Nuclear Matrix Elements Research Articles

Improved Limit on Neutrinoless Double-Beta Decay in ^{130} Te with CUORE.

We report new results from the search for neutrinoless double-beta decay in ^{130} Te with the CUORE detector. This search benefits from a fourfold increase in exposure, lower trigger thresholds, and analysis improvements relative to our previous results. We observe a background of (1.38±0.07)×10^{-2} counts/(keV kg yr)) in the 0νββ decay region of interest and, with a total exposure of 372.5kg yr, we attain a median exclusion sensitivity of 1.7×10^{25} yr. We find no evidence for 0νββ decay and set a 90% credibility interval Bayesian lower limit of 3.2×10^{25} yr on the ^{130} Te half-life for this process. In the hypothesis that 0νββ decay is mediated by light Majorana neutrinos, this results in an upper limit on the effective Majorana mass of 75-350meV, depending on the nuclear matrix elements used.

Double beta decay without invoking closure

The nuclear matrix elements of PU operators entering in the 0v ßß-decay of 76Ge-->76Se have been calculated explicitly in the context of QRPA within the model space 0f7/2 - 0h11/2. T h e validity of the closure approximation has been tested and seems to be quite satisfactory for those matrix elements which are not usually suppressed. Our results indicate that they are dominated by multipoles other than 0+ and 1+ and that the matrix elements are comparable to those of shell model calculations.

Experimental Aspects of Nuclear Matrix Elements for Double Beta Decays and Astro Neutrinos

We report briefly recent experimental studies of nuclear responses (square of nuclear matrix element NME) for astro-neutrinos and double beta decays (DBDs) by single EC/β decays, charge exchange reactions (CERs) and ordinary muou captures (OMCs). The NMEs are shown to be uniformly reduced with respect to quasi-particle and pnQRPA NMEs in wide multipole and momentum regions. The reduction is expressed by the quenching coefficient . Impact of the reduction on astro-neutrino and DBD studies is discussed.

Nuclear matrix elements of neutrinoless double beta decay for masses 130 and 136 in the shell model

The nuclear matrix elements (NMEs) for the 0νββ decays from 130Te to 130Xe and from 136Xe to 136Ba are calculated in the nuclear shell model. In order to investigate the model dependence on the NMEs, pair-truncated shell-model calculations are also performed. It is found that the NMEs are sensitive to the ground-state correlations. In particular, the isovector monopole-pairing interactions largely affect the NMEs.

Sensitivity of nuclear matrix elements of 0νββ of Ca48 to different components of the two-nucleon interaction

In the present work, we examine the sensitivity of nuclear matrix elements (NMEs) for light neutrino-exchange mechanism of neutrinoless double beta decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) of $^{48}\mathrm{Ca}$ to the central, spin-orbit, and tensor components of two-nucleon interaction. The NMEs are calculated in the nuclear shell-model framework in $fp$-model space using frequently used GXPF1A interaction and a new effective interaction named GX1R of $pf$ shell. The decomposition of the shell-model two-nucleon interactions into their individual components is performed using spin-tensor decomposition. The NMEs are calculated in closure approximation by using optimal value of the closure energy. The results shows that the total NMEs calculated with the central component of the interactions are of positive sign. By adding spin-orbit part to central part of the interactions, sign of the total NMEs gets change, and in absolute value, NMEs decreases by about $15\text{--}18%$. Sign change in total NMEs are again seen by adding tensor part to the $\text{central}+\text{spin}\ensuremath{-}\text{orbit}$ part of the interactions. Similar trends of sign change are also observed for Fermi, Gamow-Teller, and tensor matrix elements. Thus we infer that SO and T part mostly cancel the effects of each other in NMEs calculations. For both the interactions, the total NMEs calculated with the C part is found to be $20%$ enhanced as compared to the NMEs calculated with the total interactions. With new GX1R interaction, there is about $1\text{--}3%$ increments in the total NMEs as compared to NMEs with GXPF1A interaction. This increments comes from the modifications of isospin $T=1$ tensor force two-nucleon matrix elements to bring the characteristic properties of tensor force into the GX1R interaction.

