  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.
