1,720,969 research outputs found
CORRECTIONS TO THE SEMICLASSICAL QUANTIZATION OF THE SU(3) SHELL-MODEL
No full textWe 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
A note on the toda criterion for interacting dipole-quadrupole vibrations
No full textThe 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
ORDER AND CHAOS IN ROTO-VIBRATIONAL STATES OF ATOMIC-NUCLEI
No full textUsing a classical analytical criterion (that of curvature) and numerical results (Poincare 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
THE ONSET OF CHAOS WITH A QUADRUPOLE-QUADRUPOLE INTERACTION
No full textThe transition from order to chaos in atomic nuclei has been studied analytically and numerically using a quadrupole-quadrupole residual interaction. This interaction leads to chaotic behaviour, but the critical energy E(C) similar or equal to 12.6 MeV, corresponding to the onset of chaos, is higher than that of the experimental one
SHORT ORBIT DISTRIBUTION IN THE SEMICLASSICAL LIMIT OF THE SU(3) NUCLEAR-MODEL
No full textThree different families of short periodic orbits in the semiclassical SU(3) nuclear model were studied and their stability calculated. Then, knowing the shortest period T(min) of the closed trajectories, the long-range behaviour of the DELTA-3 statistic was determined
ACCURACY OF THE SEMICLASSICAL APPROXIMATION - THE PULLEN-EDMONDS HAMILTONIAN
Full text linkA test on the numerical accuracy of the semi-classical approximation as a function of the principal quantum number has been performed for the Pullen-Edmonds model, a two-dimensional, non-integrable, scaling-invariant perturbation of the resonant harmonic oscillator. A perturbative interpretation is obtained of the recently observed phenomenon of the accuracy decrease on the approximation of individual energy levels at the increase of the principal quantum number. Moreover, the accuracy provided by the semi-classical approximation formula is on average the same as that provided by quantum perturbation theory
Spectral statistics of the triaxial rigid rotator: Semiclassical origin of their pathological behavior
No full textIn 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 analogs 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
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