibrational correlations in forming the odd-even mass difference
• Quartet correlations near the surface of $N=Z$ nuclei
• Further exploration of binding energy residuals using machine learning and the development of a composite ensemble model
• Particle-hole symmetry parameters for nuclei
• Symmetry energies for $A=24$ and $48$ and the USD and KB3 shell model Hamiltonians
• 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