Neutrinoless double-$\beta$ decay of ${}^{124}$Sn, ${}^{130}$Te, and ${}^{136}$Xe in the Hamiltonian-based generator-coordinate method

Abstract

We present a generator-coordinate method for realistic shell-model Hamiltonians that closely approximates the full shell model calculations of the matrix elements for the neutrinoless double-$\beta$ decay of ${}^{124}$Sn, ${}^{130}$Te, and ${}^{136}$Xe. We treat not only quadrupole deformations but also the proton-neutron pairing amplitudes as generator coordinates. We validate this method by calculating and comparing spectroscopic quantities with the exact shell model results and experimental data. Our Hamiltonian-based generator-coordinate method produces $0\nu \beta \beta$ matrix elements much closer to the shell model ones, compared to the existing energy-density-functional-based generator-coordinate approaches. The remaining overestimation of $0\nu \beta \beta$ nuclear matrix element suggests that additional correlations may be needed to be taken into account for ${}^{124}$Sn, ${}^{130}$Te, and ${}^{136}$Xe when calculating with the Hamiltonian-based generator-coordinate method. The validation of this method may open the possibility of calculating $0\nu \beta \beta$ matrix element of ${}^{150}$Nd in a large shell-model space.

7 pages, 5 figures, 3 tables

References in corpus (28)

• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Disassembling the Nuclear Matrix Elements of the Neutrinoless double beta Decay
• Energy density functional study of nuclear matrix elements for neutrinoless $\beta \beta$ decay
• Anatomy of nuclear matrix elements for neutrinoless double-beta decay
• $0\nu \beta \beta$ and $2\nu \beta \beta$ nuclear matrix elements in the interacting boson model with isospin restoration
• The influence of pairing on the nuclear matrix elements of the neutrinoless double beta decays
• Nuclear matrix elements for double-β decay
• $0\nu \beta \beta$ and $2\nu \beta \beta$ nuclear matrix elements, QRPA, and isospin symmetry restoration
• The 0nbb-decay nuclear matrix elements with self-consistent short-range correlations
• A nucleus-dependent valence-space approach to nuclear structure
• Limits on the neutrino mass from neutrinoless double-$\beta$ decay
• Systematic study of nuclear matrix elements in neutrinoless double-beta decay with a beyond mean-field covariant density functional theory
• Improved short-range correlations and 0nbb nuclear matrix elements of 76Ge and 82Se
• Short-range correlations and neutrinoless double beta decay
• Beyond Mean-Field Calculations for Odd-A Nuclei
• Arbitrary mass Majorana neutrinos in neutrinoless double beta decay
• The $0\nu \beta \beta$-decay nuclear matrix element for light and heavy neutrino mass mechanisms from deformed QRPA cacluations for ${}^{76}$Ge, ${}^{82}$Se, ${}^{130}$Te, ${}^{136}$Xe and ${}^{150}$Nd with isospin restoration
• Shell model studies of the ${}^{130}Te$ neutrinoless double-beta decay
• A monopole-optimized effective interaction for tin isotopes
• Large-scale shell-model analysis of the neutrinoless $\beta \beta$ decay of ${}^{48}$Ca
• Collectivity in the light Xenon isotopes: A shell model study
• $0\nu \beta \beta$ nuclear matrix elements and the occupancy of individual orbits
• Proton-Neutron Pairing Amplitude as a Generator Coordinate for Double-Beta Decay
• Shell model analysis of competing mechanism to the double-beta decay of ${}^{48}$Ca
• Neutrinoless double-beta decay matrix elements in large shell-model spaces with the generator-coordinate method
• Octupole correlations in low-lying states of 150Nd and 150Sm and their impact on neutrinoless double-beta decay
• Symmetry Conserving Configuration Mixing description of odd mass nuclei

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• Variational approximations to exact solutions in shell-model valence spaces: calcium isotopes in the pf-shell
• Symmetry-projected variational calculations with the numerical suite TAURUS I. Variation after particle-number projection
• The union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double-beta decay
• Benchmarking ${}^{136}$Xe Neutrinoless $\beta \beta$ Decay Matrix Element Calculations with the ${}^{138}\mathrm{Ba}(p,t)$ Reaction
• Global calculation of two-neutrino double-$\beta$ decay within the finite amplitude method in nuclear density functional theory
• Present Status of Nuclear Shell-Model Calculations of Neutrinoless Double-Beta Decay Matrix Elements
• Two-neutrino double-beta decay matrix elements based on relativistic nuclear energy density functional
• A Pfaffian formulation for matrix elements of three-body operators in multiple quasi-particle configurations
• Nuclear matrix elements calculation for $0\nu \beta \beta$ decay of ${}^{124}$Sn using nonclosure approach in nuclear shell model
• Ab initio study in the island of inversion within the two-major-shell valence space
• The study of $0\nu \beta \beta$ decay of ${}^{136}$Xe using nonclosure approach in nuclear shell model