Unified Semiclassical Approach to Isoscalar Collective Modes in Heavy Nuclei

Abstract

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.

Nature of Isoscalar Dipole Resonances in Heavy Nuclei

“…In this paper the collective isoscalar dipole excitations are considered within the translationinvariant kinetic model of small oscillations of finite Fermi systems [20]. This model makes it possible to find an analytic expression for the dynamic fluctuations of the distribution function in the phase space under collective isoscalar dipole excitations.…”

“…In Ref. [21], the isoscalar dipole response function was studied within the kinetic model [20], taking into account a residual interaction between nucleons. It was found that the response function has two-resonance structure and reproduces the experimental values for the centroid energies of the low-and high-energy isoscalar dipole resonances in heavy nuclei.…”

Residual Interaction Effect on Isoscalar Dipole Modes in Heavy Nuclei

“…In so doing, we suppose the system to be saturated in the spin-isospin space, so that there is no necessity in introducing those variables explicitly. The dynamical equations for our model can be written in the following form [21]:…”

“…In this work, the isoscalar dipole excitations of heavy nuclei are considered in the framework of the kinetic model describing small vibrations in a finite Fermi system confined by a moving surface [21]. This work is a continuation of work [15], in which the main attention was focused on the study of isoscalar dipole excitations in the zeroth-order approximation, i.e.…”

Isoscalar dipole response of heavy nuclei in low-energy region within kinetic model

“…In this paper, the collective isoscalar dipole excitations are considered within a translationinvariant kinetic model of small oscillations of finite Fermi systems [17]. In Section 2, we briefly recall the formalism of the kinetic model of collective dipole excitations in nuclei.…”