A. F. R. de Toledo Piza

An extended Weyl-Wigner transformation for special finite spaces

We extend the Weyl-Wigner transformation to those particular degrees of freedom described by a finite number of states using a technique of constructing operator bases developed by Schwinger. Discrete transformation kernels are presented instead of continuous coordinate-momentum pair system and systems such as the one-dimensional canonical continuous coordinate-momentum pair system and the two-dimensional rotation system are described by special limits. Expressions are explicitly given for the spin one-half case.

Studies in isobaric analog resonances. I. Gross properties

Abstract The gross-structure of isobaric analog resonances in the N, Z + 1 system is described in terms of the intermediate structure associated with the analogs of the low-lying states of the N + 1, Z nucleus. These analog states are shown to act as “doorway states” of a rather special nature in producing generally asymmetric gross anomalies in the elastic and inelastic scattering. This description leads to a model-independent parametrization of the isobaric analog resonances. A discussion of (p, n) processes involving isobaric analog resonances is also given.

DAMPING OF ISOBARIC ANALOGUE STATES

Abstract The spreading width of analogue states due to the Coulomb interactions in a nucleus is calculated. The coupling to single-particle, two-particle-one-hole and three-particle-two-hole configurations is considered. The effect of nuclear interactions is taken account in the large energy separation between the analogue and the configuration states (symmetry energy displacement) and in the natural distribution of the latter representing their fragmentation. The spreading widths are found to be small, less than 3 keV in 89 Y and 91 Nb.

Theory of multiphonon excitation in heavy-ion collisions

We study the effects of channel coupling in the excitation dynamics of giant resonances in relativistic heavy ions collisions. For this purpose, we use a semiclassical approximation to the coupled-channels problem and separate the Coulomb and the nuclear parts of the coupling into their main multipole components. In order to assess the importance of multistep processes, we neglect the resonance widths and solve the set of coupled equations exactly. Finite widths are then considered. In this case, we handle the coupling of the ground state with the dominant giant dipole resonance exactly and study the excitation of the remaining resonances within the coupled-channels Born approximation. A comparison with recent experimental data is made. Relativistic Coulomb excitation ~RCE! is a well established tool to unravel interesting aspects of nuclear structure @1#. Examples are the studies of multiphonon resonances in the SIS accelerator at the GSI facility, in Darmstadt, Germany @2,3#. Important properties of nuclei far from stability @4# have also been studied with this method. The RCE induced by large-Z projectiles and/or targets, often yields large cross sections in grazing colisions. This results from the large nuclear response ~in the region of the giant resonances! to the acting electromagnetic fields. As a consequence, a strong coupling between the excited states is expected This coupling might be responsible for the large discrepancies between experimental data of RCE and the calculations based on first-order perturbation theory @1‐3#, or the harmonic oscillator model. In the present paper, we apply a semiclassical method @5# to the coupled-channels ~CC! problem and study RCE in several collisions between heavy ions. In this method, the projectile-target relative motion is approximated by a classical trajectory and the excitation of the giant resonances is treated quantum mechanically @6,7#. The use of this method is justified due to the small wavelengths associated with the relative motion. In Sec. II, we neglect the resonance widths and introduce the semiclassical CC equations for relativistic Coulomb excitation. The time-dependent matrix elements of the main multipole components of the Coulomb ~Sec. II A! and nuclear ~Sec. II B! parts of the coupling interaction are calculated. The CC equations are then solved in some limiting cases. Section III is devoted to the excitation of resonances of finite widths. Generalizing the schematic treatment of Ref. @6#, we present an ‘‘exact’’ solution for the coupling between the ground state ~g.s.! and the dominant GDR. The excitation of the weaker resonances are then evaluated through the coupled-channels Born approximation ~CCBA!, from the g.s. and GDR amplitudes. In Sec. IV we apply the results of the previous sections to specific cases and make a comparison with recent experimental data. Finally, in Sec. V, we summarize our results and present the conclusions of this work.

The hydrogen atom as an entangled electron–proton system

We illustrate the description of correlated subsystems by studying the simple two-body hydrogen atom. We study the entanglement of the electron and proton coordinates in the exact analytical solution. This entanglement, which we quantify in the framework of the density matrix formalism, describes correlations in the electron–proton motion.

Symmetries and time evolution in discrete phase spaces: a soluble model calculation

Using the flexibility and constructive definition of the Schwinger bases, we developed different mapping procedures to enhance different aspects of the dynamics and of the symmetries of an extended version of the two-level Lipkin model. The classical limits of the dynamics are discussed in connection with the different mappings. Discrete Wigner functions are also calculated.

Phases of quantum states in completely positive non-unitary evolution

We define an operational notion of phases in interferometry for a quantum system undergoing a completely positive non-unitary evolution. This definition is based on the concepts of quantum measurement theory. The suitable generalization of the Pancharatnan connection allows us to determine the dynamical and geometrical parts of the total phase between two states linked by a completely positive map. These results reduce to the known expressions of the total, dynamical and geometrical phases for pure and mixed states evolving unitarily.

STUDIES IN ISOBARIC ANALOG RESONANCES. II. FINE STRUCTURE.

Abstract The properties of the fine structure observed in connection with isobaric analog resonances in the elastic scattering of protons are examined in terms of the damping mechanism for the analog state. The observed asymmetries of the strength function are shown to be associated with phase correlations between damping and escape amplitudes. Correlations of the necessary type will possibly result from the virtual coupling through the open channel between the analog states and the nearby compound-nucleus states of normal symmetry. A brief discussion of the possible role of doorway states in feeding the latter is also given.

Effective dynamics of quantum subsystems

A formal framework to describe the effective dynamics of subsystems of isolated quantum systems is set up. It provides for a standard decomposition of this effective dynamics in terms of ingredients of two distinct types, namely (a) a mean-field unitary contribution; and (b) a non-unitary contribution which arises from the dynamical evolution of quantum correlations in the entire system, and which are essentially related to changes of the coherence properties of the subsystem. We show quite generally that this effective dynamics is non-hamiltonian and closely related in form to equations of the transport type.

The semiclassical coherent state propagator for systems with spin

We derive the semiclassical limit of the coherent state propagator for systems with two degrees of freedom of which one degree of freedom is canonical and the other a spin. Systems in this category include those involving spin–orbit interactions and the Jaynes–Cummings model in which a single electromagnetic mode interacts with many independent two-level atoms. We construct a path integral representation for the propagator of such systems and derive its semiclassical limit. As special cases we consider separable systems, the limit of very large spins and the case of spin-1/2.