Symplectic Basis for Constructing Intrinsic Wave Functions of the Three-Body System

Abstract

Symplectic models appeared as a useful tool to describe the dynamics of collective quadrupole and monopole excitations in nuclei.l)-5) But this approach is not convenient for the investigation of dynamics of the cluster degrees of freedom. If collective excitations described by the cluster motion have a characteristic intrinsic . function, it is necessary to use some corresponding manifolds of the intrinsic fl,mction. Furthermore, if the manifolds .of the intrinsic function for the cluster motion can be constructed by using the symplectic generators, we can make a unified treatment of the cluster and symplectic excitations. In this work, by using generating functions for the intrinsic excitations we show that it is possible to keep a principal building stone of the Sp (4, R) model describing the intrinsic dynamics in degrees of freedom of a three-nucleon system (a threeparticle system). Since these degrees of freedom are described by relative distances between the particles, the basis states have a connection with the cluster channel wave functions. In order to carry out calculations of a three-nucleon system within this model, we make the necessary expressions of matrix elements with the basis states. In § 2, we introduce the generating functions and the Sp(4, R) generators. Using the generating functions, the basis functions in the generating parameter space are given in § 3. In § 4, matrix elements of the nucleon-nucleon interaction are also discussed for the basis functions. For the practical study of a three-nucleon system, asymptotic wave functions of the breathing mode (§ 5) and the basis for a (1 +2)-cluster channel (§ 6) are investigated. Finally, we give a conclusion in § 7.