Calculation of double beta decay matrix elements: A status report

The current status of efforts to calculate double beta decay matrix elements is summarized. Particular focus is put on the two most popular theoretical approaches in use for such calculations, the nuclear shell model and the proton-neutron Quasi Particle Random Phase Approximation. Some brief comments regarding double beta decay to excited states are also made. Presented at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. My participation in the workshop was supported in part by the National Science Foundation under grant # PHY-9600445.     

Double beta decay experiments

The present status of double beta decay experiments is reviewed. The results of the most sensitive experiments are discussed. Proposals for future double beta decay experiments with a sensitivity to the 〈m _ν〉 at the level of (0.01–0.1) eV are considered.     

Neutrinoless ββ decay and the electron neutrino mass

We discuss the nuclear structure elements participant in the calculation of the half-life of the neutrinoless double beta decay, and the consequences upon the adopted limits of the electron-neutrino mass. Presented by O. Civitarese at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

Non-collapsing QRPA for neutrinoless double beta decay

The standard quasiparticle random phase approximation(QRPA) is widely used to describe the neutrinoless double beta decay process. Although it has been quite successful in many cases of interest, it has some shortcomings. The most important one is that its solutions collapse for physical values of the particle-particle strength. We shall show that modifications can be done which can extend the validity of this standard QRPA beyond the point of collapse. Such modifications are: The introduction of proton-neutron pairing, the inclusion of the Pauli principle and the extension of the Hilbert space. If all these modifications are introduced into the standard QRPA then the collapse does not occur for physical values of the particle-particle strengths. Thus, one might be able to extract more accurate values on the effective neutrino mass by using the best available experimental limits on the half life of neutrinoless double beta decay. Presented by G. Pantis at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

New BCS and renormalized QRPA formalism with application to double beta decay

A new analysis of the renormalized proton–neutron quasiparticle random phase approximation based on simultaneous recalculation of the one-body density matrix and the pairing tensor has been used to study the double beta decay. We demonstrated that inclusion of the quasiparticle correlations at the BCS level reduces ground state correlations in the particle–particle channel of the proton–neutron interaction. We also simplified the RQRPA equations significantly obtaining a low-dimensioned set of linear equations for the quasiparticle densities. The formalism was applied to the double beta decay of ⁷⁶Ge. Received: 4 January 1999 / Revised version: 29 March 1999     

Shell model calculations for heavy deformed nuclei

The pseudo SU(3) model is shown to be a powerful scheme for describing the excitation spectra as well asB(E2) andB(M1) transition strengths in heavy deformed nuclei. It is also useful for describing double beta decay amplitudes for transitions from the ground state of an even-even nucleus to the ground and excited states of the daughter nucleus, both for the two and zero neutrino emitting modes. The existence of selection rules which strongly restricts the decays is discussed. Anti-correlations between the quadrupole deformation and the Gamow-Teller (GT⁺) strength are found in an extension of the pseudo SU(3) model which explicitly includes pairing, which is also able to describe the fragmentation of the scissors mode. The projected shell model is introduced and proposed as an alternate means for studying single and double beta decay processes. Presented by J.G. Hirsch at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. This work was supported in part by CONACyT (México), CONICET (Argentina), NSF and DOE (U.S.A.).     

A neodymium-loaded liquid scintillator

One promising approach to the search for neutrinoless double beta (0ν2β) decay is the use of liquid scintillators with double β-decay sources dissolved in them. The ¹⁵⁰Nd isotope is the one best suited to observing this process. Samples of liquid scintillators based on linear alkylbenzene with a neodymium mass fraction of 0.32% are described in this work; neodymium 4-methyloctanoate was used as a Nd-loaded additive. The spectral-luminescent and scintillation properties of the new materials were studied. The possibility of using the obtained compounds in experiments to search for 0ν2β decay is demonstrated.     

Observation of the neutron radiative decay

The aim of this work is the experimental observation of and research into a rare neutron mode, the radiative beta decay, where a new particle, the radiative gamma quantum, is formed along with the expected decay products: a beta electron, a recoil proton, and an antineutrino. The discovery of this rare neutron decay mode was conducted through identification of triple-coincidence events: simultaneous registration of a beta electron, a proton, and a radiative gamma quantum. The ordinary neutron decay was registered by double coincidences of a beta electron and a recoil proton. The statistics collected allow one to deduce the branching ratio (BR) BR = (3.2 ± 1.6) × 10⁻³ (90% C.L.) in the gamma energy region greater than 35 keV. This value of BR is consistent with standard electroweak theory. The text was submitted by the authors in English. An erratum to this article is available at .     

Phase shift analysis and extraction of structure functions for Coulomb distortion on (e, e'p) reactions at high electron energies

New results for the double beta decay of ⁷⁶ Ge are presented. They are extracted from data obtained with the HEIDELBERG-MOSCOW experiment, which operates five enriched ⁷⁶ Ge detectors in an extreme low-level environment in the Gran Sasso underground laboratory. The two-neutrino-accompanied double beta decay is evaluated for the first time for all five detectors with a statistical significance of 47.7 kg y resulting in a half-life of T _1/2 ^2ν = [1.55±0.01(stat)^+0.19 _-0.15(syst)]×10²¹ y. The lower limit on the half-life of the 0νββ decay obtained with pulse shape analysis is T _1/2 ^0ν > 1.9×10²⁵(3.1×10²⁵) y with 90% C.L. (68% C.L.) (with 35.5 kg y). This results in an upper limit of the effective Majorana-neutrino mass of 0.35 eV (0.27 eV) using the matrix elements of A. Staudt et al.'s work (Europhys. Lett. 13, 31 (1990)). This is the most stringent limit at present from double beta decay. No evidence for a majoron-emitting decay mode is observed. Received: 22 August 2001 / Accepted: 18 October 2001     

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.     

