258 research outputs found
Symmetry Breaking and Bifurcations in the Periodic Orbit Theory: II -- Spheroidal Cavity --
We derive a semiclassical trace formula for the level density of the
three-dimensional spheroidal cavity. To overcome the divergences and
discontinuities occurring at bifurcation points and in the spherical limit, the
trace integrals over the action-angle variables are performed using an improved
stationary phase method. The resulting semiclassical level density oscillations
and shell energies are in good agreement with quantum-mechanical results. We
find that the births of three-dimensional orbits through the bifurcations of
planar orbits in the equatorial plane lead to considerable enhancement of shell
effect for superdeformed shapes.Comment: 49 pages, 18 figures, using PTPTeX.cls(included), submitted to Prog.
Theor. Phy
Stability and Symmetry Breaking in Metal Nanowires
A general linear stability analysis of simple metal nanowires is presented
using a continuum approach which correctly accounts for material-specific
surface properties and electronic quantum-size effects. The competition between
surface tension and electron-shell effects leads to a complex landscape of
stable structures as a function of diameter, cross section, and temperature. By
considering arbitrary symmetry-breaking deformations, it is shown that the
cylinder is the only generically stable structure. Nevertheless, a plethora of
structures with broken axial symmetry is found at low conductance values,
including wires with quadrupolar, hexapolar and octupolar cross sections. These
non-integrable shapes are compared to previous results on elliptical cross
sections, and their material-dependent relative stability is discussed.Comment: 12 pages, 4 figure
Periodic-Orbit Bifurcations and Superdeformed Shell Structure
We have derived a semiclassical trace formula for the level density of the
three-dimensional spheroidal cavity. To overcome the divergences occurring at
bifurcations and in the spherical limit, the trace integrals over the
action-angle variables were performed using an improved stationary phase
method. The resulting semiclassical level density oscillations and
shell-correction energies are in good agreement with quantum-mechanical
results. We find that the bifurcations of some dominant short periodic orbits
lead to an enhancement of the shell structure for "superdeformed" shapes
related to those known from atomic nuclei.Comment: 4 pages including 3 figure
Nuclear level density in the statistical semiclassical micro-macroscopic approach
Level density is derived for a finite system with strongly interacting
nucleons at a given energy E, neutron N and proton Z particle numbers,
projection of the angular momentum M, and other integrals of motion, within the
semiclassical periodic-orbit theory (POT) beyond the standard Fermi-gas
saddle-point method. For large particle numbers, one obtains an analytical
expression for the level density which is extended to low excitation energies U
in the statistical micro-macroscopic approach (MMA).The interparticle
interaction averaged over particle numbers is taken into account in terms of
the extended Thomas-Fermi component of the POT. The shell structure of
spherical and deformed nuclei is taken into account in the level density. The
MMA expressions for the level density reaches the well-known macroscopic
Fermi-gas asymptote for large excitation energies U and the finite combinatoric
power-expansion limit for low energies U. We compare our MMA results for the
averaged level density with the experimental data obtained from the known
excitation energy spectra by using the sample method under statistical and
plateau conditions. Fitting the MMA to these experimental data on the
averaged level density by using only one free physical parameter - inverse
level density parameter K - for several nuclei and their long isotope chain at
low excitation energies U, one obtains the results for K. These values of K
might be much larger than those deduced from neutron resonances. The shell,
isotopic asymmetry, and pairing effects are significant for low excitation
energies.Comment: 31 pages, 7 figures, 1 tabl
Paring correlations within the micro-macroscopic approach for the level density
Level density is calculated for the two-component close- and
open-shell nuclei with a given energy , and neutron and proton
numbers, taking into account pairing effects within the microscopic-macroscopic
approach (MMA). These analytical calculations have been carried out by using
the semiclassical statistical mean-field approximations beyond the saddle-point
method of the Fermi gas model in a low excitation-energies range. The level
density , obtained as function of the system entropy , depends
essentially on the condensation energy through the excitation
energy in super-fluid nuclei. The simplest super-fluid approach, based on
the BCS theory, accounts for a smooth temperature dependence of the pairing gap
due to particle number fluctuations. Taking into account the pairing
effects in magic or semi-magic nuclei, excited below neutron resonances, one
finds a notable pairing phase transition.Pairing correlations sometimes improve
significantly the comparison with experimental data.Comment: 8 pages, 2 figures, 2 table
Microscopic-macroscopic level densities for low excitation energies
Level density is derived within the micro-macroscopic
approximation (MMA) for a system of strongly interacting Fermi particles with
the energy and additional integrals of motion , in line with
several topics of the universal and fruitful activity of A.S. Davydov. Within
the extended Thomas Fermi and semiclassical periodic orbit theory beyond the
Fermi-gas saddle-point method we obtain , where
is the modified Bessel function of the entropy . For small
shell-structure contribution one finds , where is the
number of additional integrals of motion. This integer number is a dimension of
, for the case of two-component atomic nuclei,
where and are the numbers of neutron and protons, respectively. For
much larger shell structure contributions, one obtains, . The
MMA level density reaches the well-known Fermi gas asymptote for large
excitation energies, and the finite micro-canonical combinatoric limit for low
excitation energies. The additional integrals of motion can be also the
projection of the angular momentum of a nuclear system for nuclear rotations of
deformed nuclei, number of excitons for collective dynamics, and so on. Fitting
the MMA total level density, , for a set of the integrals of
motion , to experimental data on a long nuclear isotope chain
for low excitation energies, one obtains the results for the inverse
level-density parameter , which differs significantly from those of neutron
resonances, due to shell, isotopic asymmetry, and pairing effects.Comment: 24 pages, 4 figures, 1 table. arXiv admin note: substantial text
overlap with arXiv:2109.0183
Semiclassical approach to the low-lying collective excitations in nuclei
For low-lying collective excitations we derived the inertia within the semiclassical Gutzwiller approach to the onebody Green’s function at lowest orders in h. The excitation energies, reduced probabilities and energy-weighted sum rules are in agreement with main features of the experimental data
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