Octupole response and stability of spherical shape in heavy nuclei

Abstract

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 $1\hbar\omega$ and $3\hbar\omega$ 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 $3^{-}$ 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 equation for finite systems of fermions with pairing

“…The static nuclear mean field is approximated with a spherical cavity of radius R = 1.2 A 1 3 fm and the A nucleons are treated on the same footing, i. e., we do not distinguish between neutrons and protons. Moreover, we chose A = 208 for ease of comparison with previous calculations of uncorrelated response functions [12,13]. Shell effects are not included in our semiclassical picture and the results shown below should be considered as an indication of the qualitative effects to be expected in heavy nuclei.…”

“…In the evaluation of the collective response, the value of parameters κ L is the same as in [12,13], that is: κ 2 = −1 × 10 −3 MeV/fm 4 and κ 3 = −2 × 10 −5 MeV/fm 6 .…”

Nuclear Response from the Vlasov Equation

“…The fixed-surface solution gives an adequate description of the giant quadrupole resonance, but fails to display extra strength in the region of surface excitations. Figure 2 (from Abrosimov et al (2003b)) instead displays the octupole (dV ext ¼ r 3 Y 3M (rˆ)) strength function for the same hypothetical nucleus of Figure 1, calculated with the two different boundary conditions (the solid and dashed curves have the same meaning as in Figure 1). The octupole V. I.…”

“…This question can be partially answered by comparing with experimental data the response to an external force evaluated by using different boundary conditions. Such a program has been carried out by our group for isoscalar (i.e., with neutron and proton densities oscillating in phase) excitations in heavy nuclei (Abrosimov et al 1999(Abrosimov et al , 2002a(Abrosimov et al , 2003a(Abrosimov et al , 2003b(Abrosimov et al , 2002b. This article is a review of that work.…”

Unified Semiclassical Approach to Isoscalar Collective Modes in Heavy Nuclei

“…In the present contribution we review a study the isoscalar collective modes in nuclei 6,7 made by using a semiclassical approach that includes the single-particle degrees of freedom explicitly and thus allows for an account the coupling between individual nucleons and surface motion. Our model is based on the linearized Vlasov kinetic equation for finite systems with moving surface 8,9 .…”