Shell corrections for finite depth potentials with bound states only

A new method of calculating unique values of ground-state shell corrections for finite depth potentials is shown, which makes use of bound states only. It is based on (i) a general formulation of extracting the smooth part from any fluctuating quantity proposed by Strutinsky and Ivanjuk, (ii) a generalized Strutinsky smoothing condition suggested recently by Vertse et al., and (iii) the technique of the Lanczos $\sigma$ factors. Numerical results for some spherical heavy nuclei ($^{132,154}$Sn, $^{180,208}$Pb and $^{298}$114) are presented and compared to those obtained with the Green's function oscillator expansion method.Comment: 5 pages, 2 tables and 3 figures. Accepted in Physics Letters

The Effect of Nuclear Rotation on the Collective Transport Coefficients

We have examined the influence of rotation on the potential energy and the transport coefficients of the collective motion (friction and mass coefficients). For axially symmetric deformation of nucleus Th-224 we have found that at excitations corresponding to temperatures T > 1 MeV the shell correction to the liquid drop energy practically does not depend on the angular rotation. The friction and mass coefficients obtained within the linear response theory for the same nucleus at temperatures larger than T=2 MeV are rather stable with respect to rotation provided that the contributions from spurious states arising due to the violation of rotation symmetry are removed. At smaller excitations both friction and mass parameters corresponding to the elongation mode are growing functions of rotational frequency.Comment: 16 pages, 5 eps figures, Latex, submitted to Nucl.Phys.

Giant-dipole Resonance and the Deformation of Hot, Rotating Nuclei

The development of nuclear shapes under the extreme conditions of high spin and/or temperature is examined. Scaling properties are used to demonstrate universal properties of both thermal expectation values of nuclear shapes as well as the minima of the free energy, which can be used to understand the Jacobi transition. A universal correlation between the width of the giant dipole resonance and quadrupole deformation is found, providing a novel probe to measure the nuclear deformation in hot nuclei.Comment: 6 pages including 6 figures. To appear in Phys. Rev. Lett. Revtex

Behavior of the giant-dipole resonance in 120^{120}Sn and 208^{208}Pb at high excitation energ

The properties of the giant-dipole resonance (GDR) are calculated as a function of excitation energy, angular momentum, and the compound nucleus particle decay width in the nuclei $^{120}$Sn and $^{208}$Pb, and are compared with recent experimental data. Differences observed in the behavior of the full-width-at-half-maximum of the GDR for $^{120}$Sn and $^{208}$Pb are attributed to the fact that shell corrections in $^{208}$Pb are stronger than in $^{120}$Sn, and favor the spherical shape at low temperatures. The effects shell corrections have on both the free energy and the moments of inertia are discussed in detail. At high temperature, the FWHM in $^{120}$Sn exhibits effects due to the evaporation width of the compound nucleus, while these effects are predicted for $^{208}$Pb.Comment: 28 pages in RevTeX plus eight postscript figures. Submitted to Nucl. Phys.

Neutron stars and the fermionic Casimir effect

The inner crust of neutron stars consists of nuclei of various shapes immersed in a neutron gas and stabilized by the Coulomb interaction in the form of a crystal lattice. The scattering of neutrons on nuclear inhomegeneities leads to the quantum correction to the total energy of the system. This correction resembles the Casimir energy and turns out to have a large influence on the structure of the crust.Comment: 6 pages, 1 figure, presented at the Fifth Workshop on Quantum Field Theory under the Influence of External Conditions, Leipzig, Germany, September 10-15, 2001, to appear in Int. J. Mod. Phys.

A Particle number conserving shell-correction method

The shell correction method is revisited. Contrary to the traditional Strutinsky method, the shell energy is evaluated by an averaging over the number of particles and not over the single-particle energies, which is more consistent with the definition of the macroscopic energy. In addition, the smooth background is subtracted before averaging the sum of single-particle energies, which significantly improves the plateau condition and allows to apply the method also for nuclei close to the proton or neutron drip lines. A significant difference between the shell correction energy obtained with the traditional and the new method is found in particular for highly degenerated single-particle spectra (as i.e. in magic nuclei) while for deformed nuclei (where the degeneracy is lifted to a large extent) both estimates are close, except in the region of super or hyper-deformed states.Comment: 11 pages in LaTeX, 7 figure

Quantum and semiclassical study of magnetic anti-dots

We study the energy level structure of two-dimensional charged particles in inhomogeneous magnetic fields. In particular, for magnetic anti-dots the magnetic field is zero inside the dot and constant outside. Such a device can be fabricated with present-day technology. We present detailed semiclassical studies of such magnetic anti-dot systems and provide a comparison with exact quantum calculations. In the semiclassical approach we apply the Berry-Tabor formula for the density of states and the Borh-Sommerfeld quantization rules. In both cases we found good agreement with the exact spectrum in the weak magnetic field limit. The energy spectrum for a given missing flux quantum is classified in six possible classes of orbits and summarized in a so-called phase diagram. We also investigate the current flow patterns of different quantum states and show the clear correspondence with classical trajectories.Comment: 14 pages, 13 figure

Mathematical modeling of vibration field on the lathes machine tools

The design of transitional and withstand dynamic processes is carried out in the occasion of main motion. Differential equalizations in the derivatives of part, which describe oscillation of branches of transmission in the variables of Euler, are presented. The design of the dynamic moving of spindle and both branches of transmission is executed as systems with the up-diffused parameters

Nuclear prolate-shape dominance with the Woods-Saxon potential

We study the prolate-shape predominance of the nuclear ground-state deformation by calculating the masses of more than two thousand even-even nuclei using the Strutinsky method, modified by Kruppa, and improved by us. The influences of the surface thickness of the single-particle potentials, the strength of the spin-orbit potential, and the pairing correlations are investigated by varying the parameters of the Woods-Saxon potential and the pairing interaction. The strong interference between the effects of the surface thickness and the spin-orbit potential is confirmed to persist for six sets of the Woods-Saxon potential parameters. The observed behavior of the ratios of prolate, oblate, and spherical nuclei versus potential parameters are rather different in different mass regions. It is also found that the ratio of spherical nuclei increases for weakly bound unstable nuclei. Differences of the results from the calculations with the Nilsson potential are described in detail.Comment: 16 pages, 17 figure

Semiclassical analysis of the lowest-order multipole deformations of simple metal clusters

We use a perturbative semiclassical trace formula to calculate the three lowest-order multipole (quadrupole \eps_2, octupole \eps_3, and hexadecapole \eps_4) deformations of simple metal clusters with $90 \le N \le 550$ atoms in their ground states. The self-consistent mean field of the valence electrons is modeled by an axially deformed cavity and the oscillating part of the total energy is calculated semiclassically using the shortest periodic orbits. The average energy is obtained from a liquid-drop model adjusted to the empirical bulk and surface properties of the sodium metal. We obtain good qualitative agreement with the results of quantum-mechanical calculations using Strutinsky's shell-correction method.Comment: LaTeX file (v2) 6 figures, to be published in Phys. Lett.