Weak-interaction and nuclear-structure aspects of nuclear double beta decay

doi:10.1016/S0370-1573(97)00087-2

Physics Reports

Volume 300, Issues 3–4, 1 July 1998, Pages 123-214

https://doi.org/10.1016/S0370-1573(97)00087-2 Get rights and content

Abstract

Weak-interaction and nuclear-structure aspects of double beta decay are reviewed. Starting from effective electroweak lagrangians, decay rates for the two-neutrino and neutrinoless modes of the nuclear double beta decay transitions are defined and second-order perturbative expressions for the nuclear decay amplitudes are given. Nuclear matrix elements of the relevant operators are presented, as extracted from data and from shell-model and QRPA calculations as well as from other theoretical approximations. The analysis is performed both for the two-neutrino and neutrinoless modes of the decay. The expressions for ground-state-to-ground-state and ground-state-to-excited-state transitions are presented. Updated experimental and theoretical information on β⁻β⁻ decays in ⁴⁸Ca, ⁷⁶Ge, ⁸²Se, ⁹⁶Zr, ¹⁰⁰Mo, ¹¹⁶Cd, ¹²⁴Sn, ¹²⁸Te, ¹³⁰Te, ¹³⁶Xe, ¹⁵⁰Nd, and on β⁺β⁺, β⁺ EC and double EC decays in ⁷⁸Kr, ⁹²Mo, ⁹⁶Ru, ¹⁰⁶Cd, ¹²⁴Xe, ¹³⁰Ba, ¹³⁶Ce is analyzed and compared with theoretical results. The relevance of single-beta-decay transitions feeding some of the nuclei where double-beta-decay transitions occur is pointed out. The systematics of various phase-space factors and extracted matrix elements is presented.

Introduction

The nuclear double beta decay is a very rare nuclear decay mode which, for a long period of time was considered just out of reach, both experimentally and theoretically. However, the direct measurements of nuclear-double-beta-decay half-lives in the decay of ⁸²Se by Elliot et al. [94] and ⁷⁶Ge by Miley et al. [173] and by Vasenko et al. [266], the subsequent results obtained by other experimental groups 7, 9, 91, 96, 98, 162 for other nuclei and the very recent measurement of the decay of ⁴⁸Ca by Balysh et al. [18], constitute important advances in the field since the pioneering work of Wu et al. [278].

From the theoretical side, the consequences upon fundamental concepts of nuclear and particle physics, potentially signaled by this rare decay, have been explored by Georgi and Glashow [115] and Fritzsch and Minkowski [111] and by many others in the last three or four decades (for a review of the grand-unification theories see [165]). The link of nuclear and particle physics, as revealed in the understanding of nuclear electroweak decays, was reviewed years ago by Leader and Predazzi [166], Vergados [269] and by Boehm and Vogel [46] while more specific aspects of the problem have been reviewed by 51, 85, 106, 125, 200 and more recently by 259, 122, 152, 153, 155. However, the sensitivity of the theoretical predictions based on nuclear models, particularly when dealing with the range of physically acceptable values of nuclear double-beta-decay observables, and the variety of nuclear models proposed since the above reports were published largely justifies the need of an up-dated review, like the one which we are trying to convey herewith.

In reviewing the available theoretical information on nuclear double-beta-decay processes we have avoided the discussion of already well known ingredients and we have summarized, instead, the main aspects of each model. Since the list of contributions (as listed in the references) is considerably large, a detailed presentation of each of them would be impossible and unwanted omissions in the citations may also occur for which we apologize in advance.

In presenting these results we have kept in mind that theoretical results in this field are of no use unless they are given in a way which allows an unambiguous comparison with data. To answer the question about the agreement between data and models we have chosen to review the available results on a case-by-case basis, rather than trying to draw general conclusions which perhaps would not be valid for the complete set of data [262].

Since the calculation of double-beta-decay observables relies on both the models of electroweak decays and nuclear-structure models the essentials of them will be presented in 2 Weak-interaction Lagrangian, 3 Nuclear models for double beta decay, basically to clarify the significance of the expressions given in 4 Two-neutrino double beta decay, 5 Neutrinoless double beta decaywhere the application of the resulting formalism to the two-neutrino and neutrinoless double-beta-decay modes is pursued. Section 6is devoted to the case-by-case discussion of the known double-beta-decay systems.

The rest of the report has been organized as shown in the table of contents.

Section snippets

Weak-interaction Lagrangian

The standard model of the electroweak interactions, due to Weinberg, Salam and Glashow, is perhaps the most illustrative example about a theory based on the use of concepts belonging to gauges theories and symmetry-breaking mechanisms with a solid bearing with nature. In spite of its success the theory, however, relies upon a number of premises which may (or may not) remain valid if new scenarios about neutrino-mass hierarchies, right-handed interactions and lepton-flavour mixing are

Nuclear models for double beta decay

General nuclear-structure concepts have been applied to the description of nuclear double-beta-decay (NDBD) transitions, as in the earliest studies by 120, 121, 125, 154, 228. The first calculations of the relevant transition amplitudes were performed by using very limited shell model basis 125, 228. Assuming that the weak-interaction sector of the problem was known to a desired accuracy the emphasis of the early studies was centered upon the way in which nuclear wave functions can be handled

Two-neutrino double beta decay

This chapter will be devoted to the definition of the half-life expressions, with the associated nuclear matrix elements, for the two-neutrino NDBD, and to the comparison of an extremely simplified nuclear model with available experimental data in a hope for better seeing the overall trends exhibited by the nuclear matrix elements and to make more transparent the results of more realistic theoretical approaches. It has to be noted that no quantitative predictions are expected to evolve by the

Neutrinoless double beta decay

In Section 2of this report we have laid the conceptual background of the neutrinoless double beta (0νββ) decay: the structure of the most general weak-interaction lagrangian with its connections to different aspects of the Majorana neutrinos. In this section we review briefly different aspects of the neutrinoless double beta decay, mainly those aspects which are essential to understand the discussion of the results of Section 6. Thus, emphasis is put to presentation of the background of those

Discussion

In this section we shall comment on the theoretical results for double beta decay on a case-by-case basis. The aim of the section is to present the key results obtained by using different models, i.e. to illustrate the situation in the double-beta-decay matrix-element calculations from the perspective of the theory. In this review we concentrate on recent results and do not try to cover all the history of the double-beta-decay calculations. This is especially true for the transitions to the

Summary and conclusions

From the results of the previous chapters we can extract some definite conclusions about the status of the agreement between data and theory as well as about the status of the theory, more specifically, of the nuclear-structure component of the theory. They are the following:

•
Conclusions about the double Gamow–Teller matrix element M^(2ν)_GT: In the presence of strong cancellations among the main components of the wave functions the matrix elements M^(2ν)_GT are mostly driven by small components of

Acknowledgements

This work has been partially supported by the Academy of Finland, the University of Jyväskylä, Finland, the CONICET and ANPCYT of Argentina and by the J.S. Guggenheim Memorial Foundation, USA.

The help of Matias Aunola and Jussi Toivanen with some of the tables and figures presented in this report is acknowledged with thanks.

The authors would like to thank Professors Pertti Lipas and Daniel Bes for many years of guidance and discussions about the fundamentals of nuclear structure.

One of the

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Weak-interaction and nuclear-structure aspects of nuclear double beta decay

Abstract

Introduction

Section snippets

Weak-interaction Lagrangian

Nuclear models for double beta decay

Two-neutrino double beta decay

Neutrinoless double beta decay

Discussion

Summary and conclusions

Acknowledgements

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