Relativistic description of nuclear matrix elements in neutrinoless double-$\beta$ decay

Abstract

Neutrinoless double-$\beta$ ($0\nu \beta \beta$) decay is related to many fundamental concepts in nuclear and particle physics beyond the standard model. Currently there are many experiments searching for this weak process. An accurate knowledge of the nuclear matrix element for the $0\nu \beta \beta$ decay is essential for determining the effective neutrino mass once this process is eventually measured. We report the first full relativistic description of the $0\nu \beta \beta$ decay matrix element based on a state-of-the-art nuclear structure model. We adopt the full relativistic transition operators which are derived with the charge-changing nucleonic currents composed of the vector coupling, axial-vector coupling, pseudoscalar coupling, and weak-magnetism coupling terms. The wave functions for the initial and final nuclei are determined by the multireference covariant density functional theory (MR-CDFT) based on the point-coupling functional PC-PK1. The low-energy spectra and electric quadrupole transitions in ${}^{150}$Nd and its daughter nucleus ${}^{150}$Sm are well reproduced by the MR-CDFT calculations. The $0\nu \beta \beta$ decay matrix elements for both the $0_1^{+}\to 0_1^{+}$ and $0_1^{+}\to 0_2^{+}$ decays of ${}^{150}$Nd are evaluated. The effects of particle number projection, static and dynamic deformations, and the full relativistic structure of the transition operators on the matrix elements are studied in detail. The resulting $0\nu \beta \beta$ decay matrix element for the $0_1^{+}\to 0_1^{+}$ transition is $5.60$, which gives the most optimistic prediction for the next generation of experiments searching for the $0\nu \beta \beta$ decay in ${}^{150}$Nd.

17 pages, 9 figures; table added

References in corpus (26)

• Relativistic Continuum Hartree Bogoliubov Theory for Ground State Properties of Exotic Nuclei
• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• New parametrization for the nuclear covariant energy density functional with point-coupling interaction
• Exotic modes of excitation in atomic nuclei far from stability
• Phase space factors for double-$\beta$ decay
• 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
• 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
• Erratum: Assessment of uncertainties in QRPA $0\nu \beta \beta$-decay nuclear matrix elements [Nucl. Phys. A 766, 107 (2006)]
• The 0nbb-decay nuclear matrix elements with self-consistent short-range correlations
• Precise half-life values for two neutrino double beta decay
• Spin-isospin resonances: A self-consistent covariant description
• Improved short-range correlations and 0nbb nuclear matrix elements of 76Ge and 82Se
• Nuclear matrix elements of neutrinoless double beta decay with improved short-range correlations
• Microscopic description of nuclear quantum phase transitions
• A microscopic benchmark-study of triaxiality in low-lying states of 76Kr
• Configuration mixing of angular-momentum projected triaxial relativistic mean-field wave functions. II. Microscopic analysis of low-lying states in magnesium isotopes
• Beyond the relativistic mean-field approximation (II): configuration mixing of mean-field wave functions projected on angular momentum and particle number
• Axially deformed relativistic Hartree Bogoliubov with separable pairing force
• Nuclear deformation and neutrinoless double-$\beta$ decay of ${}^{94,96}$Zr, ${}^{98,100}$Mo, ${}^{104}$Ru, ${}^{110}$Pd, ${}^{128,130}$Te and ${}^{150}$Nd nuclei in mass mechanism
• Neutrinoless double beta decay of ${}^{150}$Nd with account for deformation
• A beyond mean field analysis of the shape transition in the Neodymium isotopes
• Three-dimensional angular momentum projected relativistic point-coupling approach for the low-lying excited states in ${}^{24}$Mg

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• Variational approach with the superposition of the symmetry-restored quasi-particle vacua for nuclear shell-model calculations
• Two-neutrino double-beta decay of ${}^{150}$Nd to excited final states in ${}^{150}$Sm
• Triaxially deformed relativistic point-coupling model for $\Lambda$ hypernuclei: a quantitative analysis of hyperon impurity effect on nuclear collective properties
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• Ab initio studies of double Gamow-Teller transition and its correlation with neutrinoless double beta decay
• Global calculation of two-neutrino double-$\beta$ decay within the finite amplitude method in nuclear density functional theory
• Neutrinoless double beta decay in Left-Right symmetric model with double seesaw mechanism
• Neutrinoless double-$\beta$ decay and double Gamow-Teller transitions
• 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
• Shape transition of Nd and Sm isotopes and neutrinoless double-beta decay nuclear matrix element of ${}^{150}$Nd
• Configuration interaction projected density functional theory: effects of four-quasiparticle configurations and time-odd interactions
• Multireference covariant density-functional theory for the low-lying states of odd-mass nuclei
• Partial restoration of spin-isospin SU(4) Symmetry and the One-QRPA method in Double Beta Decay
• Impact of isovector pairing fluctuation on neutrinoless double-beta decay in multi-reference covariant density functional theory
• NMEs for $0\nu \beta \beta (0^{+}\to 2^{+})$ of two-nucleon mechanism for ${}^{76}$Ge
• Nuclear matrix elements of neutrinoless double-beta decay in covariant density functional theory with different mechanisms
• Nuclear matrix elements calculation for $0\nu \beta \beta$ decay of ${}^{124}$Sn using nonclosure approach in nuclear shell model
• Effect of Spin-Dependent Short-Range Correlations on Nuclear Matrix Elements for Neutrinoless Double Beta Decay of ${}^{48}$Ca
• $0\nu \beta \beta$ to the first $2^{+}$ state with two-nucleon mechanism for L-R symmetric model
• Subspace-projected multireference covariant density functional theory
• Benchmarking nuclear matrix elements of $0\nu \beta \beta$ decay with high-energy nuclear collisions
• Two-neutrino $\beta \beta$ decay to excited states at next-to-leading order
• Sensitivity of neutrinoless double beta decays from a combined analysis of ground and excited states
• The study of $0\nu \beta \beta$ decay of ${}^{136}$Xe using nonclosure approach in nuclear shell model