Nuclear collective dynamics within Vlasov approach

TL;DR

This paper uses the Vlasov equation to study isovector modes in nuclear matter, revealing how the symmetry energy's slope influences collective excitations like the Pygmy Dipole Resonance in isotopic chains.

Contribution

It introduces a Vlasov-based approach to analyze the impact of symmetry energy slope on nuclear collective modes and dipole responses in finite nuclei.

Findings

Dipole polarizability depends on the symmetry energy slope.

The Pygmy Dipole Resonance energy sum rule scales linearly with isospin squared.

Sensitivity of collective modes to symmetry energy parameters is demonstrated.

Abstract

We discuss, in an investigation based on Vlasov equation, the properties of the isovector modes in nuclear matter and atomic nuclei in relation with the symmetry energy. We obtain numerically the dipole response and determine the strength function for various systems, including a chain of Sn isotopes. We consider for the symmetry energy three parametrizations with density providing similar values at saturation but which manifest very different slopes around this point. In this way we can explore how the slope affects the collective response of finite nuclear systems. We focus first on the dipole polarizability and show that while the model is able to describe the expected mass dependence, A^{5/3}, it also demonstrates that this quantity is sensitive to the slope parameter of the symmetry energy. Then, by considering the Sn isotopic chain, we investigate the emergence of a collective mode, the Pygmy Dipole Resonance (PDR), when the number of neutrons in excess increases. We show that the total energy-weighted sum rule exhausted by this mode has a linear dependence with the square of isospin I=(N-Z)/A, again sensitive to the slope of the symmetry energy with density. Therefore the polarization effects in the isovector density have to play an important role in the dynamics of PDR. These results provide additional hints in the investigations aiming to extract the properties of symmetry energy below saturation.