A Pfaffian formulation for matrix elements of three-body operators in multiple quasi-particle configurations

Abstract

We present a Pfaffian formula to calculate matrix elements of three-body operators in symmetry-restoration beyond-mean-field methods, including the case of multiple quasi-particle configurations. Detailed derivation based on [Mizusaki et al., Phys. Lett. B 715, 219 (2012)] and [Hu et al., Phys. Lett. B 734, 162 (2014)] is provided, and potential applications in generator coordinate method with chiral interactions, as well as in study of nuclear matrix elements in neutrinoless double beta decay are discussed.

References in corpus (53)

• Modern Theory of Nuclear Forces
• Chiral effective field theory and nuclear forces
• Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond
• Energy density functional study of nuclear matrix elements for neutrinoless $\beta \beta$ decay
• Time-dependent density-functional description of nuclear dynamics
• Mean field and beyond description of nuclear structure with the Gogny force: A review
• Beyond the relativistic mean-field approximation (III): collective Hamiltonian in five dimensions
• Triaxial Angular Momentum Projection and Configuration Mixing calculations with the Gogny force
• Configuration mixing of angular-momentum projected triaxial relativistic mean-field wave functions
• Configuration mixing of angular-momentum and particle-number projected triaxial HFB states using the Skyrme energy density functional
• Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of ${}^{48}$Ca
• Shape and pairing fluctuations effects on neutrinoless double beta decay nuclear matrix elements
• Systematic study of nuclear matrix elements in neutrinoless double-beta decay with a beyond mean-field covariant density functional theory
• Triaxial projected shell model approach
• The sign of the overlap of HFB wave functions
• Symmetry restoration in mean-field approaches
• Beyond Mean-Field Calculations for Odd-A Nuclei
• Symmetry restoration in Hartree-Fock-Bogoliubov based theories
• State-of-the-art of beyond mean field theories with nuclear density functionals
• Generator-coordinate reference states for spectra and $0\nu \beta \beta$ decay in the in-medium similarity renormalization group
• From Asymmetric to Symmetric Fission in the Fermium Isotopes within the Time-Dependent GCM Formalism
• 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
• Quenching of nuclear matrix elements for $0\nu \beta \beta$ decay by chiral two-body currents
• Evaluation of overlaps between arbitrary Fermionic quasiparticle vacua
• FELIX-2.0: New version of the finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation
• Mixing of quasiparticle excitations and gamma-vibrations in transitional nuclei
• Toward extremes of angular momentum: Application of the Pfaffian algorithm in realistic calculations
• FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation
• Matrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states
• Variation after full projection with triaxially deformed nuclear mean field
• Configuration interaction in symmetry-conserving covariant density functional theory
• Numeric and symbolic evaluation of the pfaffian of general skew-symmetric matrices
• Triaxial shape fluctuations and quasiparticle excitations in heavy nuclei
• A new and practical formulation for overlaps of Bogoliubov vacua
• Technical aspects of the evaluation of the overlap of Hartree- Fock- Bogoliubov wave functions
• Shell model method for Gamow-Teller Transitions in heavy, deformed nuclei
• A new formulation to calculate general HFB matrix elements through Pfaffian
• Urca Cooling in Neutron Star Crusts and Oceans: Effects of Nuclear Excitations
• Microscopic description of quadrupole-octupole coupling in neutron-rich actinides and superheavy nuclei with the Gogny-D1M energy density functional
• Projection of angular momentum via linear algebra
• Neutrinoless double-$\beta$ decay of ${}^{124}$Sn, ${}^{130}$Te, and ${}^{136}$Xe in the Hamiltonian-based generator-coordinate method
• Norm-overlap formula of Hartree-Fock-Bogoliubov states with odd number parity
• Nuclear matrix elements of neutrinoless double-$\beta$ decay in the triaxial projected shell model
• Systematic study of near yrast band structures in odd-mass ${}^{125-137}$Pr and ${}^{127-139}$Pm isotopes
• The union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double-beta decay
• Why does the sign problem occur in evaluating the overlap of HFB wave functions?
• Convergence and efficiency of angular momentum projection for many-body systems
• Decay widths at the scission point in nuclear fission
• Benchmarking projected Hartree-Fock as an approximation
• Generator coordinate method with a conjugate momentum: application to the particle number projection
• New algorithm in the variation after projection calculations for non-yrast nuclear states
• A convenient implementation of the overlap between arbitrary Hartree-Fock-Bogoliubov vacua for projection

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