The union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double-beta decay

Abstract

Good many-body methods for medium and heavy nuclei are important. Here we combine ideas from standard generator-coordinate methods (GCM) and the so-called Monte Carlo shell model, and set forth a novel approach: starting from a mean-field solution (Hartree-Fock-Bogoliubov), we create a set of non-orthogonal basis states, by using low-lying vibrational quasiparticleTamm-Dancoff modes, and then project onto states of good angular momentum and particle number. The results we benchmark against full shell model calculations. Even with just a few such modes we find improvement over standard GCM calculations in excitation spectra. We also find significant improvement in $0\nu \beta \beta$ nuclear matrix elements.

6 pages, 1 figure; updated to changes from refereeing and editing for published version, including minor retitling

References in corpus (13)

• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Anatomy of nuclear matrix elements for neutrinoless double-beta decay
• The 0nbb-decay nuclear matrix elements with self-consistent short-range correlations
• Configuration mixing of angular-momentum and particle-number projected triaxial HFB states using the Skyrme energy density functional
• Beyond the relativistic mean-field approximation (II): configuration mixing of mean-field wave functions projected on angular momentum and particle number
• Shell model studies of the ${}^{130}Te$ neutrinoless double-beta decay
• A monopole-optimized effective interaction for tin isotopes
• Proton-Neutron Pairing Amplitude as a Generator Coordinate for Double-Beta Decay
• Neutrinoless double-beta decay matrix elements in large shell-model spaces with the generator-coordinate method
• Angular Momentum Projected Configuration Interaction with Realistic Hamiltonians
• Triaxial shape fluctuations and quasiparticle excitations in heavy nuclei
• Projection of angular momentum via linear algebra

Cited by in corpus (10)

• Toward the discovery of matter creation with neutrinoless double-beta decay
• Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• 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
• Optimization of generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double-beta decay: ridge regression for nuclei with axial deformation
• A Pfaffian formulation for matrix elements of three-body operators in multiple quasi-particle configurations
• Finding the best basis states for the variation after projection nuclear wave functions
• $\alpha$ + ${}^{92}$Zr cluster structure in ${}^{96}$Mo
• Ab initio study in the island of inversion within the two-major-shell valence space