Muon-capture rates and their relation with the double-beta decay

We discuss the non-radiative μ ⁻ capture (i.e. ordinary muon capture, OMC) in light nuclei in terms of the nuclear shell model, and in the medium-and heavy-mass nuclei in terms of the quasiparticle random-phase approximation. A new probe of the double-beta-decay matrix elements, namely the use of the OMC to states of the intermediate nucleus of the double beta decay, is also addressed. Presented by J. Suhonen at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

Extension of the renormalized quasiparticle random phase approximation

The quasiparticle random phase approximation is extended in order to restore of the Pauli principle beyond the renormalized approach by treating the so-called scattering terms in the QRPA phonon operators. It has been shown that this new framework can be described in a case of a single nuclear shell occupied by both protons and neutrons in terms of the QRPA(14,3) algebra. An application of the formalism to the double beta decay of calcium⁴⁸Ca is discussed to some extent. Presented by W.A. Kamiński at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. This work has been supported in part by the State Committee for Scientific Research (Poland), Contract No. 2 P03B 189 09.     

Neutron-proton pairing and double-beta decay in algebraic models

Nuclear models based on Lie algebras provide insight into collective phenomena. Here neutron-proton pairing, which plays an important role in double beta decay, is discussed in two such models, one based on SO(5) and the second on SO(8). The latter model is used to test the accuracy of the Quasiparticle Random Phase Approximation and improvements to it. Presented at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. This work was supported in part by the U.S. Department of Energy under Grant DE-FG02-97ER41019.     

Two-neutrino double beta decay to excited states

Both doubleβ ⁻ and doubleβ ⁺/EC decay transitions to excited final states in the two-neutrino mode are discussed, their gross properties reviewed and a compilation of recent calculations presented. A brief presentation of the involved nuclear models is given. The close connection between the single and double beta decays is discussed. Presented at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

Probing the mechanism of neutrinoless double beta decay with SuperNEMO

The SuperNEMO experiment is being designed to search for neutrinoless double beta decay. Its experimental technique of tracking and calorimetry provides the means to discriminate different underlying mechanisms for neutrinoless double beta decay by measuring the angular and energy distributions of electrons. The results of a study by the SuperNEMO Collaboration and F. Deppisch (in preparation) [7] for identifying light Majorana neutrino exchange and right-handed currents are presented.     

Beta decay of highly charged ions

Ion storage rings and ion traps provide the very first opportunity to address nuclear beta decay under conditions prevailing in hot stellar plasmas during nucleosynthesis, i.e. at high atomic charge states. Experiments are summarized that were performed in this field during the last decade at the ion storage-cooler ring ESR in Darmstadt. Special emphasis is given to the first observation of bound-state beta decay, where the created electron remains bound in an inner orbital of the daughter atom. The impact of this specific ‘stellar’ decay mode for s-process nucleosynthesis as well as for nuclear ‘eon clocks’ is outlined. Finally, a new technique, single-ion decay spectroscopy, is presented, where one observes two-body beta decay characteristics (i.e. orbital electron capture or bound-state beta decay) of highly charged, single ions for well-defined nuclear and atomic quantum states of both the mother – and the daughter – ion.     

A Limit of Neutrinoless Double Beta Decay of 48Ca

A search for the neutrinoless double beta decay of ⁴⁸Ca is carried out in a coal mine which is located 512m underground near Beijing.Large scintillation crystals of natural CaF₂ were used as both the detector and the double beta decay source.Result obtained after a total of 7588.5 hours of data taking gives 1.1×10²² years (68%C.L.) as the lower limit of the half-life of the neutrinoless double beta decay of ⁶⁸Ca.     

Neutrinoless Double Beta Decay-A New Formalism

A new method-the operator expansion method is used in neutrinoless double beta decay processes. Both the neutrino mass and mixing of right-handed leptonic current are included. It is shown that for nuclear neutrinoless double beta decay in 2n mechanism, there appear some new terms besides the terms given by the conventional treatment based on closure approximation. The ββ with a Majoron emission is also discussed.     

Hiding neutrinoless double beta decay in the minimal seesaw model with the TM1 or μ–τ reflection symmetry

In Asaka et al (2021 Phys. Rev. D 103, 015014), Asaka, Ishida and Tanaka put forward an interesting possibility that the neutrinoless double beta decay can be hidden in the minimal seesaw model with the two right-handed neutrinos having a hierarchical mass structure: the lighter one is lighter enough than the typical Fermi-momentum scale of nuclei while the heavier one is sufficiently heavy to decouple from the neutrinoless double beta decay. Then, in the basis where the mass matrices of the charged leptons and right-handed neutrinos are diagonal, for some particular texture of the Dirac neutrino mass matrix ${M}_{{\rm{D}}}^{}$, the neutrinoless double beta decay can be hidden. In this paper, on top of this specified model, we study the interesting scenario that ${M}_{{\rm{D}}}^{}$ further obeys the TM1 symmetry or μ–τ reflection symmetry which are well motivated by the experimental results for the neutrino mixing parameters.