Double Beta Decay Nuclear Matrix Research Articles

Improved Statistical Analysis for the Neutrinoless Double-Beta Decay Matrix Element of 136Xe

Neutrinoless double beta decay nuclear matrix element (M0ν) for 136Xe was recently analyzed using a statistical approach (Phys. Rev. C 107, 045501 (2023)). In the analysis, three initial shell model effective Hamiltonians were randomly altered, and their results for 23 measured observables were used to infer credibility for the M0ν nuclear matrix element (NME) based on a Bayesian Model Averaging approach. In that analysis, a reasonable Gamow-Teller quenching factor of 0.7 was assumed for each starting effective Hamiltonian. Given that the result of the statistical analysis was sensible to this choice, we are here improving that analysis by assuming that the Gamow-Teller quenching factor is also randomly chosen within reasonabe limits for all three starting Hamiltonians. The outcomes are slightly higher expectation values and uncertainties for the M0ν NME.

Double charge-exchange reactions for the nuclear matrix elements of neutrinoless double beta decay

Double charge exchange (DCE) reactions induced by heavy ions are crucial tools to access information relevant for neutrinoless double beta decay nuclear matrix elements. In this context the NUMEN project aims to investigate, for each system of interest, the DCE reaction channel together with the whole set of reactions promoted by the same projectile/target interaction in the same experimental conditions and within the same theoretical framework.

Heavy-ion induced quasi-elastic reactions in view of the NUMEN project

Double charge exchange (DCE) reactions induced by heavy ions and other direct reactions characterized by same projectile and target are crucial tools to access information relevant for neutrinoless double beta decay nuclear matrix elements. In this context the NUMEN project aims to investigate, for each system of interest, not only the DCE channel but also the whole set of reactions promoted by the same projectile/target interaction in the same experimental conditions and within the same theoretical framework. An example of the application of such a multi-channel approach is presented here.

Multichannel experimental and theoretical approach to the C12(O18,F18)B12 single-charge-exchange reaction at 275 MeV: Initial-state interaction and single-particle properties of nuclear wave functions

Background: Single-charge-exchange reactions are appropriate tools to study the nuclear response to one-particle/one-hole isospin probes, gaining additional interest from the connection to beta decay. This analogy has been recently extended to second order, connecting double-charge-exchange reactions and double beta decays. Nowadays, the availability of powerful experimental setups and advanced nuclear theories and models allows one to access precious information on key nuclear structure aspects embedded in the widely sought neutrinoless double beta decay. Purpose: We intend to bring to light the main nuclear structure and reaction features involved in the O18+C12 collision at 275 MeV incident energy. In this paper, the main focus is on the role of the initial- and final-state interactions in the overall reaction dynamics and on the single-particle nuclear structure properties accessed via the study of single-nucleon transfer reactions. Forthcoming articles will be devoted to go into the details of the response to one- and two-particle/hole isospin probes. Methods: Cross-section energy spectra and angular distributions were measured in a unique experimental setup for the C12(O18,O18)C12 elastic and inelastic scattering, the C12(O18,O17)C13 one-neutron stripping, the C12(O18,F19)B11 one-proton pickup, and the C12(O18,F18)B12 single-charge-exchange nuclear reactions. A unique comprehensive and coherent theoretical calculation, able to describe the whole network of direct reactions using state-of-the-art nuclear structure and reaction theories, was performed, and it is presented for the first time in this article. This holistic approach, applied both to the experimental and theoretical analysis, is the main feature and worth of the work here presented. Results: The energy and angular resolutions achieved in each reaction channel allowed us to isolate specific transitions and to map the diffraction patterns in the angular distributions. The cross-section calculations describe well the experimental data, both in terms of the absolute values and diffraction patterns. Although the distorted wave Born approximation (DWBA) calculations prove to be accurate in describing all the studied channels, better results are achieved when the couplings to inelastic transitions in both the incoming and outgoing partitions are introduced, as done in the coupled channels Born approximation (CCBA) calculations. Otherwise, no real improvement is found when the coupling effects among different partitions are explicitly taken into account in the coupled reaction channels (CRC) calculations. Conclusions: The multichannel approach proposed in this paper is a promising method for accurate investigations of direct reactions originating in heavy-ion collisions. This is quite appealing for the precise spectroscopy of heavy nuclei proposed in many areas of nuclear physics. An example is the NUMEN project with its challenging commitment to provide valuable information on neutrinoless double beta decay nuclear matrix elements from single- and double-charge-exchange cross-section measurements.1 MoreReceived 18 July 2022Accepted 23 January 2023DOI:https://doi.org/10.1103/PhysRevC.107.024605©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCharge-exchange reactionsCollective modelsDirect reactionsNuclear many-body theoryOptical, coupled-channel & distorted wave modelsShell modelSpectroscopic factors & electromagnetic momentsTransfer reactionsProperties6 ≤ A ≤ 19TechniquesNuclear data analysis & compilationNuclear reactionsSpectrometers & spectroscopic techniquesNuclear Physics

