26 research outputs found
Effects of surface vibrations on quadrupole response of nuclei
The effect of quadrupole-type surface vibrations on the quadrupole response
function of heavy nuclei is studied by using a model based on the solution of
the linearized Vlasov equation with moving-surface boundary conditions. By
using a separable approximation for the residual interaction, an analytical
expression is obtained for the moving-surface response function. Comparison of
the fixed- and moving-surface strength functions shows that surface vibrations
are essential in order to achieve a unified description of the two
characteristic features of the quadrupole response: the giant resonance and the
low-lying states. Calculations performed by setting the surface tension equal
to zero shows that the low-lying strength is strongly affected by the surface
tension.Comment: Appendix added, version to be published in Nucl. Phys.
Octupole response and stability of spherical shape in heavy nuclei
The isoscalar octupole response of a heavy spherical nucleus is analyzed in a
semiclassical model based on the linearized Vlasov equation. The octupole
strength function is evaluated with different degrees of approximation. The
zero-order fixed-surface response displays a remarkable concentration of
strength in the and regions, in excellent
agreement with the quantum single-particle response. The collective
fixed-surface response reproduces both the high- and low-energy octupole
rsonances, but not the low-lying collective states, while the
moving-surface response function gives a good qualitative description of all
the main features of the octupole response in heavy nuclei. The role of
triangular nucleon orbits, that have been related to a possible instability of
the spherical shape with respect to octupole-type deformations, is discussed
within this model. It is found that, rather than creating instability, the
triangular trajectories are the only classical orbits contributing to the
damping of low-energy octupole excitations.Comment: 10 pages, Latex file, 7 ps figure
Self-consistency and collective effects in semiclassical pairing theory
A simple model, in which nuclei are represented as homogeneous spheres of
symmetric nuclear matter, is used to study the effects of a self-consistent
pairing interaction on the nuclear response. Effects due to the finite size of
nuclei are suitably taken into account. The semiclassical equations of motion
derived in a previous paper for the time-dependent Hartree-Fock-Bogoliubov
problem are solved in an improved (linear) approximation in which the pairing
field is allowed to oscillate and to become complex. The new solutions are in
good agreement with the old ones and also with the result of well-known quantum
approaches. The role of the Pauli principle in eliminating one possible set of
solutions is also discussed. The pairing-field fluctuations have two main
effects: they restore the particle-number symmetry which is broken in the
constant- approximation and introduce the possibility of collective
eigenfrequencies of the system due to the pairing interaction. A numerical
study with values of parameters appropriate for nuclei, shows an enhancement of
the density-density strength function in the region of the low-energy giant
octupole resonance, while no similar effect is present in the region of the
high-energy octupole resonance and for the giant monopole and quadrupole
resonances.Comment: 31 pages, 6 eps figure
Velocity dependent interactions and a new sum rule in bcc He
Recent neutron scattering experiments [PRL,{\bf 88},p.195301 (2002)] on solid
He, discovered a new optic-like mode in the bcc phase. This excitation was
predicted by a recently proposed model that describes the correlated atomic
zero-point motion in bcc Helium in terms of dynamic electric dipole moments.
Modulations of the relative phase of these dipoles between different atoms
describes the anomalously soft T(110) phonon and two new optic-like modes,
one of which was recently found in the neutron scattering experiments. In this
work we show that the correlated dipolar interactions can be written as a
velocity dependent interaction. This then results in a modified f-sum rule for
the T(110) phonon, in good agreement with the recent experimental data.Comment: 5 pages, 3 figure
Probabilistic Approach to Pattern Selection
The problem of pattern selection arises when the evolution equations have
many solutions, whereas observed patterns constitute a much more restricted
set. An approach is advanced for treating the problem of pattern selection by
defining the probability distribution of patterns. Then the most probable
pattern naturally corresponds to the largest probability weight. This approach
provides the ordering principle for the multiplicity of solutions explaining
why some of them are more preferable than other. The approach is applied to
solving the problem of turbulent photon filamentation in resonant media.Comment: LaTex, 22 page