A possible quantum fluid-dynamical approach to vortex motion in nuclei

Abstract

The essential point of Bohr-Mottelson theory is to assume a irrotational flow. As was already suggested by Marumori and Watanabe, the internal rotational motion, i.e., the vortex motion, however, may exist also in nuclei. So, we have a necessity of taking the vortex motion into consideration. In a classical fluid dynamics, there are various ways to treat the internal rotational velocity. The Clebsch representation, v(x) = -\nabla \phi(x) + \lambda(x) \nabla \psi(x) (\phi ; velocity potential, \lambda and \psi: Clebsch parameters) is very powerful and has an advantage deriving equations of fluid motion from a Lagransian. Making the best use of the advantage, Kronig-Thellung, Ziman and Ito obtained a Hamiltonian including the internal rotational motion, the vortex motion, through the term \lambda(x) \nabla \psi(x). Going to quantum fluid dynamics, Ziman and Thellung finally derived a roton spectrum of liquid Helium II postulated by Landau. Is it possible to apply such the manner to a description of the collective vortex motion in nuclei? The description of such a collective motion has never been treated in the Bohr-Mottelson model (BMM) for a long time. In this paper, we will investigate a possibility of describing the vortex motion in nuclei basing on the theories of Ziman and Ito together with Marumori's work.Comment: 23 pages, no figures, Publication versio

Velocity operator approach to a Fermion system

“…He transformed the quantum-fluid Hamiltonian (3.24) to one in configuration space and obtained the classical-fluid Hamiltonian for the case of irrotational flow [7,11]. From this view point, very recently, we have developed a quantum-fluid approach to vortex motion in nuclei [14]. In this work we have introduced Clebsch parameterization making it possible to describe canonically quantum-fluid dynamics and have done Clebsch-parameterized gauge potential possessing Chern-Simons number (quantized helicity) [15,16,17].…”