Present Status of Nuclear Shell-Model Calculations of 0νββ Decay Matrix Elements (original) (raw)
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Shell model calculations for neutrinoless double beta decay
Journal of Physics: Conference Series, 2015
Nuclear matrix elements (NMEs) for neutrinoless double beta decay (0νββ) are computed for the mechanism of exchange of heavy neutrinos. The calculations are performed with a shell model (ShM) code recently developed, for three experimentally interested nuclei, 48 Ca, 76 Ge, and 82 Se. We study the different nuclear effects, such as short range correlations (SRCs), finite nuclear size (FNS) and higher order terms in the nucleon currents (HOC) on the final values of the NMEs, and find that their influence is stronger than in the case of the light neutrino exchange mechanism. We compare our results with similar results from literature and discuss the differences.
Study of nuclear effects in the computation of the 0νββ decay matrix elements
Journal of Physics G: Nuclear and Particle Physics, 2013
We analyze the effects that different nuclear structure approximations associated with the short range correlations (SRC), finite nucleon size (FNS), higher order terms in the nucleon currents (HOC) and with some nuclear input parameters, have on the values of the nuclear matrix elements (NMEs) for the neutrinoless double beta (0νββ) decay. The calculations are performed with a new Shell Model(ShM) code which allows a fast computation of the two-body matrix elements of the transition operators. The treatment of SRC, FNS and HOC and the use of quenched or unquenched values for the axial vector coupling constant produces the most important effects on the NMEs values. Equivalent effects of some of these approximations are also possible, which may lead (accidentally) to close final results. We found that the cumulative effect of all these nuclear ingredients on the calculated nuclear matrix elements NMEs is significant. Since the NMEs values are often obtained with different approximations and/or with different input parameters, a convergent view point on their inclusion/neglecting and an uniformization of the calculations are needed, in order to enter in an era of precision concerning the computation of the NMEs for double beta decay.
Neutrinoless Double Beta Decay The Nuclear Matrix Elements Revisited
Journal of Physics: Conference Series, 2011
We explore the influence of the deformation on the nuclear matrix elements of the neutrinoless double beta decay (NME), concluding that the difference in deformation-or more generally in the amount of quadrupole correlations-between parent and grand daughter nuclei quenches strongly the decay. We correlate these differences with the seniority structure of the nuclear wave functions. In this context, we examine the present discrepancies between the NME's obtained in the framework of the Interacting Shell Model and the Quasiparticle RPA. In our view, part of the discrepancy can be due to the limitations of the spherical QRPA in treating nuclei which have strong quadrupole correlations. We surmise that the NME's in a basis of generalized seniority are approximately model independent, i. e. they are "universal". We discuss as well how varies the nuclear matrix element of the 76 Ge decay when the wave functions of the two nuclei involved in the transition are constrained to reproduce the experimental occupancies. In the Interacting Shell Model description the value of the NME is enhanced about 15% compared to previous calculations, whereas in the QRPA the NME's are reduced by 20%-30%. This diminishes the discrepancies between both approaches. In addition, we update the effects of the short range correlations on the NME's in the light of the recently proposed parametrizations obtained by renormalizing the 0νββ transition operator at the same footing than the effective interaction.
Nuclear matrix elements for neutrinoless double-beta decay and double-electron capture
Journal of Physics G: Nuclear and Particle Physics, 2012
A new generation of neutrinoless double beta decay (0νββ-decay) experiments with improved sensitivity is currently under design and construction. They will probe inverted hierarchy region of the neutrino mass pattern. There is also a revived interest to the resonant neutrinoless doubleelectron capture (0νECEC), which has also a potential to probe lepton number conservation and to investigate the neutrino nature and mass scale. The primary concern are the nuclear matrix elements. Clearly, the accuracy of the determination of the effective Majorana neutrino mass from the measured 0νββ-decay half-life is mainly determined by our knowledge of the nuclear matrix elements. We review recent progress achieved in the calculation of 0νββ and 0νECEC nuclear matrix elements within the quasiparticle random phase approximation. A considered self-consistent approach allow to derive the pairing, residual interactions and the two-nucleon short-range correlations from the same modern realistic nucleon-nucleon potentials. The effect of nuclear deformation is taken into account. A possibility to evaluate 0νββ-decay matrix elements phenomenologically is discussed.