Consistent large-scale shell-model analysis of the two-neutrino ββ and single β branchings in 48Ca and 96Zr

Two-neutrino double-beta-decay matrix elements M2ν and single beta-decay branching ratios were calculated for 48Ca and 96Zr in the interacting nuclear shell model using large single-particle valence spaces with well-tested two-body Hamiltonians. For 48Ca the matrix element M2ν=0.0511 is obtained, which is 5.5% smaller than the previously reported value of 0.0539. For 96Zr this work reports the first large-scale shell-model calculation of the nuclear matrix element, yielding a value M2ν=0.0747 with extreme single-state dominance. These matrix elements, combined with the available ββ-decay half-life data, yield effective values of the weak axial coupling which in turn are used to produce in a consistent way the β-decay branching ratios of (7.5±2.8)% for 48Ca and (18.4±0.09)% for 96Zr. These are larger than obtained in previous studies, implying that the detection of the β-decay branches could be possible in dedicated experiments sometime in the (near) future.

Tests of a Cooling System for Thin Targets Submitted to Intense Ion Beams for the NUMEN Experiment

The NUMEN experiment, hosted at LNS (Catania, Italy), aims to determine the Nuclear Matrix Elements (NMEs) involved in 0νββ decay via heavy-ion induced Double Charge Exchange (DCE) reactions. High intensity beams of about 50 µA and of energies ranging from 15 to 60 MeV/u are necessary, due to the low DCE cross sections and the use of very thin targets (several hundreds of nm) needed to reach the required energy resolution. These intense beams produce a considerable amount of heat inside the target, which can be dissipated by depositing the targets on a highly thermally conductive substrate, HOPG (Highly Oriented Pyrolytic Graphite), and coupling it with a suitable designed target-cooler system. The heat transfer from the beam spot to the cold region has been studied by solving numerically the heat equation to determine the evolution in space and time of the temperature inside the target. According to calculations, the temperatures of most of the target isotopes remain under the melting points. Experimental tests with a laser were initiated to validate the whole cooling system and the calculations

Weak magnetism and pseudoscalar coupling in neutrino mass mechanism of neutrinoless double beta-decay

In the calculations of the nuclear matrix element of Majorana neutrino mass mechanism of neutrinoless double beta decay so far only contributions from vector/axialvector part and weak magnetism of the nuclear current have been included, while other contributions have been neglected. In the present work we are examining the effect of weak magnetism and induced pseudoscalar coupling. We have performed calculations within the proton-neutron renormaiized quasiparticie random phase approximation and we have found that these additional contributions of the nucleon current, result in a considerable reduction of the nuclear matrix elements of all nuclei which we have considered. This reduction of the nuclear matrix element makes the extracted limits of the lepton number violating parameters ( < mu >, < g > and < 77^ >) less stringent yielding the best value for < mv > less than 0.62 eV for 76Ge.

Axial-vector weak coupling at medium momentum for astro neutrinos and double beta decays

Neutrino nuclear responses associated with medium momentum transfer of q = 20–80 MeV/c for astro neutrinos and double beta decays (DBDs) were studied by using charge exchange (3He, t) reactions on 128Te and 130Te. Gamow–Teller and spin-dipole nuclear matrix elements (NMEs) are found to be reduced uniformly in the wide momentum region of q = 20–80 MeV/c with respect to pnQRPA NMEs by the coefficient of kNM ≈ 0.35, while the Fermi NME for the isobaric analog state is given by the sum rule limit in the momentum transfer region. The reduction is discussed in terms of the quenching of the axial vector coupling gAeff for astro-neutrinos and DBDs.

Nuclear transition matrix elements for neutrinoless double-β decay of 76Ge isotope within PHFB approach

Employing projected–Hartree–Fock–Bogoliubov (PHFB) model, nuclear transition matrix elements (NTMEs) [Formula: see text] for the neutrinoless double-[Formula: see text] decay of [Formula: see text]Ge isotope are calculated within mechanisms involving light as well as heavy Majorana neutrinos, and classical Majorons. By considering the spin-tensor decomposition of realistic KUO and empirical JUN45 effective two-body interactions, it is noticed that the effect due to SRC on NTMEs [Formula: see text] and [Formula: see text] involving the exchange of light and heavy Majorana neutrinos, respectively, is maximally incorporated by the central part of the effective two-body interaction, which varies by a small amount with the inclusion of spin-orbit and tensor components. Presently, the model-dependent uncertainties in the average NTMEs [Formula: see text] and [Formula: see text] turn out to be about 10% and 37%, respectively.

Lattice QCD and neutrino-nucleus scattering

This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD in neutrino-oscillation physics, which inevitably entails nucleon and nuclear structure. In addition to discussing pertinent lattice-QCD calculations of nucleon and nuclear matrix elements, the interplay with models of nuclei is discussed. This program of lattice- QCD calculations is relevant to current and upcoming neutrino experiments, becoming increasingly important on the timescale of LBNF/DUNE and HyperK.