Double Beta Decay: A Shell Model Approach

Studies of weak interaction in nuclei are important tools for testing different aspects of the fundamental symmetries of the Standard Model. Neutrinoless double beta decay offers an unique venue of investigating the possibility that neutrinos are Majorana fermions and that the lepton number conservation law is violated. Here, I use a shell model approach to calculate the nuclear matrix elements needed to extract the lepton-number-violating parameters of a few nuclei of experimental interest from the latest experimental lower limits of neutrinoless double beta decay half-lives. The analysis presented here could reveal valuable information regarding the dominant neutrinoless double beta decay mechanism if experimental half-life data become available for different isotopes. A complementary shell model analysis of the two-neutrino double beta decay nuclear matrix elements and half-lives is also presented.

Comparison of Microscopic Interacting Boson Model and Quasiparticle Random Phase Approximation 0νββ Decay Nuclear Matrix Elements

The fundamental nature of the neutrino is presently a subject of great interest. A way to access the absolute mass scale and the fundamental nature of the neutrino is to utilize the atomic nuclei through their rare decays, the neutrinoless double beta (0νββ) decay in particular. The experimentally measurable observable is the half-life of the decay, which can be factorized to consist of phase space factor, axial vector coupling constant, nuclear matrix element, and function containing physics beyond the standard model. Thus reliable description of nuclear matrix element is of crucial importance in order to extract information governed by the function containing physics beyond the standard model, neutrino mass parameter in particular. Comparison of double beta decay nuclear matrix elements obtained using microscopic interacting boson model (IBM-2) and quasiparticle random phase approximation (QRPA) has revealed close correspondence, even though the assumptions in these two models are rather different. The origin of this compatibility is not yet clear, and thorough investigation of decomposed matrix elements in terms of different contributions arising from induced currents and the finite nucleon size is expected to contribute to more accurate values for the double beta decay nuclear matrix elements. Such comparison is performed using detailed calculations on both models and obtained results are then discussed together with recent experimental results.

Recent results for the one-proton transfer reaction in the 18O+48Ti collision at 275 MeV

The 18O+48Ti reaction was studied at the energy of 275 MeV for the first time under the NUMEN and NURE experimental campaigns with the aim to investigate the complete net of reaction channels potentially involved in the 48Ca→48Ti double charge exchange transition. Such a transition is of great interest because of its relevance to the extraction of 48Ca→48Ti double beta decay nuclear matrix element. The relevant experiment was carried out at the MAGNEX facility of INFN-LNS in Catania. Angular distribution measurements for the various reaction products were performed by using the MAGNEX large acceptance magnetic spectrometer. The present contribution is focused on the analysis of the one-proton transfer channel with emphasis on the particle identification technique and the estimation of background contaminations.

Investigating the relation between heavy ion double charge exchange nuclear reactions and double beta decays

Heavy ion double charge exchange reactions (DCE) are discussed, within DWBA, in synergy with the main goal of the NUMEN project, i. e. to extract information on the 0νββ decay nuclear matrix element from DCE cross section measurements. The first step to reach this goal is to assess the analogy between the DCE nuclear matrix element and that describing 0νββ decay; then it is necessary to single out a term related to the desired double beta decay nuclear matrix element from the DCE cross-section expression (cross section factorization).Heavy ion DCE processes, are depicted in terms of sequence of two correlated or uncorrelated Single Charge Exchange (SCE) reactions, resembling in this way 0νββ and 2νββ decay, respectively. Here, the formalism for describing DCE reactions within the latter scenario is described.Once provided the formalism leading both to SCE and DCE cross section factorization, together with its limitations, a preliminary comparison with experimental DCE data is shown.

Double charge exchange reactions as a probe for neutrinoless double beta decay nuclear matrix elements

The formalism to describe heavy-ion double charge exchange (DCE) processes in the eikonal and small-momentum transfer approximations introduced in Phys. Rev. C 98, 061601(R) (2018) is briefly discussed. It is also shown that, under the previous approximations, the heavy-ion DCE cross-section can be factorized in terms of a reaction and a nuclear part. A double charge exchange effective potential is explicitly derived in the closure approximation and also for the first time the explicit form of the DCE nuclear matrix elements, that are of the form of double Gamow-Teller and double Fermi. The recent hypothesis of a linear correlation between double Gamow-Teller neutrinoless double beta decay and DCE nuclear matrix elements is confirmed thanks to the first explicit derivation of DCE nuclear matrix elements, and by means of microscopic IBM2 calculations.

