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The order-to-chaos transition in the dynamics of independent classical and quantum gas of particles was studied by means of the computer simulations within the nuclear model based on the time-dependent mean-field approach. The excitation of the classical gas for containers whose surfaces are rippled according to Legendre polynomials P2, P3 is followed for twenty periods of oscillations. For different vibration frequencies of small amplitude vibrations of such a container near the spherical equilibrium shape we obtained for the classical gas much smaller excitation energies than those predicted by the wall formula. With increasing equilibrium deformation they become significantly larger and for P3 vibrations they are close to the wall formula limit. Notable shell effects were found in the excitation energies of the quantum gas in the Woods-Saxon potential with the corresponding relatively sharp (diffuseness equals to 0.1 fm) moving surfaces for small-amplitude slow vibrations.

The effective-surface approximation is extended taking into account derivatives of the symmetry-energy density per particle with respect to the mean particle density. The isoscalar and isovector particle densities in this extended effective-surface approximation are derived. The improved expressions of the surface symmetry energy, in particular, its surface tension coefficients in the sharp-edged proton-neutron asymmetric nuclei take into account important gradient terms of the energy density functional. For most Skyrme forces the surface symmetry-energy constants and the corresponding neutron skins and isovector stiffnesses are calculated as functions of the Swiatecki derivative of the nongradient term of the symmetry-energy density per particle with respect to the isoscalar density. Using the analytical isovector surface-energy constants in the framework of the Fermi-liquid droplet model we find energies and sum rules of the isovector giant-dipole resonance structure in a reasonable agreement with the experimental data, and they are compared with other theoretical approaches., 23 pages, 11 figures, 2 tables. arXiv admin note: text overlap with arXiv:1301.5749

The moment of inertia for nuclear collective rotations is derived within a semiclassical approach based on the Inglis cranking and Strutinsky shell-correction methods, improved by surface corrections within the nonperturbative periodic-orbit theory. For adiabatic (statistical-equilibrium) rotations it was approximated by the generalized rigid-body moment of inertia accounting for the shell corrections of the particle density. An improved phase-space trace formula allows to express the shell components of the moment of inertia more accurately in terms of the free-energy shell correction. Evaluating their ratio within the extended Thomas-Fermi effective-surface approximation, one finds good agreement with the quantum calculations., Comment: 9 pages,4 figures

The isoscalar and isovector particle densities and the surface tension coefficients at the average binding energy are used to derive analytical expressions of the neutron skin thickness and the isovector stiffness of sharp edged proton-neutron asymmetric nuclei. For most Skyrme forces these quantities are significantly larger than the well known ones. Using the analytical isovector surface energy constants in the framework of the hydrodynamical and the Fermi-liquid droplet models the mean energies and the sum rules of the isovector giant dipole resonances are in fair agreement with the experimental data., Comment: 22 pages, 5 figures, 2 tables

Statistics of the single-particle levels in a deformed Woods-Saxon potential is analyzed in terms of the Poisson and Wigner nearest-neighbor distributions for several deformations and multipolarities of its surface distortions. We found the significant differences of all the distributions with a fixed value of the angular momentum projection of the particle, more closely to the Wigner distribution, in contrast to the full spectra with Poisson-like behavior. Important shell effects are observed in the nearest neighbor spacing distributions, the larger the smaller deformations of the surface multipolarities.

The moment of inertia for nuclear collective rotations is derived within a semiclassical approach based on the cranking model and the Strutinsky shell-correction method by using the non-perturbative periodic-orbit theory in the phase-space variables. This moment of inertia for adiabatic (statistical-equilibrium) rotations can be approximated by the generalized rigid-body moment of inertia accounting for the shell corrections of the particle density. A semiclassical phase-space trace formula allows us to express the shell components of the moment of inertia quite accurately in terms of the free-energy shell corrections for integrable and partially chaotic Fermi systems, which is in good agreement with the corresponding quantum calculations.

The effective surface approximation is extended accounting for derivatives of the symmetry energy density per particle. Using the analytical isovector surface energy constants within the Fermi-liquid droplet model, one obtains energies and sum rules of the isovector dipole resonance structure in a reasonable agreement with the experimental data and other theoretical approaches., Comment: 9 pages, 5 figures, 21st Nuclear Physics Workshop, Kazimierz Dolny, Poland, 23rd-28th September, 2014

The nuclear isovector-dipole strength structure is analyzed in terms of the main and satellite (pygmy) peaks within the Fermi-liquid droplet model. Such a structure is sensitive to the value of the surface symmetry-energy constant obtained analytically for different Skyrme forces in the leptodermous effective surface approximation. Energies, sum rules and transition densities of the main and satellite peaks for specific Skyrme forces are qualitatively in agreement with the experimental data and other theoretical calculations., 6 pages, 2 figures, 1 table

The collective dynamics of a quantum gas of independent particles was studied for a slow collective motion within the nuclear model based on the time-dependent mean-field approach. Leading smooth semiclassical corrections to the friction and inertia coefficients for small multipole distortions of the infinitely deep square-well potential were obtained within the periodic orbit theory. The smooth inertia is mostly larger than its irrotational flow value.

The order-to-chaos transition in the dynamics of the quantum gas of independent particles was studied within the nuclear model based on the time-dependent mean-field approach. The excitation of the quantum gas in the Woods–Saxon potential with a small diffuseness of its surface rippled according to the Legendre polynomials P2 and P3 are obtained for a slow and small amplitude collective motion. We found strong correlations between time-derivatives of the excitation energies (one-body friction coefficients) and shell-correction energies as functions of the particle number. Semiclassical estimates of the friction coefficients were obtained within the periodic orbit theory by using the uniform approximation.