General Treatment of Vortical, Toroidal, and Compression Modes

TL;DR

This paper analyzes vortical, toroidal, and compression nuclear modes using the RPA method with Skyrme interactions, clarifying their relationships and dominant current contributions in $^{208}$Pb.

Contribution

It derives a simple relation between vortical, toroidal, and compression operators based on vorticity concepts and analyzes their properties within a consistent theoretical framework.

Findings

Isoscalar vortical and toroidal modes are dominated by convection current.

Isovector vortical and toroidal modes are dominated by magnetization current.

The compression mode is fully convective.

Abstract

The multipole vortical, toroidal, and compression modes are analyzed. Following the vorticity concept of Ravenhall and Wambach, the vortical operator is derived and related in a simple way to the toroidal and compression operators. The strength functions and velocity fields of the modes are analyzed in $^{208}$Pb within the random-phase-approximation using the Skyrme force SLy6. Both convection and magnetization nuclear currents are taken into account. It is shown that the isoscalar (isovector) vortical and toroidal modes are dominated by the convection (magnetization) nuclear current while the compression mode is fully convective. The relation between the above concept of the vorticity to the hydrodynamical vorticity is briefly discussed.