Ne20+Ge76 elastic and inelastic scattering at 306 MeV

Background: Double charge exchange (DCE) nuclear reactions have recently attracted much interest as tools to provide experimentally driven information about nuclear matrix elements of interest in the context of neutrinoless double-beta decay. In this framework, a good description of the reaction mechanism and a complete knowledge of the initial and final-state interactions are mandatory. Presently, not enough is known about the details of the optical potentials and nuclear response to isospin operators for many of the projectile-target systems proposed for future DCE studies. Among these, the 20Ne + 76Ge DCE reaction is particularly relevant due to its connection with 76Ge double-beta decay. Purpose: We intend to characterize the initial-state interaction for the 20Ne + 76Ge reactions at 306 MeV bombarding energy and determine the optical potential and the role of the couplings between elastic channel and inelastic transitions to the first low-lying excited states. Methods: We determine the experimental elastic and inelastic scattering cross-section angular distributions, compare the theoretical predictions by adopting different models of optical potentials with the experimental data, and evaluate the coupling effect through the comparison of the distorted-wave Born approximation calculations with the coupled channels ones. Results: Optical models fail to describe the elastic angular distribution above the grazing angle (9.4{\deg}). A correction in the geometry to effectively account for deformation of the involved nuclear systems improves the agreement up to about 14{\deg}. Coupled channels effects are crucial to obtain good agreement at large angles in the elastic scattering cross section.

Isoscalar pairing interaction for the quasiparticle random-phase approximation approach to double- β and β decays

We have proposed in a series of previous articles a method to determine the effective axial-vector current coupling and the strength of the isoscalar proton-neutron pairing interaction for calculating the nuclear matrix elements of the neutrinoless double-$\ensuremath{\beta}$ ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decay by the quasiparticle random-phase approximation (QRPA). The combination of these two parameters has had an uncertainty in the QRPA approach, but now this uncertainty is removed by introducing a mathematical identity derived under the closure approximation to the nuclear matrix element of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay. In this article, we apply our method to the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decays of $^{136}\mathrm{Xe}$ and $^{130}\mathrm{Te}$ and show the nuclear matrix elements and reduced half-lives. Our calculation is tested first by a self-check method using the two-neutrino double-$\ensuremath{\beta}$ decay, and this test ensures the application of our method to $^{136}\mathrm{Xe}$. It turns out, however, that our method is not successful in $^{130}\mathrm{Te}$. Further tests are made for our calculation, and satisfactory results are obtained for $^{136}\mathrm{Xe}$.

Union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double- β decay

Good many-body methods for medium and heavy nuclei are important. Here we combine ideas from standard generator-coordinate methods (GCM) and the so-called Monte Carlo shell model, and set forth a novel approach: starting from a mean-field solution (Hartree-Fock-Bogoliubov), we create a set of non-orthogonal basis states, by using low-lying vibrational quasiparticleTamm-Dancoff modes, and then project onto states of good angular momentum and particle number. The results we benchmark against full shell model calculations. Even with just a few such modes we find improvement over standard GCM calculations in excitation spectra. We also find significant improvement in $0\nu\beta\beta$ nuclear matrix elements.

Evidence for Rigid Triaxial Deformation in Ge76 from a Model-Independent Analysis

An extensive, model-independent analysis of the nature of triaxial deformation in ^{76}Ge, a candidate for neutrinoless double-beta (0νββ) decay, was carried out following multistep Coulomb excitation. Shape parameters deduced on the basis of a rotational-invariant sum-rule analysis provided considerable insight into the underlying collectivity of the ground-state and γ bands. Both sequences were determined to be characterized by the same β and γ deformation parameter values. In addition, compelling evidence for low-spin, rigid triaxial deformation in ^{76}Ge was obtained for the first time from the analysis of the statistical fluctuations of the quadrupole asymmetry deduced from the measured E2 matrix elements. These newly determined shape parameters are important input and constraints for calculations aimed at providing, with suitable accuracy, the nuclear matrix elements relevant to 0νββ.

