Nuclear vorticity in isoscalar E1 modes: Skyrme-RPA analysis

Two basic concepts of nuclear vorticity, hydrodynamical (HD) and Rawenthall-Wambach (RW), are critically inspected. As a test case, we consider the interplay of irrotational and vortical motion in isoscalar electric dipole E1(T=0) modes in $^{208}$Pb, namely the toroidal and compression modes. The modes are described in a self-consistent random-phase-approximation (RPA) with the Skyrme force SLy6. They are examined in terms of strength functions, transition densities, current fields, and formfactors. It is shown that the RW conception (suggesting the upper component of the nuclear current as the vorticity indicator) is not robust. The HD vorticity is not easily applicable either because the definition of a velocity field is too involved in nuclear systems. Instead, the vorticity is better characterized by the toroidal strength which closely corresponds to HD treatment and is approximately decoupled from the continuity equation.