F. Cannata

Systems with higher-order shape invariance: spectral and algebraic properties

Abstract We study systems of two intertwining relations of first or second order for the same (up to a constant shift) partner Schrodinger operators. It is shown that the corresponding Hamiltonians possess a higher order shape invariance which is equivalent to the ladder equation. We analyze with particular attention irreducible second order Darboux transformations which together with the first order act as building blocks. For the third order shape-invariance irreducible Darboux transformations entail only one sequence of equidistant levels while for the reducible case the structure consists of up to three infinite sequences of equidistant levels and, in some cases, singlets or doublets of isolated levels.

Breakdown of SU4 invariance and total muon capture rates: 4He, 12C, 16O, 40Ca

Abstract We study the energy dependence of the first forbidden Fermi and Gamov Teller matrix elements, using sum rule techniques which give us a simple tool for the evaluation of the SU(4) breaking effect. A satisfactory agreement with experimental data is obtained.

Remarks on the general solution for the flat Friedmann universe with exponential scalar-field potential and dust

We show that the simple extension of the method of obtaining the general exact solution for the cosmological model with the exponential scalar-field potential to the case when the dust is present fails, and we discuss the reasons of this puzzling phenomenon.

The persistence of supermultiplet selection rules in nuclear weak and electromagnetic transitions

Abstract The nuclear supermultiplet symmetry, although broken, is shown to be useful in interpreting the existence of the isovector giant magnetic dipole resonances. Supermultiplet doorways are responsible for the saturation of the magnetic dipole strength. Persistence of the nuclear SU(4) selection rules in light nuclei and its relevance to the allowed muon capture and related processes are examined.

Overcritical PT-Symmetric Square Well Potential in the Dirac Equation

Abstract We study scattering properties of a PT -symmetric square well potential with real depth larger than the threshold of particle–antiparticle pair production as the time component of a vector potential in the Dirac equation. Spontaneous pair production inside the well becomes tiny beyond the strength at which discrete bound states with real energies disappear, consistently with a spontaneous breakdown of PT symmetry.

Local realizations of q-oscillators in quantum mechanics

Abstract Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schrodinger type. In contrast to the standard harmonic oscillators, such systems exhibit a continuous spectrum. The general realization scheme of the q-oscillator algebra on the space of wave functions for a one-dimensional Schrodinger Hamiltonian shows the existence of non-Fock irreducible representations associated to the continuous part of the spectrum and directly related to the deformation. An algorithm for the mapping of energy levels is described.

PT Symmetric Schrodinger Operators: Reality of the Perturbed Eigenvalues ?

We prove the reality of the perturbed eigenvalues of some PT symmetric Hamiltonians of physical interest by means of stability methods. In particular we study 2-dimensional generalized harmonic oscillators with polynomial perturbation and the one- dimensional x 2 (ix) for 1 < < 0.

Pseudo-Hermiticity of an exactly solvable two-dimensional model

We study a two-dimensional exactly solvable non-Hermitian PT-non-symmetric quantum model with real spectrum, which is not amenable to separation of variables, by supersymmetrical methods. Here we focus attention on the property of pseudo-Hermiticity, biorthogonal expansion and pseudo-metric operator. To our knowledge this is the first time that pseudo-Hermiticity is realized explicitly for a non-trivial two-dimensional case. It is shown that the Hamiltonian of the model is not diagonalizable.

Double shape invariance of the two-dimensional singular Morse model

A second shape invariance property of the two-dimensional generalized Morse potential is discovered. Though the potential is not amenable to conventional separation of variables, the above property allows to build purely algebraically part of the spectrum and corresponding wave functions, starting from one definite state, which can be obtained by the method of SUSY-separation of variables, proposed recently.

An analysis of the contribution of isospin two ππ resonant states in the -np -> π+π+π- annihilation reaction

Abstract The results of a search for a possible evidence of a π + π + resonant state in the n p→π + π + π − annihilation reaction with data collected by the OBELIX Experiment are presented. The study has been performed by means of a partial wave analysis in the frame of the isobar model. Production fractions for a possible π + π + resonance have been evaluated. The observed effects at the π + π + threshold may be described reasonably well by the contributions of f 2 (1270), f 0 (1500), f 2 (1565) and ρ (1450) states and their interferences, but a meaningful statistical indication for a π + π + scalar state at about 1400 MeV emerges from the analysis.