Application of the Dyson-type non-unitary representation of the self-consistent collective-coordinate method to simple models (I). SU(3) model

A reformulation of the self-consistent collective-coordinate (SCC) method has recently been given in a Dyson-type non-unitary representation. This method seems very useful to evaluate the coupling effect between the collective and non-collective degrees of freedom in nuclear many-body systems. In order to see how well it works, it is applied to an exactly solvable SU(3) model. The optimized boundary condition proposed by Matsuo and Matsuyanagi is used in solving the basic equations of the SCC method. The collective hamiltonian derived by the SCC method is quantized by using the canonical quantization procedure, in which we propose the Dyson ordering of operators. The resultant eigenstates of the quantized hamiltonian are compared with those of the exact calculation and the Dyson boson mapping.