Semiclassical approaches to nuclear dynamics

TL;DR

This paper develops a semiclassical framework for nuclear dynamics, combining the extended Gutzwiller approach with the Fermi-liquid droplet model to accurately describe collective excitations and transport properties in nuclei.

Contribution

It introduces a semiclassical method that integrates shell corrections into nuclear transport coefficients, improving agreement with experimental data beyond traditional quantum approaches.

Findings

Good agreement with experimental data on giant dipole resonances.

Shell effects diminish exponentially with increasing temperature.

Semiclassical moments of inertia match quantum results across deformations.

Abstract

The extended Gutzwiller trajectory approach is presented for the semiclassical description of nuclear collective dynamics, in line with the main topics of the fruitful activity of V.G. Solovjov. Within the Fermi-liquid droplet model, the leptodermous effective surface approximation was applied to calculations of energies, sum rules and transition densities for the neutron-proton asymmetry of the isovector giant-dipole resonance and found to be in good agreement with the experimental data. By using the Strutinsky shell correction method, the semiclassical collective transport coefficients such as nuclear inertia, friction, stiffness, and moments of inertia can be derived beyond the quantum perturbation approximation of the response function theory and the cranking model.The averaged particle-number dependence of the low-lying collective vibrational states are described in good agreement with basic experimental data, mainly due to an enhancement of the collective inertia as compared to its irrotational flow value. Shell components of the moment of inertia are derived in terms of the periodic-orbit free-energy shell corrections. A good agreement between the semiclassical extended Thomas-Fermi moments of inertia with shell corrections and the quantum results is obtained for different nuclear deformations and particle numbers. Shell effects are shown to be exponentially dampted out with increasing temperature in all the transport coefficients.