Relativistic description of nuclear matrix elements in neutrinoless double-β decay
Neutrinoless double-beta (0νββ) decay is related to many fundamental concepts in nuclear and particle physics beyond the Standard Model. We report the first full relativistic description of the nuclear matrix element (NME) governing this process by multi-reference covariant density functional theory (MR-CDFT) based on the point-coupling functional PC-PK1. The dynamic correlations are taken into account by configuration mixing of both particle number and angular momentum projected quadrupole deformed mean-field states for the initial and final nuclei. The 0νββ NMEs for both the 0 + 1 → 0 + 1 and 0 + 1 → 0 + 2 decays in 150 Nd are evaluated. The effects of particle number projection, and static and dynamic deformations on the nuclear wave functions, as well as those of the full relativistic structure of the transition operator on the NMEs are studied in detail. The low-energy spectra and electric quadrupole transitions are well reproduced by the full generator coordinate method (GCM) calculation. The resulting NME for the 0 + 1 → 0 + 1 transition is 5.60, which gives the most optimistic prediction for the next generation of experiments searching for the 0νββ decay in 150 Nd.
2016
We analyze the effects that different nuclear structure approximations associated with the short range correlations (SRC), finite nucleon size (FNS), higher order terms in the nucleon currents (HOC) and with some nuclear input parameters, have on the values of the nuclear matrix elements (NMEs) for the neutrinoless double beta (0νββ) decay. The calculations are performed with a new Shell Model(ShM) code which allows a fast computation of the two-body matrix elements of the transition operators. The treatment of SRC, FNS and HOC and the use of quenched or unquenched values for the axial vector coupling constant produces the most important effects on the NMEs values. Equivalent effects of some of these approximations are also possible, which may lead (accidentally) to close final results. We found that the cumulative effect of all these nuclear ingredients on the calculated nuclear matrix elements NMEs is significant. Since the NMEs values are often obtained with different approximations and/or with different input parameters, a convergent view point on their inclusion/neglecting and an uniformization of the calculations are needed, in order to enter in an era of precision concerning the computation of the NMEs for double beta decay.
Neutrinoless Double-Beta Decay and Realistic Shell Model
EPJ Web of Conferences
We report on the calculation of the neutrinoless double-ß decay nuclear matrix element for 76Ge within the framework of the realistic shell model. The effective shell-model Hamiltonian and the two-body transition operator describing the decay are derived by way of many-body perturbation theory. Particular attention is focused on the role played by the so-called Pauli blocking effect in the derivation of the effective operator.
Physical Review C, 2017
We use the generator-coordinate method with realistic shell-model interactions to closely approximate full shell-model calculations of the matrix elements for the neutrinoless double-beta decay of 48 Ca, 76 Ge, and 82 Se. We work in one major shell for the first isotope, in the f 5/2 pg 9/2 space for the second and third, and finally in two major shells for all three. Our coordinates include not only the usual axial deformation parameter β, but also the triaxiality angle γ and neutron-proton pairing amplitudes. In the smaller model spaces our matrix elements agree well with those of full shell-model diagonalization, suggesting that our Hamiltonian-based GCM captures most of the important valence-space correlations. In two major shells, where exact diagonalization is not currently possible, our matrix elements are only slightly different from those in a single shell.
Uncertainties in nuclear matrix elements for neutrinoless double-beta decay
Journal of Physics G: Nuclear and Particle Physics, 2015
I briefly review calculations of the matrix elements governing neutrinoless double-beta decay, focusing on attempts to assign uncertainties. At present, systematic error dominates statistical error and assigning uncertainty is difficult. For some purposes, however, statistical assessment of uncertainty is profitable and, after describing the nuclear models in which matrix elements are commonly calculated, I highlight some statistical uncertainty analysis within the quasiparticle random-phase approximation. I also propose, in broad terms, strategies for reducing both systematic and statistical error.