Gallagher-Moszkowski splitting in deformed odd-odd nuclei within a microscopic approach

Abstract

Low-lying bandhead states in axially prolate deformed odd-odd nuclei have long been described essentially within the rotor+two-quasiparticle picture. This approach allows one to explain the appearance of so-called Gallagher-Moszkowski doublets of bandheads with $K={\Omega }_n\pm {\Omega }_p$, sum and difference of neutron and proton angular momentum projections on the symmetry axis. According to an empirical rule stated by Gallagher and Moszkowski the spin-aligned configuration lies lower in energy than the spin-anti-aligned configuration. A recent study by Robledo, Bernard and Bertsch in Phys. Rev. C 89, 021303(R) (2014) within the Gogny energy-density functional with selfconsistent blocking of the unpaired nucleons showed that calculations fail to reproduce this rule in about half of the cases and points to the density-dependent term of the functional as responsible of this failure. In this paper we aim at pushing further this analysis to exhibit the mechanism underlying the energy splitting in a Gallagher-Moszkowski doublet. We work in the framework of the Skyrme energy-density functional approach, including BCS pairing correlations with selfconsistent blocking. We use the SIII parametrization with time-odd terms and seniority pairing matrix elements extending a previous study of K-isomeric states in even-even nuclei [Phys. Rev. C 105, 044329 (2022)]. We find that the energy splitting results from a competition between the spin-spin, density-dependent and current-current terms of the Skyrme energy-density functional. In doublets where the larger K value is lower in energy the Gallagher-Moszkowski rule is always satisfied by the SIII Skyrme energy-density functional. In doublets, on the contrary, where the smaller K value lies lower, the energy splittings are calculated to be rather small and often a disagreement with the Gallagher-Moszkowski rule occurs.

arXiv commentTo be submitted to Phys. Rev. C

References in corpus (22)

• The TDHF Code Sky3D
• Mean field and beyond description of nuclear structure with the Gogny force: A review
• Particle transfer reactions with the time-dependent Hartree-Fock theory using a particle number projection technique
• Configuration mixing of angular-momentum and particle-number projected triaxial HFB states using the Skyrme energy density functional
• Particle-Number Restoration within the Energy Density Functional Formalism
• Octupole deformation in the ground states of even-even nuclei: a global analysis within the covariant density functional theory
• Beyond Mean-Field Calculations for Odd-A Nuclei
• Landscape of pear-shaped even-even nuclei
• Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VIII) hfodd (v2.73y): a new version of the program
• The tensor part of the Skyrme energy density functional. III. Time-odd terms at high spin
• Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
• Configuration mixing description of the nucleus ${}^{44}$S
• Variational multiparticle-multihole configuration mixing method applied to pairing correlations in nuclei
• The shape of gold
• Configuration interaction in symmetry-conserving covariant density functional theory
• Angular momentum and parity projected multidimensionally constrained relativistic Hartree-Bogoliubov model
• A Number-Conserving Theory for Nuclear Pairing
• Spin constraints on nuclear energy density functionals
• Consistency of two different approaches to determine the strength of a pairing residual interaction in the rare-earth region
• Fission barriers of two odd-neutron actinide nuclei taking into account the time-reversal symmetry breaking at the mean-field level
• Beyond-mean-field description of octupolarity in dysprosium isotopes with the Gogny-D1M energy density functional
• Generator coordinate method for nuclear octupole excitations: status and perspectives