Estimation of nuclear matrix elements of double-$$\varvec{\beta }$$ decay from shell model and quasiparticle random-phase approximation

The nuclear matrix element (NME) of neutrinoless double-$$\beta $$ β ($$0\nu \beta \beta $$ 0 ν β β ) decay is an essential input for determining the neutrino effective mass, if the half-life of this decay is measured. Reliable calculation of this NME has been a long-standing problem because of the diversity of the predicted values of the NME, which depends on the calculation method. In this study, we focus on the shell model and the QRPA. The shell model has a rich amount of the many-particle many-hole correlations, and the quasiparticle random-phase approximation (QRPA) can obtain the convergence of the calculation results with respect to the extension of the single-particle space. It is difficult for the shell model to obtain the convergence of the $$0\nu \beta \beta $$ 0 ν β β NME with respect to the valence single-particle space. The many-body correlations of the QRPA may be insufficient, depending on the nuclei. We propose a new method to phenomenologically modify the results of the shell model and the QRPA compensating for the insufficiencies of each method using the information of other methods in a complementary manner. Extrapolations of the components of the $$0\nu \beta \beta $$ 0 ν β β NME of the shell model are made toward a very large valence single-particle space. We introduce a modification factor to the components of the $$0\nu \beta \beta $$ 0 ν β β NME of the QRPA. Our modification method yields similar values of the $$0\nu \beta \beta $$ 0 ν β β NME for the two methods with respect to $$^{48}$$ 48 Ca. The NME of the two-neutrino double-$$\beta $$ β decay is also modified in a similar but simpler manner, and the consistency of the two methods is improved.

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.

Experimental Approaches to Neutrino Nuclear Responses for ββ Decays and Astro-Neutrinos

Fundamental properties of neutrinos are investigated by studying double beta decays (ββ-decays), while atro-neutrino nucleo-syntheses and astro-neutrino productions are investigated by studying inverse beta decays (inverse β-decays) induced by astro-neutrinos. Neutrino nuclear responses for these ββ and β-decays are crucial for these neutrino studies in nuclei. This reports briefly perspectives on experimental studies of neutrino nuclear responses (square of nuclear matrix element) for ββ-decays and astro-neutrinos by using nuclear and leptonic (muon) charge-exchange reactions

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.

Present Status of Nuclear Shell-Model Calculations of 0νββ Decay Matrix Elements

Neutrinoless double beta (0νββ) decay searches are currently among the major foci of experimental physics. The observation of such a decay will have important implications in our understanding of the intrinsic nature of neutrinos and shed light on the limitations of the Standard Model. The rate of this process depends on both the unknown neutrino effective mass and the nuclear matrix element (M0ν) associated with the given 0νββ transition. The latter can only be provided by theoretical calculations, hence the need of accurate theoretical predictions of M0ν for the success of the experimental programs. This need drives the theoretical nuclear physics community to provide the most reliable calculations of M0ν. Among the various computational models adopted to solve the many-body nuclear problem, the shell model is widely considered as the basic framework of the microscopic description of the nucleus. Here, we review the most recent and advanced shell-model calculations of M0ν considering the light-neutrino-exchange channel for nuclei of experimental interest. We report the sensitivity of the theoretical calculations with respect to variations in the model spaces and the shell-model nuclear Hamiltonians.

Neutrino-Mass Sensitivity and Nuclear Matrix Element for Neutrinoless Double Beta Decay

Neutrinoless double beta decay (DBD) is a useful probe to study neutrino properties such as the Majorana nature, the absolute neutrino mass, the CP phase and the others, which are beyond the standard model. The nuclear matrix element (NME) for DBD is crucial to extract the neutrino properties from the experimental transition rate. The neutrino-mass sensitivity, i.e., the minimum neutrino-mass to be measured by the DBD experiment, is very sensitive to the DBD NME. Actually, the NME is one of the key elements for designing the DBD experiment. Theoretical evaluation for the DBD NME, however, is very hard. Recently experimental studies of charge-exchange nuclear and leptonic reactions have shown to be used to get single-β NMEs associated with the DBD NME. Critical discussions are made on the neutrino-mass sensitivity and the NME for the DBD neutrino-mass study and on the experimental studies of the single-β NMEs and nuclear structures associated with DBD NMEs.

Nuclear Response to Second-Order Isospin Probes in Connection to Double Beta Decay

One of the key ingredients needed to extract quantitative information on neutrino absolute mass scale from the possible measurement of the neutrinoless double-beta (0νββ) decay half-lives is the nuclear matrix element (NME) characterizing such transitions. NMEs are not physical observables and can only be deduced by theoretical calculations. However, since the atomic nuclei involved in the decay are many-body systems, only approximated values are available to date. In addition, the value of the coupling constants to be used for the weak interaction vertices is still an open question, which introduces a further indetermination in the calculations of NMEs. Several experimental approaches were developed in the years with the aim of providing useful information to further constrain the theory. Here we give an overview of the role of charge exchange reactions in this scenario, focusing on second-order processes, namely the double charge exchange (DCE) reactions.

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.