Session JB: Mini-Symposium on Nuclear Structure Aspects of Double Beta Decay

Recent advances in the theory of double beta decay

The theory of double beta decay will be briefly reviewed. Recent results in the calculation of phase space factors (PSF) and nuclear matrix elements (NME) will be presented. The presentation will include PSF for both double electron and double positron decay and NME for both light and heavy neutrino exchange.   

Neutron-capture cross-section measurements of $^{74}$Ge and $^{76}$Ge in the energy region 0.4-14.8 MeV for neutrinoless double $\beta $ decay applications

Fast neutron capture cross sections for the reactions $^{74}$Ge(n,$\gamma $)$^{75}$Ge and $^{76}$Ge(n,$\gamma $)$^{77}$Ge have been measured in the neutron energy region 0.4-14.8 MeV with the activation method. The results are important to identify backgrounds in the neutrinoless double-$\beta $ decay experiments GERDA and MAJORANA, which use germanium as both source and detector. Isotopically enriched targets which consisted of 86\% of $^{76}$Ge and 14\% of $^{74}$Ge were irradiated with mono-energetic neutrons produced via $^{3}$H(p,n)$^3$He, $^2$H(d,n)$^3$He and $^3$H(d,n)$^4$He reactions. The cross sections were determined relative to $^{197}$Au(n,$\gamma $)$^{198}$Au, $^{115}$In(n,n$^{'}$)$^{115m}$In and $^{197}$Au(n,2n)$^{196}$Au standard cross sections. The activities of the products were measured using high-resolution $\gamma $-ray spctroscopy. The present results are compared with the evaluated data from ENDF/B-VII.1 and TALYS.   

Large-scale beta and double-beta decay computations in quasiparticle random-phase approximation

The quasiparticle random-phase approximation (QRPA) has traditionally been one of the main tools for evaluating double-beta-decay matrix elements. We recently studied four experimentally important double-beta decays---those of $^{76}$Ge, $^{130}$Te, $^{136}$Xe, and $^{150}$Nd---with a massive QRPA calculation built on top of a self-consistent Hartree-Fock-Bogoliubov mean field allowing for axial deformation. Our results and challenges arising from the limitations of the approach are discussed, as well as our ongoing work to improve the speed and flexibility of large-scale QRPA calculations for charge-changing processes, such as beta decay, by the Finite Amplitude Method.   

Shell-Model Calculations of Two-Nucleon Tansfer Related to Double Beta Decay

I will discuss theoretical results for two-nucleon transfer cross sections for nuclei in the regions of $^{48}$Ca, $^{76}$Ge and $^{136}$Xe of interest for testing the wavefuntions used for the nuclear matrix elements in double-beta decay. Various reaction models are used. A simple cluster transfer model gives relative cross sections. Thompson's code Fresco with direct and sequential transfer is used for absolute cross sections. Wavefunctions are obtained in large-basis proton-neutron coupled model spaces with the code NuShellX with realistic effecive Hamiltonians such as those used for the recent results for $^{136}$Xe [M. Horoi and B. A. Brown, Phys. Rev. Lett. 110, 222502 (2013)].   

Double beta decay shell model nuclear matrix elements for $^{48}$Ca including sd-shell orbitals

There is a significant discrepancy between the neutrinoless double beta decay nuclear matrix element (NME) for $^{48}$Ca calculated in the shell model and by other methods, such as the Interacting Boson Model (IBM-2) or the Generator Coordinate Method (GCM). In particular, the shell model NME calculated in the $pf$ valence space it's significantly smaller than the IBM-2 and the GCM results. These last two methods use significantly larger model spaces, an argument often used to justify the discrepancy. We investigated the NME in the extended sd-pf valence space and we found a small increase, but not as much as suggested by the IBM-2 and GCM results.   

$0\nu\beta\beta$-decay of ${}^{48}$Ca in the shell model

We discuss neutrinoless double beta ($0\nu\beta\beta$) decay of ${}^{48}$Ca and test the closure approximation, a widely used approach for $0\nu\beta\beta$ nuclear matrix element calculations. In the shell model framework we calculate $0\nu\beta\beta$ nuclear matrix element of ${}^{48}$Ca using both closure approximations and the nonclosure approach, and we estimate the uncertainties associated with the closure approximation. We also demonstrate that the nonclosure approach can be used to calculate $0\nu\beta\beta$ decay rates of heavy nuclei, such ${}^{72}$Ge or ${}^{82}$Se, thus avoiding unmanageable computational costs.   

Calculation of nuclear matrix element of double-beta decay including the effects of quadrupole and isoscalar pairing fluctuations

We calculate the nuclear matrix element of 0$\nu$ $\beta\beta$ decay of $^{76}$Ge in the closure approximation by describing the initial and final states using the particle-number and angular-momentum projected generator coordinate method (GCM). As the generator coordinates, we choose the quadruple deformation and isoscalar ($T=0$) pairing gaps, since the quadrupole correlations are essential for the ground state properties, while the nuclear matrix element strongly depends on the residual isoscalar pairing interaction. The present GCM approach takes into account the both correlations beyond the small-amplitude approximations; the GCM allows to describe the phase transition, and gives accurate description for the transitional/shape coexisting ground states, and moreover, the matrix element is reliable even near the transition to the isoscalar-pair phase. The calculation requires the generalized scheme for the Hartree-Fock-Bogoliubov in which the neutrons and protons are mixed in the quasiparticles. The developed codes has been checked with the $SO(8)$ schematic model, and then applied to the 0$\nu$ $\beta\beta$ decay of $^{76}$Ge using the separable interactions consisting of isovector, isoscalar pairings and the Gamow-Teller particle-hole interactions.   

Half-life Predictions for Double Beta Decay and Competing Modes

The fundamental nature and direct determination of the neutrino mass through double-$\beta$ decay is at the present time one of the most important areas of experimental and theoretical research in nuclear and particle physics. Even though, double electron decay is the most promising decay mode at the moment, in very recent years interest in the double positron decay, positron emitting electron capture and double electron capture has been renewed. The probability of neutrinoless double electron capture can be resonantly enhanced by some orders of magnitude and recent progress in high-precision Penning-trap mass spectrometry has finally provided suitable means for a determination of atomic masses with a sufficient precision. This has given rise to the campaign for a search for resonantly enhanced transitions. Using complete and improved calculation of phase space factors for $\beta\beta$-decay including competing modes, $EC\beta$ and $ECEC$, and nuclear matrix elements from microscopic interacting boson model we make realistic predictions for the expected half-lives in neutrinoless double-$\beta$ decay, as well as for the less studied competing modes, in terms of neutrino masses.