Single Particle Levels and ββ-Decay Matrix Elements in The Interacting Boson Model

Recently a new method to calculate the occupancies of single particle levels in atomic nuclei was developed in the context of the microscopic interacting boson model, in which neutron and proton degrees of freedom are treated explicitly (IBM-2). The energies of the single particle levels constitute a very important input for the calculation of the occupancies in this method, and further they play important role in the calculation of double beta decay nuclear matrix elements. Here we discuss how the 0νββ, 0νhββ, and 2νββ-decay nuclear matrix elements (NMEs) are affected when the energies of single particle levels are changed.

0νββ -decay nuclear matrix element for light and heavy neutrino mass mechanisms from deformed quasiparticle random-phase approximation calculations for Ge76, Se82, Te130, Xe136 , and Nd150 with isospin restoration

In this work, with restored isospin symmetry, we evaluated the neutrinoless double beta decay nuclear matrix elements for $^{76}$Ge, $^{82}$Se, $^{130}$Te, $^{136}$Xe and $^{150}$Nd for both the light and heavy neutrino mass mechanisms using the deformed QRPA approach with realistic forces. We give detailed decompositions of the nuclear matrix elements over different intermediate states and nucleon pairs, and discuss how these decompositions are affected by the model space truncations. Compared to the spherical calculations, our results show reductions from $30\%$ to about $60\%$ of the nuclear matrix elements for the calculated isotopes mainly due to the presence of BCS overlap factor between the initial and final ground states. The comparison between different nucleon-nucleon forces with corresponding Short-Range-Correlations (src) shows, that the choice of the NN force gives roughly $20\%$ deviations for light exchange neutrino mechanism and much larger deviations for the heavy neutrino exchange mechanism.

Neutrinoless double beta decay: Theoretical challenges

The recent progress in theoretical description of the neutrinoless double beta decay (0νββ-decay) is briefly reviewed. A possible effect of nuclear medium on exchange of three light neutrinos is addressed. It is shown that non-standard neutrino interaction generates in-medium Majorana neutrino masses, which influences the 0νββ-decay rate. A subject of interest is also a problem of reliable calculation of the 0νββ-decay nuclear matrix elements. An impact of the quenching of the axial-vector coupling constant on double beta decay processes is discussed. A connection between two-neutrino and neutrinoless double beta decay nuclear matrix elements is analyzed.

Properties of neutrinoless double beta decay nuclear matrix elements studied along isotopic chains

We use energy density functional methods to compute the nuclear matrix elements (NME) of neutrinoless double beta decay (0 ) in the Cadmium isotopic chain. The interconnected role of deformation, pairing, configuration mixing in the NMEs is discussed in the candidate 116 Cd and extended to the whole isotopic chain. In addition, strong shell e ects are found and compared to a generalized seniority model.

0ν2β NUCLEAR MATRIX ELEMENTS AND NEUTRINO MAGNETIC MOMENTS

We compare different methods of obtaining the neutrinoless double beta decay nuclear matrix elements (NME). On the example of 76 Ge we use the NME to calculate the Majorana neutrino transition magnetic moments, generated through particle–sparticle R-parity violating loop diagrams whithin the minimal supersymmetric standard model.

Influence of Pairing on the Nuclear Matrix Elements of the NeutrinolessββDecays

We study in this Letter the neutrinoless double beta decay nuclear matrix elements (NME's) in the framework of the interacting shell model. We analyze them in terms of the total angular momentum of the decaying neutron pair and as a function of the seniority truncations in the nuclear wave functions. This point of view turns out to be very adequate to gauge the accuracy of the NME's predicted by different nuclear models. In addition, it gives back the protagonist role in this process to the pairing interaction, the one which is responsible for the very existence of double beta decay emitters. We show that low seniority approximations, comparable to those implicit in the quasiparticle RPA in a spherical basis, tend to overestimate the NME's in several decays.

The 0+ → 0+ positron double- β decay with emission of two neutrinos in the nuclei 96Ru, 102Pd, 106Cd and 108Cd

Theoretical results for %the $0^{+}\to 0^{+}$ positron double-$\beta$ decay with emission of two neutrinos in the nuclei $^{96}$Ru, $^{102}$Pd, $^{106}$Cd and $^{108}$Cd are presented. The study employs the Hartree-Fock-Bogoliubov model to obtain the wave functions of the parent and daughter nuclei, in conjunction with the summation method to estimate the double beta decay nuclear matrix elements. The reliability of the intrinsic wave functions of $^{96,102}$Ru, $% ^{96}$Mo, $^{102,106,108}$Pd and $^{106,108}$Cd nuclei are tested by comparing the theoretically calculated spectroscopic properties with the available experimental data. Calculated half-lives $T_{1/2}^{2\nu}$ of $% ^{96}$Ru, $^{102}$Pd, $^{106}$Cd and $^{108}$Cd nuclei for 2$\nu $ $\beta ^{+}\beta ^{+}$, 2$\nu $ $\beta ^{+}EC$ and 2$\nu $ $ECEC$ modes are presented. The effect of deformation on the nuclear transition matrix element $M_{2\nu}$ is also studied.