Renormalized proton-neutron quasiparticle random-phase approximation and its application to double beta decay

Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review

The nuclear matrix elements that govern the rate of neutrinoless double beta decay must be accurately calculated if experiments are to reach their full potential. Theorists have been working on the problem for a long time but have recently stepped up their efforts as ton-scale experiments have begun to look feasible. Here we review past and recent work on the matrix elements in a wide variety of nuclear models and discuss work that will be done in the near future. Ab initio nuclear-structure theory, which is developing rapidly, holds out hope of more accurate matrix elements with quantifiable error bars.

Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations

In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N(4)). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as ⟨Ŝ(2)⟩ are also developed and tested.

Equivalence of particle-particle random phase approximation correlation energy and ladder-coupled-cluster doubles

The recent proposal to determine the (exact) correlation energy based on pairing matrix fluctuations by van Aggelen et al. ["Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random phase approximation," preprint arXiv:1306.4957 (2013)] revived the interest in the simplest approximation along this path: the particle-particle random phase approximation (pp-RPA). In this paper, we present an analytical connection and numerical demonstrations of the equivalence of the correlation energy from pp-RPA and ladder-coupled-cluster doubles. These two theories reduce to identical algebraic matrix equations and correlation energy expressions. The numerical examples illustrate that the correlation energy missed by pp-RPA in comparison with coupled-cluster singles and doubles is largely canceled out when considering reaction energies. This theoretical connection will be beneficial to design density functionals with strong ties to coupled-cluster theories and to study molecular properties at the pp-RPA level relying on well established coupled cluster techniques.

Theory of neutrinoless double-beta decay

Neutrinoless double-beta decay, which is a very old and yet elusive process, is reviewed. Its observation will signal that the lepton number is not conserved and that the neutrinos are Majorana particles. More importantly it is our best hope for determining the absolute neutrino-mass scale at the level of a few tens of meV. To achieve the last goal certain hurdles must be overcome involving particle, nuclear and experimental physics. Nuclear physics is important for extracting useful information from the data. One must accurately evaluate the relevant nuclear matrix elements--a formidable task. To this end, we review the sophisticated nuclear structure approaches which have recently been developed, and which give confidence that the required nuclear matrix elements can be reliably calculated employing different methods: (a) the various versions of the quasiparticle random phase approximations, (b) the interacting boson model, (c) the energy density functional method and (d) the large basis interacting shell model. It is encouraging that, for the light neutrino-mass term at least, these vastly different approaches now give comparable results. From an experimental point of view it is challenging, since the life times are long and one has to fight against formidable backgrounds. One needs large isotopically enriched sources and detectors with high-energy resolution, low thresholds and very low background. If a signal is found, it will be a tremendous accomplishment. The real task then, of course, will be the extraction of the neutrino mass from the observations. This is not trivial, since current particle models predict the presence of many mechanisms other than the neutrino mass, which may contribute to or even dominate this process. In particular, we will consider the following processes: The neutrino induced, but neutrino-mass independent contribution. Heavy left and/or right-handed neutrino-mass contributions. Intermediate scalars (doubly charged, etc). Supersymmetric (SUSY) contributions. We will show that it is possible to disentangle the various mechanisms and unambiguously extract the important neutrino-mass scale, if all the signatures of the reaction are searched for in a sufficient number of nuclear isotopes.