arXiv subjects
Publications and source records attributed to V. R. Manfredi.
For r-process nucleosynthesis the beta decay rates for a number of neutron-rich intermediate heavy nuclei are calculated. The model for the beta strength function is able to reproduce the observed half~lives quite well.
In this paper we investigate the local and global spectral properties of the triaxial rigid rotator. We demonstrate that, for a fixed value of the total angular momentum, the energy spectrum can be divided into two sets of energy levels, whose classical analog are librational and rotational motions. By using diagonalization, semiclassical and algebric methods, we show that the energy levels follow the anomalous spectral statistics of the one-dimensional harmonic oscillator.
The aim of this work is to study the spectral statistics of the asymmetric rotor model (triaxial rigid rotator). The asymmetric top is classically integrable and, according to the Berry-Tabor theory, its spectral statistics should be Poissonian. Surprisingly, our numerical results show that the nearest neighbor spacing distribution $P(s)$ and the spectral rigidity $Δ_3(L)$ do not follow Poisson statistics. In particular, $P(s)$ shows a sharp peak at $s=1$ while $Δ_3(L)$ for small values of $L$ follows the Poissonian predictions and asymptotically it shows large fluctuations around its mean value. Finally, we analyze the information entropy, which shows a dissolution of quantum numbers by breaking the axial symmetry of the rigid rotator.
We investigate the spectral statistics of the asymmetric rotor model (triaxial rigid rotator). The asymmetric top is classically integrable and, according to the Berry-Tabor theory, its spectral statistics should be Poissonian. Surprisingly, our numerical results show that the nearest neighbor spacing distribution $P(s)$ and the spectral rigidity $Δ_3(L)$ do not follow Poisson statistics.
In the field of quantum chaos, the study of energy levels plays an important role. The aim of this review paper is to critically discuss some of the main contributions regarding the connection between classical dynamics, semi-classical quantization and spectral statistics of energy levels. In particular, we analyze in detail degeneracies and quasi-crossings in the eigenvalues of quantum Hamiltonians which are classically non-integrable. Summary: 1. Introduction; 2. Quasi-Crossing and Chaos; 3. Molecular Spectroscopy; 4. Nuclear Models; 4.1 Zirnbauer-Verbaashot-Weidenmuller Model; 4.2 Lipkin-Meshow-Glick Model; 5. Particle Physics and Field Theory; 6. Conclusions.
Nowadays there is no universally accepted definition of quantum chaos. In this paper we review and critically discuss different approaches to the subject, such as Quantum Chaology and the Random Matrix Theory. Then we analyze the problem of dynamical chaos and the time scales associated with chaos suppression in quantum mechanics. Summary: 1. Introduction 2. Quantum Chaology and Spectral Statistics 3. From Poisson to GOE Transition: Comparison with Experimental Data 3.1 Atomic Nuclei 3.2 The Hydrogen Atom in the Strong Magnetic Field 4. Quantum Chaos and Field Theory 5. Alternative Approaches to Quantum Chaos 6. Dynamical Quantum Chaos and Time Scales 6.1 Mean-Field Approximation and Dynamical Chaos 7. Conclusions
In this paper we discuss in detail the nonlinear equations of the mean--field approximation and their connection to the exact many--body Schrödinger equation. Then we analyze the mean--field approach and the nonlinear dynamics of a trapped condensate of weakly--interacting bosons.
The spectral distribution method with modified Kuo-Brown interaction is extended to the study of the upper half as well as to odd-A nuclei, of the fp shell. The calculations show similar success to that obtained for the lower half.
We perform large shell model calculations for Calcium isotopes in the full fp shell by using the realistic Kuo-Brown interaction. The Calcium isotopes are especially interesting because the nearest-neighbour spacing distribution P(s) of low-lying energy levels shows significant deviations from the predictions of the Gaussian Orthogonal Ensemble of random--matrix theory. This contrasts with other neighbouring nuclei which show fully chaotic spectral distributions. We study the chaotic behaviour as a function of the excitation energy. In addition, a clear signature of chaos suppression is obtained when the single-particle spacings are increased. In our opinion the relatively weak strength of the neutron-neutron interaction is unable to destroy the regular single-particle mean-field motion completely. In the neighbouring nuclei with both protons and neutrons in valence orbits, on the other hand, the stronger proton-neutron interaction would appear to be sufficient to destroy the regular mean-field motion.
In atomic nuclei, ordered and chaotic states generally coexist. In this paper the transition from ordered to chaotic states will be discussed in the framework of roto-vibrational and shell models. In particular for $^{160}Gd$, in the roto-vibrational model, the Poincarè sections clearly show the transition from order to chaos for different values of rotational frequency. Furthermore, the spectral statistics of low-lying states of several $fp$ shell nuclei are studied with realistic shell-model calculations.
The Toda criterion of the Gaussian curvature is applied to calculate analytically the transition energy from regular to chaotic motion in a schematic model describing the interaction between collective dipole and quadrupole modes in atomic nuclei.
In atomic nuclei, as in other many-body systems, the classical phase space is mixed, so ordered and chaotic states generally coexist. In this contribution we discuss some models, showing the transition from order to chaos. In several cases a clear correspondence between classical and quantum chaos has been established. In particular the transition from ordered to chaotic states will be discussed in the framework of the shell and roto-vibrational models.
The structure of nuclei in the lower half of fp shell is investigated by the spectral distribution method using the modified Kuo-Brown interaction. This interaction recently showed success in reproducing observed properties through detailed shell model studies. Spectral distribution studies avoid explicit diagonalization and hold promise for applications to astrophysics.
The spectral statistics of low--lying states of several $fp$ shell nuclei are studied with realistic shell--model calculations. For Ca isotopes, we find significant deviations from the predictions of the random--matrix theory which suggest that some spherical nuclei are not as chaotic in nature as the conventional view assumes.
We show that the collective vibrational model of atomic nuclei displays quantum chaos. To avoid the problems related to the tunneling effects, a Green function deterministic numerical method has been used to evaluate the energy levels.
We apply the canonical perturbation theory to the semi--quantal hamiltonian of the SU(3) shell model. Then, we use the Einstein--Brillowin--Keller quantization rule to obtain an analytical semi--quantal formula for the energy levels, which is the usual semi--classical one plus quantum corrections. Finally, a test on the numerical accuracy of the semiclassical approximation and of its quantum corrections is performed.
The spectral statistics of low--lying states of $fp$ shell nuclei are studied by performing large shell--model calculations with a realistic nuclear interaction. For $Ca$ isotopes, we find deviations from the predictions of the random--matrix theory which suggest that some spherical nuclei are not as chaotic in nature as the conventional view assumes.
Using a classical analytical criterion (that of curvature) and numerical results (Poincarè sections and spectral statistics), a transition order--chaos--order in the roto--vibrational model of atomic nuclei has been shown. Numerical calculations were performed for some deformed nuclei.