Variational approach with the superposition of the symmetry-restored quasi-particle vacua for nuclear shell-model calculations

Abstract

We propose a variational calculation scheme utilizing the superposition of the angular-momentum, parity, number projected quasiparticle vacua, that is especially suitable for applying to medium-heavy nuclei in shell-model calculations. We derive a formula for the energy variance with quasi-particle vacua and apply the energy-variance extrapolation to the present scheme for further precise estimation of the exact shell-model energy. The validity of the method is presented for the shell-model calculation of ${}^{132}$Ba in the $50\le Z,N\le 82$ model space. We also discuss the feasibility of this scheme in the case of the ${}^{150}$Nd in the $50\le Z\le 82$ and $82\le Z\le 126$ model space and demonstrate that its neutrinoless-double-beta-decay matrix element is obtained showing good convergence.

References in corpus (53)

• The Shell Model as Unified View of Nuclear Structure
• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Evolution of shell structure in exotic nuclei
• Disassembling the Nuclear Matrix Elements of the Neutrinoless double beta Decay
• Energy density functional study of nuclear matrix elements for neutrinoless $\beta \beta$ decay
• Thick-Restart Block Lanczos Method for Large-Scale Shell-Model Calculations
• Generalized Lanczos Algorithm for Variational Quantum Monte Carlo
• The influence of pairing on the nuclear matrix elements of the neutrinoless double beta decays
• Quantum Phase Transition in the Shape of Zr isotopes
• Magnetic moments of the 2${}_1^{+}$ states around ${}^{132}$Sn
• Shell Model Study of the Double Beta Decays of ${}^{76}$Ge, ${}^{82}$Se and ${}^{136}$Xe
• Novel shape evolution in exotic Ni isotopes and configuration-dependent shell structure
• Large-Scale Calculations of the Double-Beta Decay of 76Ge, 130Te, 136Xe, and 150Nd in the Deformed Self-Consistent Skyrme Quasiparticle Random-Phase Approximation
• Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of ${}^{48}$Ca
• Systematic study of nuclear matrix elements in neutrinoless double-beta decay with a beyond mean-field covariant density functional theory
• The sign of the overlap of HFB wave functions
• The CUPID-Mo experiment for neutrinoless double-beta decay: performance and prospects
• Factorization in large-scale many-body calculations
• Limits on Majoron-emitting double-beta decays of Xe-136 in the KamLAND-Zen experiment
• Exotic neutron-rich medium-mass nuclei with realistic nuclear forces
• Novel shape evolution in Sn isotopes from magic numbers 50 to 82
• The calculation of the neutrinoless double-beta decay matrix element within the realistic shell model
• Symmetry restoration in Hartree-Fock-Bogoliubov based theories
• Double Gamow-Teller transitions and its relation to neutrinoless $\beta \beta$ decay
• Large-scale shell-model analysis of the neutrinoless $\beta \beta$ decay of ${}^{48}$Ca
• Benchmarks of the full configuration interaction, Monte Carlo shell model, and no-core full configuration methods
• Multi-Phonon $\gamma$-Vibrational Bands and the Triaxial Projected Shell Model
• Relativistic description of nuclear matrix elements in neutrinoless double-$\beta$ decay
• Generator-coordinate reference states for spectra and $0\nu \beta \beta$ decay in the in-medium similarity renormalization group
• Advanced density matrix renormalization group method for nuclear structure calculations
• Underlying structure of collective bands and self-organization in quantum systems
• Neutrinoless double-beta decay matrix elements in large shell-model spaces with the generator-coordinate method
• {\it Ab initio} nuclear structure - the large sparse matrix eigenvalue problem
• Novel Extrapolation Method in the Monte Carlo Shell Model
• Shell Model Monte Carlo Studies of $\gamma$-Soft Nuclei
• Neutrinoless double beta decay of ${}^{150}$Nd with account for deformation
• An extrapolation method for shell model calculations
• Evaluation of overlaps between arbitrary Fermionic quasiparticle vacua
• Importance-Truncated Large-Scale Shell Model
• No-Core MCSM calculation for ${}^{10}$Be and ${}^{12}$Be low-lying spectra
• Extrapolation Method for the No-Core Shell Model
• Variational approximations to exact solutions in shell-model valence spaces: calcium isotopes in the pf-shell
• Octupole correlations in low-lying states of 150Nd and 150Sm and their impact on neutrinoless double-beta decay
• Variational procedure for nuclear shell-model calculations and energy-variance extrapolation
• Precise estimation of shell model energy by second order extrapolation method
• Norm-overlap formula of Hartree-Fock-Bogoliubov states with odd number parity
• Efficient computation of Hamiltonian matrix elements between non-orthogonal Slater determinants
• New variational Monte Carlo method with an energy variance extrapolation for large-scale shell-model calculations
• A Constrained-Path Quantum Monte-Carlo Approach for the Nuclear Shell Model
• Variational Monte Carlo method for shell-model calculations in odd-mass nuclei and restoration of symmetry
• An efficient method to evaluate energy variances for extrapolation methods
• Effect of residual many-body forces due to the evolution in the in-medium similarity renormalization group method

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• Symmetry restoration in mean-field approaches
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• Variational approximations to exact solutions in shell-model valence spaces: systematic calculations in the $sd$-shell
• Variation after projection calculations for high-spin states
• Shape transition of Nd and Sm isotopes and neutrinoless double-beta decay nuclear matrix element of ${}^{150}$Nd
• Accurate and precise quantum computation of valence two-neutron systems
• Large-scale shell-model study of two-neutrino double-beta decay of ${}^{82}$Se, ${}^{94}$Zr, ${}^{108}$Cd, ${}^{124}$Sn, ${}^{128}$Te, ${}^{130}$Te, ${}^{136}$Xe, and ${}^{150}$Nd
• Constraints on the nuclear Schiff moment from its correlation with electromagnetic properties
• Nuclear structure properties of ${}^{193-200}$Hg isotopes within large-scale shell model calculations
• Finding the best basis states for the variation after projection nuclear wave functions
• Mixing of one-particle-one-hole projected states with the variation after projection wave functions
• Exact solutions of the nuclear shell-model secular problem: Discrete Non-Orthogonal Shell Model within a Variation After Projection approach
• Probing Quadruple Deformation in Transitional Nuclei via Angular Momentum Projection