Two-neutrino Double Beta Decay Matrix Research Articles

Matrix elements of the two-neutrino double beta decay of 76Ge using deformed BCS and Lipkin–Nogami approaches

Herein, the effect of quadrupole deformation has been thoroughly studied using the generalized BCS and Lipkin–Nogami (LN) pairing approaches for both like- and unlike-particle pairing modes. The pairing treatment of the realistic NN-interaction with these two approaches is then used to calculate the two-neutrino double beta decay matrix elements, (MGT2ν), through the Quasiparticle Random Phase Approximation (QRPA) theory. The results reveal significant differences in the calculated matrix elements due to the inclusion of the unlike-particle pairing mode, besides a small difference in MGT2ν values regarding the pairing approach type used in calculations. It is found that, the competition between the BCS and LN approaches in the calculation of MGT2ν, slightly depends on the inclusion or exclusion of the pn-pairing mode.

Structure of the two-neutrino double-beta decay matrix elements within perturbation theory

Structure of the two-neutrino double-beta decay matrix elements within perturbation theory

Two-neutrino double-βdecay Fermi transition and two-nucleon interaction

An exactly solvable model for a description of the two-neutrino double beta decay transition of the Fermi type is considered. By using perturbation theory an explicit dependence of the two-neutrino double beta decay matrix element on the like-nucleon pairing, particle-particle and particle-hole proton-neutron interactions by assuming a weak violation of isospin symmetry of Hamiltonian expressed with generators of the SO(5) group. It is found that there is a dominance of double beta decay transition through a single state of the intermediate nucleus. Then, an energy weighted sum rule connecting Delta Z=2 nuclei is presented and discussed. It is suggested that this sum rule can be exploited to study the residual interactions of the nuclear Hamiltonian.

Matrix elements of two–neutrino double beta decay in deformed nuclei

The two-neutrino double beta decay matrix elements for ground state to ground state transitions 76 Ge→ 76 Se and 150 Nd → 150 Sm, are calculated within the Quasiparticle Random Phase Approximation (QRPA) for deformed nuclei. The realistic residual interaction based on the Brueckner G-matrix (Bonn CD force) is used.

Effective interaction for f5pg9-shell nuclei and two-neutrino double beta-decay matrix elements

We have developed an effective interaction for shell model calculations in the model space consisting of four orbits 1p3/2, 0f5/2, 1p1/2 and 0g9/2. Starting from a renormalized Gmatrix interaction, we have modified 45 linear combinations of Hamiltonian parameters by fitting to 400 experimental binding and excitation energy data out of 87 nuclei with masses A = 63–96. The resultant effective interaction is shown to be successful for describing irregular behavior of the 0+2states in Ge isotopes. We have evaluated the two-neutrino double-beta-decay matrix elements for 76Ge and 82Se which are in reasonable agreement with the experimental data.

Effect of deformation on two-neutrino double beta decay matrix elements

We study the effect of deformation on the two-neutrino double beta decay for ground state to ground state transitions in all the nuclei whose half-lives have been measured. Our theoretical framework is a deformed QRPA based in Woods–Saxon or Hartree–Fock mean fields. We are able to reproduce at the same time the main characteristics of the two single beta branches, as well as the double beta matrix elements. We find a suppression of the double beta matrix element with respect to the spherical case when the parent and daughter nuclei have different deformations.

A large Hilbert space QRPA and RQRPA calculation of neutrinoless double beta decay

A large Hilbert space is used for the calculation of the nuclear matrix elements governing the light neutrino mass mediated mode of neutrinoless double beta decay (Ovββ-decay) of76 Ge,100 Mo,116 Cd,128 Te, and136 Xe within the proton-neutron quasiparticle random phase approximation (pn-QRPA) and the renormalized QRPA with proton-neutron pairing (full-RQRPA) methods. We have found that the nuclear matrix elements obtained with the standard pn-QRPA for several nuclear transitions are extremely sensitive to the renormalization of the particle-particle component of the residual interaction of the nuclear hamiltonian. Therefore the standard pn-QRPA does not guarantee the necessary accuracy to allow us to extract a reliable limit on the effective neutrino mass. This behavior already known from the calculation of the two-neutrino double beta decay matrix elements, manifests itself in the neutrinoless double-beta decay but only if a large model space is used. The full-RQRPA, which takes into account proton-neutron pairing and considers the Pauli principle in an approximate way, offers a stable solution in the physically acceptable region of the particle-particle strength. In this way more accurate values on the effective neutrino mass have been deduced from the experimental lower limits of the half-lifes of neutrinoless double beta decay.

Shell model Monte Carlo method for two-neutrino double beta decay.

Shell Model Monte Carlo (SMMC) techniques are used to calculate two-neutrino double beta decay matrix elements. We validate the approach against direct diagonalization for $^{48}$Ca in the complete $pf$-shell using the KB3 interaction. The method is then applied to the decay of $^{76}$Ge in the $(0f_{5/2},1p,0g_{9/2})$ model space using a newly calculated realistic interaction. Our result for the matrix element is $0.13\pm0.05$ MeV$^{-1}$, in agreement with the experimental value.

The Pauli principle, QRPA and the two-neutrino double beta decay

We examine the violation of the Pauli exclusion principle in the Quasiparticle Random Phase Approximation (QRPA) calculation of the two-neutrino double beta decay matrix elements, which has its origin in the quasi-boson approximation. For that purpose we propose a new renormalized QRPA with proton-neutron pairing method (full-RQRPA) for nuclear structure studies, which includes ground state correlation beyond the QRPA. This is achieved by using of renormalized quasi-boson approximation, in which the Pauli exclusion principle is taken into account more carefully. The full-RQRPA has been applied to two-neutrino double beta decay of $^{76}Ge$, $^{82}Se$, $^{128}Te$ and $^{130}Te$. The nuclear matrix elements have been found significantly less sensitive to the increasing strength of particle-particle interaction in the physically interesting region in comparison with QRPA results. The strong differences between the results of both methods indicate that the Pauli exclusion principle plays an important role in the evaluation of the double beta decay. The inclusion of the Pauli principle removes the difficulties with the strong dependence on the particle-particle strength $g_{pp}$ in the QRPA on the two-neutrino double beta decay.