418 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
Kinetic-theory approach to low-energy collective modes in nuclei
Two different solutions of the linearized Vlasov equation for finite systems,
characterized by fixed and moving-surface boundary conditions, are discussed in
a unified perspective. A condition determining the eigenfrequencies of
collective nuclear oscillations, that can be obtained from the moving-surface
solution, is studied for isoscalar vibrations of lowest multipolarity. Analytic
expressions for the friction and mass parameters related to the low-enegy
surface excitations are derived and their value is compared to values given by
other models. Both similarities and differences are found with respect to the
other approaches, however the close agreement obtained in many cases with one
of the other models suggests that, in spite of some important differences, the
two approaches are substantially equivalent. The formalism based on the Vlasov
equation is more transparent since it leads to analytical expressions that can
be a basis for further improvement of the model.Comment: 16 pages, 1 EPS figure, to be published in Nucl. Phys.
Kinetic-theory description of isoscalar dipole modes
A semiclassical model, based on a solution of the Vlasov equation for finite
systems with moving-surface, is employed to study the isoscalar dipole modes in
nuclei. It is shown that, by taking into account the surface degree of freedom,
it is possible to obtain an exact treatment of the centre of mass motion. It is
also shown that a method often used to subtract the spurious strength in RPA
calculations does not always give the correct result. An alternative analytical
formula for the intrinsic strength function is derived in a simple
confined-Fermi-gas model. In this model the intrinsic isoscalar dipole strength
displays essentially a two-resonance structure, hence there are two relevant
modes. The interaction between nucleons couples these two modes and changes the
compressibility of the system. The evolution of the strength profile is then
studied as a function of the compressibility of the nuclear fluid. Comparison
with available data favours values of the incompressibility parameter of
nuclear matter smaller than those suggested by the analysis of the monopole
``breathing'' mode.Comment: 17 pages, 4 figures, revised version to be published in Nucl. Phys.
Unified semiclassical approach to isoscalar collective modes in heavy nuclei
A semiclassical model based on the solution of the Vlasov equation for finite
systems with a sharp moving surface has been used to study the isoscalar
quadrupole and octupole collective modes in heavy spherical nuclei. Within this
model, a unified description of both low-energy surface modes and higher-energy
giant resonances has been achieved by introducing a coupling between surface
vibrations and the motion of single nucleons. Analytical expressions for the
collective response functions of different multipolarity can be derived by
using a separable approximation for the residual interaction between nucleons.
The response functions obtained in this way give a good qualitative description
of the quadrupole and octupole response in heavy nuclei. Although shell effects
are not explicitly included in the theory, our semiclassical response functions
are very similar to the quantum ones. This happens because of the well known
close relation between classical trajectories and shell structure. The role
played by particular nucleon trajectories and their connection with various
features of the nuclear response is displayed most clearly in the present
approach, we discuss in some detail the damping of low-energy octupole
vibrations and give an explicit expression showing that only nucleons moving on
triangular orbits can contribute to this damping.Comment: 9 pages, 2 figures, Talk presented at the 8th International Spring
Seminar on Nuclear Physics on Key Topics in Nuclear Structure, Paestum,
Italy, May 23-27, 200
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
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