Kinetic-theory approach to low-energy collective modes in nuclei

Abstract

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.

Kinetic-theory description of isoscalar dipole modes

“…motion (see also Ref. [12]). Clearly quantum calculations are, in principle, more rigorous than a semiclassical one, but our hope is that the physical insight allowed for by the semiclassical method will make our results more transparent.…”

“…The fluctuation δ̺ k (r, ω) is the time Fourier transform of the density fluctuation δ̺ k (r, t) induced by an external field V ext (r, t) = βδ(t)r k Y 1M (r). This fluctuation can be obtained by integrating over momentum the phase-space density fluctuation δn k (r, p, t) that is given by the solution of the linearized Vlasov equation, either with fixed-surface [17] or with movingsurface [11,12] boundary conditions: δ̺ k (r, t) = dp δn k (r, p, t).…”

“…[17] (the propagator D 0 L (x, y, ω) has been defined in [17]), while the quantities [12]. According to that equation…”

“…(A13) [12]). In this respect our results are also in qualitative agreement with the quantal RPA calculations of [8][9][10] and [13][14][15],that predict a two-resonance structure in the isoscalar dipole response.…”

Nuclear Response from the Vlasov Equation

“…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.…”