Global calculation of two-neutrino double-$\beta$ decay within the finite amplitude method in nuclear density functional theory

Abstract

Two-neutrino double-beta ($2\nu \beta \beta$) decay has been used to constrain the neutron-proton part of effective interactions, which in turn is used to compute the nuclear matrix elements for neutrinoless double-beta decay, the observation of which would have important consequences for fundamental physics. We carefully examine $2\nu \beta \beta$ matrix elements within the proton-neutron quasiparticle random-phase approximation with nuclear energy density functionals. We work with functionals that are fit globally to single-beta-decay half-lives and charge-exchange giant-resonance energies, but not to $2\nu \beta \beta$ half-lives themselves, to evaluate the $2\nu \beta \beta$ nuclear matrix elements for all important nuclei, including those whose half-lives have not yet been measured. Such a comprehensive evaluation in large model spaces without configuration truncation requires an efficient computational scheme; we employ a double contour integration within the finite amplitude method. The results generally reproduce the nuclear matrix element extracted from half-lives well, without the use of any of those half-lives in the fitting procedure. We present predictions of the matrix elements in a total of 27 nuclei with half-lives that are still unmeasured.

16 pages, 5 figures

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• QRPA calculations for M1 transitions with the noniterative finite amplitude method and the application to neutron radiative capture cross sections
• Five-dimensional collective Hamiltonian with improved inertial functions
• Two-neutrino $\beta \beta$ decay to excited states at next-to-leading order
• Axially Deformed Proton-Neutron Relativistic Quasiparticle Finite Amplitude Method for Charge-Exchange Transitions
• Impact of octupole deformation on the nuclear electromagnetic response