59 research outputs found
Level density of the H\'enon-Heiles system above the critical barrier Energy
We discuss the coarse-grained level density of the H\'enon-Heiles system
above the barrier energy, where the system is nearly chaotic. We use periodic
orbit theory to approximate its oscillating part semiclassically via
Gutzwiller's semiclassical trace formula (extended by uniform approximations
for the contributions of bifurcating orbits). Including only a few stable and
unstable orbits, we reproduce the quantum-mechanical density of states very
accurately. We also present a perturbative calculation of the stabilities of
two infinite series of orbits (R and L), emanating from the shortest
librating straight-line orbit (A) in a bifurcation cascade just below the
barrier, which at the barrier have two common asymptotic Lyapunov exponents
and .Comment: LaTeX, style FBS (Few-Body Systems), 6pp. 2 Figures; invited talk at
"Critical stability of few-body quantum systems", MPI-PKS Dresden, Oct.
17-21, 2005; corrected version: passages around eq. (6) and eqs. (12),(13)
improve
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
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
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
Analytical perturbative approach to periodic orbits in the homogeneous quartic oscillator potential
We present an analytical calculation of periodic orbits in the homogeneous
quartic oscillator potential. Exploiting the properties of the periodic
Lam{\'e} functions that describe the orbits bifurcated from the fundamental
linear orbit in the vicinity of the bifurcation points, we use perturbation
theory to obtain their evolution away from the bifurcation points. As an
application, we derive an analytical semiclassical trace formula for the
density of states in the separable case, using a uniform approximation for the
pitchfork bifurcations occurring there, which allows for full semiclassical
quantization. For the non-integrable situations, we show that the uniform
contribution of the bifurcating period-one orbits to the coarse-grained density
of states competes with that of the shortest isolated orbits, but decreases
with increasing chaoticity parameter .Comment: 15 pages, LaTeX, 7 figures; revised and extended version, to appear
in J. Phys. A final version 3; error in eq. (33) corrected and note added in
prin
Analytic approach to bifurcation cascades in a class of generalized H\'enon-Heiles potentials
We derive stability traces of bifurcating orbits in H\'enon-Heiles potentials
near their saddlesComment: LaTeX revtex4, 38 pages, 7 PostScript figures, 2 table
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