Recent results on Heavy-Ion induced reactions of interest for 0νββ decay

An updated overview of recent results on Heavy-Ion induced reactions of interest for neutrinoless double beta decay is reported in the framework of the NUMEN project. The NUMEN idea is to study heavy-ion induced Double Charge Exchange (DCE) reactions with the aim to get information on the nuclear matrix elements for neutrinoless double beta (0νββ) decay. Moreover, to infer the neutrino average masses from the possible measurement of the half- life of 0νββ decay, the knowledge of the nuclear matrix elements is a crucial aspect.

Muon-capture strength functions in intermediate nuclei of 0νββ decays

Capture rates of ordinary muon capture (OMC) to the intermediate nuclei of neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decays of current experimental interest are computed. The corresponding OMC (capture-rate) strength functions have been analyzed in terms of multipole decompositions. The computed low-energy OMC-rate distribution to $^{76}\mathrm{As}$ is compared with the available data of Zinatulina et al. [Phys. Rev. C 99, 024327 (2019)]. The present OMC computations are performed using the Morita-Fujii formalism by extending the original formalism beyond the leading order. The participant nuclear wave functions are obtained in extended no-core single-particle model spaces using the spherical version of proton-neutron quasiparticle random-phase approximation (pnQRPA) with two-nucleon interactions based on the Bonn one-boson-exchange $G$ matrix. The Hamiltonian parameters are taken from our earlier work [Jokiniemi et al., Phys. Rev. C 98, 024608 (2018)], except for $A=82$ nuclei for which the parameters were determined in this work. Both the OMC and $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decays involve momentum exchanges of the order of 100 MeV and thus future measurements of the OMC strength functions for $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ daughter nuclei help trace the in-medium renormalization of the weak axial couplings with the aim to improve the accuracy of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay nuclear matrix elements.

Electron capture cross sections and nuclear partition functions for fp-shell nuclei

We present calculation of electron capture cross sections (ECC), in the limit of zero momentum transfer, using the pn-QRPA model in stellar matter. Towards this aim we make use of our recently introduced recipe for estimation of nuclear partition functions. For low momentum transfer (), the nuclear matrix elements of the operator provide the leading contribution to the total cross section which we estimate using the pn-QRPA model in a multi-shell single-particle space with a schematic interaction. Key fp-shell nuclei (odd-A, even–even and odd–odd) bearing astrophysical importance were selected for the calculation of ECC in stellar environment. These fp-shell nuclei play a crucial role in presupernova evolution of massive stars and core collapse. We further present microscopic calculation of ground and excited states Gamow–Teller strength distributions and stellar electron capture rates on these suite of nuclei. We used two different sets of empirically determined pairing gaps to calculate the ECC and electron capture rates. Results are compared with experimental data and previous computations. Our calculated ECC are systematically smaller at low electron incident energies as compared to the shell-model results.

Nuclear-spin dependent parity violation in optically trapped polyatomic molecules

Improved nuclear spin-dependent parity violation measurements will enable experimental determination of poorly known electroweak coupling parameters. Here, we investigate the suitability of optically trapped linear polyatomic molecules as probes of nuclear spin-dependent parity violation. The presence of closely spaced, opposite-parity ell-doublets is a general feature of such molecules, allowing parity-violation-sensitive pairs of levels to be brought to degeneracy in magnetic fields typically 100 times smaller than in diatomics. Assuming laser cooling and trapping of polyatomics at the current state-of-the-art for diatomics, we expect to measure nuclear spin-dependent parity-violating matrix elements iW with 70 times better sensitivity than the current best measurements. Our scheme should allow for 10% measurements of iW in nuclei as light as Be or as heavy as Yb, with averaging times on the order of 10 days and 1 s, respectively.

Multipole decomposition of the rate of muon-to-electron (μ−⟶e−) conversion in Pb208

The $({\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\longrightarrow}{e}^{\ensuremath{-}})$ conversion in $^{208}\mathrm{Pb}$ nucleus is studied. For the elementary process we consider the most general effective Lagrangian responsible for the lepton-flavor violation. For the nuclear structure part, the spectrum of $^{208}\mathrm{Pb}$ is calculated by performing a diagonalization of the $\ensuremath{\delta}$-force interaction in the space of particle-hole pairs for neutrons and protons. We calculate the coherent contribution by direct summation of single-particle excitations. The noncoherent muon-to-electron conversion is calculated by summing over the contributions for all possible intermediate states in $^{208}\mathrm{Pb}$. We perform the multipole decomposition of the transition amplitude and present the nuclear matrix elements of spin-dependent and spin-independent operators appearing in the total rate of the muon to electron conversion process. The results are presented in a way to facilitate their use in model building of the electroweak process.