Double Beta Decay: Recent Developments and Projections

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 $^{18}\mathrm{O}+^{12}\mathrm{C}$ 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 $^{12}\mathrm{C}(^{18}\mathrm{O},^{18}\mathrm{O})^{12}\mathrm{C}$ elastic and inelastic scattering, the $^{12}\mathrm{C}(^{18}\mathrm{O},^{17}\mathrm{O})^{13}\mathrm{C}$ one-neutron stripping, the $^{12}\mathrm{C}(^{18}\mathrm{O},^{19}\mathrm{F})^{11}\mathrm{B}$ one-proton pickup, and the $^{12}\mathrm{C}(^{18}\mathrm{O},^{18}\mathrm{F})^{12}\mathrm{B}$ 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.

Nuclear structure theory is a domain of physics faced at present with great challenges and opportunities. A larger and larger body of high-precision experimental data has been and continues to be accumulated. Experiments on very exotic short-lived isotopes are the backbone of activity at numerous large-scale facilities. Over the years, tremendous progress has been made in understanding the basic features of nuclei. However, the theoretical description of nuclear systems is still far from being complete and is often not very precise. Many questions, both basic and practical, remain unanswered.The goal of publishing this special focus issue of Journal of Physics G: Nuclear and Particle Physics on Open Problems in Nuclear Structure Theory (OPeNST) is to construct a fundamental inventory thereof, so that the tasks and available options become more clearly exposed and that this will help to stimulate a boost in theoretical activity, commensurate with the experimental progress. The requested format and scope of the articles on OPeNST was quite flexible. The journal simply offered the possibility to provide a forum for the material, which is very often discussed at conferences during the coffee breaks but does not normally have sufficient substance to form regular publications. Nonetheless, very often formulating a problem provides a major step towards its solution, and it may constitute a scientific achievement on its own.Prospective authors were therefore invited to find their own balance between the two extremes of very general problems on the one hand (for example, to solve exactly the many-body equations for a hundred particles) and very specific problems on the other hand (for example, those that one could put in one's own grant proposal). The authors were also asked not to cover results already obtained, nor to limit their presentations to giving a review of the subject, although some elements of those could be included to properly introduce the subject matter.The focus of these collected articles is therefore on the discussion of topics that are not yet understood, or that are poorly understood. We very much welcomed presentations on: (i) contradictory approaches, models, or theories that are, at present, difficult to reconcile,(ii) unsolved theoretical problems that hamper applications of existing methods, (iii) limitations of current approaches, (iv) difficulties in deriving and justifying models and theories, (v) generic problems in understanding or describing specific experimental data,and even (vi) all possible, wildest speculations and/or conjectures. The main idea behind the focus issue was to stimulate creative, unbounded thinking and provide young, but not only young, researchers with ideas that would promote further progress in this domain of science.The community of nuclear structure theorists enthusiastically responded to the idea of publishing the volume on OPeNST. It seemed that the idea struck the right chord and many colleagues were willing to share their observations on what research directions to follow and which problems to attack. The volume turned out to be a snapshot of the domain, revealing the burning questions that the community wants to address. All the articles also have a very interesting personal touch. They sometimes even present opposing or conflicting points of view, which is exactly what one would expect within a vibrant scientific discussion. All in all, the Editors of Journal of Physics G are very happy to offer you this unique collection, which will constitute very interesting reading for all those working in nuclear structure theory.

Double beta decay, the conversion of a nucleus changing the atomic number Z by two units while leaving the atomic mass A constant, is an extremely rare nuclear decay. It can occur via the emission of two electrons or two positrons, double electron capture or a mixed mode depending on the available Q-value. Furthermore, the neutrino-less mode is of major importance for neutrino physics. This mode violates the lepton number by two units and its observation would point towards physics beyond the Standard Model. The standard interpretation is via the exchange of a light Majorana neutrino, the mass of which could be measured via a half-life determination of double beta decay. There exist 11 isotopes for the double electron mode with a Q-value above 2 MeV, and for those considered for experimental searches, the neutrino-accompanied mode has been measured in the last decade. In recent years various new developments have occurred in almost all aspects related to double beta decay. With all the mixing angles of the PMNS leptonic mixing matrix measured, the regions of interest are well determined. Furthermore, with the launch of the LHC the existence of possible TeV particles contributing to neutrino-less double beta decays can be explored, complementing the searches in underground experiments. Nuclide pairs with the potential of degenerate nuclear states which would lead to a resonance enhancement of neutrino-less double electron capture were intensively searched for with Penning traps and caused a revival of this process. Last but not least, massive progress has been made in the involved conversion factors from the experimentally accessible half-life to the quantity of interest, the neutrino mass. New phase space factors were calculated and new approaches like the interacting boson model or energy density functional approaches joined the nuclear shell model and QRPA calculations to determine the involved nuclear transitions matrix elements. This is accompanied by a massive experimental program to improve the input parameters for these calculations using charge-exchange reactions, nucleon transfer reactions and muon capture. Furthermore, Penning traps have measured almost all relevant Q-values to sub-keV precision. All these exciting new developments over the last few years triggered the idea of a focus section in Journal of Physics G: Nuclear and Particle Physics on double beta decay during a workshop on the topic held in Dresden in July 2010. In addition to the research topics mentioned before, this focus section also covers the implication of double beta decay for current particle physics and theories beyond the Standard Model.

