Neutrinoless double-beta decay matrix elements in large shell-model spaces with the generator-coordinate method

Abstract

We use the generator-coordinate method with realistic shell-model interactions to closely approximate full shell-model calculations of the matrix elements for the neutrinoless double-beta decay of ${}^{48}$Ca, ${}^{76}$Ge, and ${}^{82}$Se. We work in one major shell for the first isotope, in the $f_{5/2}p{g}_{9/2}$ space for the second and third, and finally in two major shells for all three. Our coordinates include not only the usual axial deformation parameter $\beta$, but also the triaxiality angle $\gamma$ and neutron-proton pairing amplitudes. In the smaller model spaces our matrix elements agree well with those of full shell-model diagonalization, suggesting that our Hamiltonian-based GCM captures most of the important valence-space correlations. In two major shells, where exact diagonalization is not currently possible, our matrix elements are only slightly different from those in a single shell.

8 pages, 7 figures

References in corpus (20)

• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• Improved nuclear matter calculations from chiral low-momentum interactions
• 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
• $0\nu \beta \beta$ 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
• Coupled-cluster theory for three-body Hamiltonians
• In-Medium Similarity Renormalization Group for Open-Shell Nuclei
• Systematic study of nuclear matrix elements in neutrinoless double-beta decay with a beyond mean-field covariant density functional theory
• Nuclear Structure Relevant to Neutrinoless Double Beta Decay: 76Ge and 76Se
• Nuclear Structure Relevant to Neutrinoless Double Beta Decay: the Valence Protons in 76Ge and 76Se
• Proton-Neutron Pairing Amplitude as a Generator Coordinate for Double-Beta Decay
• Accurate shell-model nuclear matrix elements for neutrinoless double-beta decay
• Triaxiality and shape coexistence in Germanium isotopes
• Corrections to the Neutrinoless Double-Beta-Decay Operator in the Shell Model