Phase transitions with finite atom number in the Dicke Model

Two-level atoms interacting with a one mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom-cavity coupling strength. Two popular examples are the number of photons inside the cavity and the number of excited atoms. Coherent states provide a mean field description, which becomes exact in the thermodynamic limit. Employing symmetry adapted (SA) SU(2) coherent states (SACS) the critical behavior can be described for a finite number of atoms. A variation after projection treatment, involving a numerical minimization of the SA energy surface, associates the finite number phase transition with a discontinuity in the order parameters, which originates from a competition between two local minima in the SA energy surface.Comment: 8 pages, 10 figures, Conference Proceedings of CEWQO-2012, to be published as a Topical Issue of the journal Physica Script

Neutrinoless Double Beta Decay in Heavy Deformed Nuclei

The zero neutrino mode of the double beta decay in heavy deformed nuclei is investigated in the framework of the pseudo SU(3) model, which has provided an accurate description of collective nuclear structure and predicted half-lives for the two neutrino mode in good agreement with experiments. In the case of $^{238}U$ the calculated zero neutrino half-life is at least three orders of magnitude greater than the two neutrino one, giving strong support of the identification of the radiochemically determined half-life as being the two neutrino double beta decay. For $^{150}Nd$ the zero neutrino matrix elements are of the order of magnitude of, but lesser than, those evaluated using the QRPA. This result confirms that different nuclear models produce similar zero neutrino matrix elements, contrary to the two neutrino case. Using these pseudo SU(3) results and the upper limit for the neutrino mass we estimate the $\beta\beta_{0\nu}$ half-lives for six nuclei. An upper limit for majoron coupling constant is extracted from the experimental data.Comment: 19 pages, LaTeX, 2 figures not included, availables as poscript files upon reques

Searching for pairing energies in phase space

We obtain a representation of pairing energies in phase space, for the Lipkin-Meshkov-Glick and general boson Bardeen-Cooper-Schrieffer pairing models. This is done by means of a probability distribution of the quantum state in phase space. In fact, we prove a correspondence between the points at which this probability distribution vanishes and the pairing energies. In principle, the vanishing of this probability distribution is experimentally accessible and additionally gives a method to visualize pairing energies across the model control parameter space. This result opens new ways to experimentally approach quantum pairing systems.Comment: 5 pages, 4 figure

Double beta decay to excited states in Nd150

The pseudo SU(3) model is used to study the double beta decay of Nd150 to the ground and excited states of Sm150 . Low lying collective excitations of Sm150 and its BE(2) intensities are well reproduced. Expressions for the two neutrino double beta decay to excited states are developed and used to describe the decay of Nd150 . The existence of selection rules which strongly restrict the decay is discussed.Comment: 22 pages, LaTeX, 1 figure with Postscript file available under request at [email protected]