Three-nucleon forces: Implementation and applications to atomic nuclei and dense matter

Weak interaction processes continue to be hot topics in fundamental physics research. In this paper, we briefly review some recent advances in the theoretical study of beta and double-beta decays that include both the nuclear and atomic part of these processes. On the nuclear side, we present a statistical approach for the computation of the nuclear matrix elements (NME) for neutrinoless double-beta (0νββ). A range of NME values, the most probable value for NME, and the associated theoretical uncertainty are given. Correlations with other related observables are shown as well. On the atomic side, we first briefly review the methods used to obtain the electrons’ wave functions. Further, we use them for the computation of some relevant kinematic quantities such as Fermi functions, electron spectra, and angular correlation between the emitted electrons. Then, we present applications of these calculations to the experimental data analysis related to the search of the Lorentz invariance violation in two-neutrino double-beta (2νββ) decay and description of the decay rates and decay rate ratios for allowed and unique forbidden electron capture (EC) processes.

The study of the neutrinoless double beta(0νββ)decay mode can provide us with important information on the neutrino properties, particularly on the electron neutrino absolute mass. In this work we revise the present constraints on the neutrino mass parameters derived from the0νββdecay analysis of the experimentally interesting nuclei. We use the latest results for the phase space factors (PSFs) and nuclear matrix elements (NMEs), as well as for the experimental lifetime limits. For the PSFs we use values computed with an improved method reported very recently. For the NMEs we use values chosen from the literature on a case-by-case basis, taking advantage of the consensus reached by the community on several nuclear ingredients used in their calculation. Thus, we try to restrict the range of spread of the NME values calculated with different methods and, hence, to reduce the uncertainty in deriving limits for the Majorana neutrino mass parameter. Our results may be useful to have an updated image on the present neutrino mass sensitivities associated with0νββmeasurements for different isotopes and to better estimate the range of values of the neutrino masses that can be explored in the future double beta decay (DBD) experiments.

Nuclear-structure theory has advanced quickly in recent years. The field is now at the point at which an accurate calculation of the nuclear matrix elements governing neutrinoless double-beta decay should soon be possible. I describe some promising theoretical many-body methods and their application to double-beta decay.

Recent Developments in the Theory of Nuclear Structure

The present article aims to give a concise account of the main developments in nuclear structure theory, from its origin in the 1930s to date, taking the modelling of inter-nucleon interactions as guideline.

A review of recent developments in double-beta decay

Grand unification, nuclear structure and the double beta-decay

The central focus of this research was the interplay between three generic classes of degrees of freedom relevant to nuclear structure theory: single-particle degrees of freedom, collective degrees of freedom, and statistical degrees of freedom, which can be thought of as an incoherent mean field or a thermal bath.

Nuclear double beta decay is one of the most promising tools for probing beyond-the-standard-model physics on beyond-accelerator energy scales. It is already now probing the TeV scale, on which new physics should manifest itself according to theoretical expectations. Only in the early 1980s was it known that double beta decay yields information on the Majorana mass of the exchanged neutrino. At present, the sharpest bound for the electron neutrino mass arises from this process. It is only in the last 10 years that the much more far-reaching potential of double beta decay has been discovered. Today, the potential of double beta decay includes a broad range of topics that are equally relevant to particle physics and astrophysics, such as masses of heavy neutrinos, of sneutrinos, as SUSY models, compositeness, leptoquarks, left-right symmetric models, and tests of Lorentz symmetry and equivalence principle in the neutrino sector. Double beta decay has become indispensable nowadays for solving the problem of the neutrino mass spectrum and the structure of the neutrino mass matrix - together with present and future solar and atmospheric neutrino oscillation experiments. Some future double beta experiments (like Genius) will be capable to be simultaneously neutrino observatories for double beta decay and low-energy solar neutrinos, and observatories for cold dark matter of ultimate sensitivity. This invaluable book outlines the development of double beta research from its beginnings until its most recent achievements, and also presents the outlook for its highly exciting future.

The present contribution does not aim at replacing the huge and often excellent literature on DFT for atomic nuclei, but tries to provide an updated introduction to this topic. The goal would be, ideally, to help a fresh this http URL. or Ph.D. student (or a researcher from other fields) to become acquainted with some basic concepts, and then move to the specialized textbooks or papers with some ability for orienteering. We first introduce the basics of DFT, and show the difference with the naive mean-field theory, that is doomed to fail as a model even in the simple case of uniform nuclear matter. We introduce the Energy Density Functionals (EDFs) that are used in nuclear structure, with few examples of their applications. The concepts of symmetry breaking and restoration are briefly discussed. We also include an introduction to the time-dependent extension of DFT that, so far, has been implemented essentially only in the adiabatic approximation and has been applied mainly to the study of nuclear vibrations. With this material, we hope that any reader is able to deal with the texts that go deeper into each of the topics, having understood that DFT is probably the best compromise in nuclear structure theory between simplicity, accuracy, and broad range of applicability.

By stipulating that like-fermions adjacent in space must be singlet paired, geometric considerations alone produce closed electron shells at the 6 noble gases and, similarly, closed nucleon shells and subshells isomorphic with those of the harmonic oscillator used in nuclear theory.