Nuclear shape fluctuations in Fermi-liquid drop model

Abstract

Within the nuclear Fermi-liquid drop model, quantum and thermal fluctuations are considered by use of the Landau-Vlasov-Langevin equation. The spectral correlation function of the nuclear surface fluctuations is evaluated in a simple model of an incompressible and irrotational Fermi liquid. The dependence of the spectral correlation function on the dynamical Fermi-surface distortion is established. The temperature at which the eigenvibrations become overdamped is calculated. It is shown that, for realistic values of the relaxation time parameter and in the high temperature regime, there is a particular eigenmode of the Fermi liquid drop where the restoring force is exclusively due to the dynamical Fermi-surface distortion.

Diffusion on the Distorted Fermi Surface

“…Usually, this is done by means of the Fermi-surface deformation. The fluid dynamic approximation gives a simple and clear-cut interpretation for the highly collectivized giant resonances and establishes a relation between the microscopic theory and phenomenological models such as the the liquid-drop one [3][4][5][6].…”

Small damping approach in Fermi-liquid theory

“…The stiffness coefficient C (ω) is caused by the dynamic Fermi surface distortion effect and it decreases strongly with increasing temperature T . Due to this fact, the stiffness coefficient C and the eigenenergy E decrease monotonically with temperature and approach the liquid drop model limit for large temperatures, see also [23]. As seen from Figure 1, the SDA leads to a significantly faster decrease of E with increasing temperature T , i.e., the SDA overestimates the decrease rate of the Fermi surface distortion effect with temperature.…”

“…Using Eqs. (1) and (3) we will derive a closed set of equations for the following p-moments of the distribution function, namely, local particle density ρ, velocity field u ν and pressure tensor P νμ , in the form (for details, see [5,21,23]) of…”

“…Note that the form of Eq. (14) is also correct for a nonMarkovian collision term, with the collision time τ being dependent on the frequency ω, see [23]. This ω-dependence is associated with memory effects in the interparticle collisions and the collision integral then takes the following form [22]:…”

Shape fluctuations in a Fermi system with nonlinear dissipativity

“…Considering the nuclear isoscalar quadrupole mode, we will assume an irrotational motion with the displacement field v( → r ) given by [31] v(…”