Abstract: A review is presented of the Hall-Post inequalities that give lower-bounds to the ground-state energy of quantum systems in terms of energies of smaller systems. New applications are given for systems experiencing both a static source and inner interactions, as well as for hydrogen-like molecules and for tetraquarks in some quark models. In the latter case, the Hall-Post inequalities constrain the possibility of deeply-bound exotic mesons below the threshold for dissociation into two quark-antiquark mesons. We also emphasize the usefulness of the Hall-Post bounds in terms of 3-body energies when some 2-body subsystems are ill defined or do not support any bound state.

Abstract: The structure of As-83,As- 85, and As-87 have been studied in fusion-fission reaction( 238)U+9Be. Fission fragments were identified in mass and atomic number using the VAMOS++ spectrometer and the coincident gamma rays were detected in the gamma-ray tracking array AGATA. New transitions in 83As and 85As are reported and placed in the level schemes. A level scheme of the excited states in 87As is proposed for the first time. The data are interpreted in frame of large-scale shell-model calculations, SU3 symmetries, and beyond mean-field frameworks. A spherical regime at magic number N = 50 is predicted and the location of the proton g9/2 orbital is proposed for the first time. Development of collectivity in a prolate deformed, gamma-soft regime in the open shell cases 85As and 87As, most neutron-rich isotopes beyond N = 50, is concluded. Data and theoretical calculations give confidence to a relatively high extrapolated excitation energy about 4 MeV of the 9/2+ state in 79Cu, one proton above 78Ni.

Abstract: We demonstrate that the application of an external magnetic field could lead to an improved background rejection in neutrinoless double-beta (0 nu beta beta) decay experiments using a high-pressure xenon (HPXe) TPC. HPXe chambers are capable of imaging electron tracks, a feature that enhances the separation between signal events (the two electrons emitted in the 0 nu beta beta decay of Xe-136) and background events, arising chiefly from single electrons of kinetic energy compatible with the end-point of the 0 nu beta beta decay (Q(beta beta)). Applying an external magnetic field of sufficiently high intensity (in the range of 0.5-1 Tesla for operating pressures in the range of 5-15 atmospheres) causes the electrons to produce helical tracks. Assuming the tracks can be properly reconstructed, the sign of the curvature can be determined at several points along these tracks, and such information can be used to separate signal (0 nu beta beta) events containing two electrons producing a track with two different directions of curvature from background (single-electron) events producing a track that should spiral in a single direction. Due to electron multiple scattering, this strategy is not perfectly efficient on an event-by-event basis, but a statistical estimator can be constructed which can be used to reject background events by one order of magnitude at a moderate cost (about 30%) in signal efficiency. Combining this estimator with the excellent energy resolution and topological signature identification characteristic of the HPXe TPC, it is possible to reach a background rate of less than one count per ton-year of exposure. Such a low background rate is an essential feature of the next generation of 0 nu beta beta experiments, aiming to fully explore the inverse hierarchy of neutrino masses.