Effects of pairing strength on the nuclear structure and double-$\beta$ decay predictions within the mapped interacting boson model

Abstract

The low-energy nuclear structure and two-neutrino double-$\beta$ ($2\nu \beta \beta$) decay are studied within the interacting boson model (IBM) that is based on the nuclear energy density functional (EDF). The IBM Hamiltonian describing the initial and final even-even nuclei, and the interacting boson fermion-fermion Hamiltonian producing the intermediate states of the neighboring odd-odd nuclei are determined by the microscopic inputs provided by the self-consistent mean-field (SCMF) calculations employing a relativistic EDF and a separable pairing force. Sensitivities of the low-lying structure and $2\nu \beta \beta$-decay properties to the pairing strength are specifically analyzed. It is shown that the SCMF calculations with decreased and increased pairing strengths lead to quadrupole-quadrupole interaction strengths in the IBM that are, respectively, significantly enhanced and reduced in magnitude. When the increased pairing is adopted, in particular, the energy levels of the excited $0^{+}$ states are lowered, and the predicted $2\nu \beta \beta$-decay nuclear matrix elements (NMEs) increase in magnitude systematically. The mapped IBM employing the increased pairing force generates effective NMEs and half-lives that are in a reasonable agreement with the experimental data for the ${}^{76}$Ge${\to }^{76}$Se, ${}^{82}$Se${\to }^{82}$Kr, and ${}^{100}$Mo${\to }^{100}$Ru decays in particular, whereas the calculation with the standard pairing strength is adequate to provide an overall good description of the effective NMEs in agreement with data.

22 pages, 13 figures, 8 tables

References in corpus (14)

• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• Relativistic Nuclear Energy Density Functionals: adjusting parameters to binding energies
• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Phase space factors for double-$\beta$ decay
• $0\nu \beta \beta$ and $2\nu \beta \beta$ nuclear matrix elements in the interacting boson model with isospin restoration
• Nuclear matrix elements for double-β decay
• Toward the discovery of matter creation with neutrinoless double-beta decay
• Structural evolution in $A\approx 100$ nuclei within the mapped interacting boson model based on the Gogny energy density functional
• Microscopic Formulation of Interacting Boson Model for Rotational Nuclei
• Single and low-lying states dominance in two-neutrino double-beta decay
• Final Results of GERDA on the Two-Neutrino Double-$\beta$ Decay Half-Life of ${}^{76}$Ge
• Coupling of pairing and triaxial shape vibrations in collective states of $\gamma$-soft nuclei
• Effect of configuration mixing on quadrupole and octupole collective states of transitional nuclei
• Parameter dependence of the $\beta$-decay properties of neutron-rich Zr isotopes within the interacting boson model

Cited by in corpus (5)

• Mapped interacting boson model for nuclear structure studies
• Radiative and exchange corrections for two-neutrino double-beta decay
• Neutrinoless $\beta \beta$ decay in the interacting boson model based on the nuclear energy density functionals
• Sensitivity analysis of $\beta$-decay half-life predictions for Ge, As, Zr and Mo nuclei within the mapped interacting boson model
• A Semi-Empirical Formula for Two-Neutrino Double-Beta Decay