Non-Unitary Realization of the Selfconsistent Collective-Coordinate Method

Abstract

Recently we reformulated the selfconsistent collective•coordinate (See) method of Marumori, Maskawa, Sakata and Kuriyama.In this reformulation, biunitary forms of state vectors are used and the resultant representation corresponds to a c-number image of the Dyson-type boson expansion theory.This non-unitary version of the see method is rederived from a general point of view in order to clarify the relation to the original unitary version.Moreover, it is shown that the expansion technique to solve the basic equations is as applicable to this new version as to the unitary one, so that applications to realistic problems are easily done. § 1. IntroductionRecently it has bec;:ome increasingly important to determine the collective subspace selfconsistently for understanding the anharmonicity or non-linearity of the large amplitude nuclear collective motion.The selfconsistent collective-coordinate (See) method,*) originally proposed by Marumori, Maskawa, Sakata and Kuriyama,l) is promising for this purpose because it can properly take into account the effect of coupling to non-collective degrees of freedom.It is known that, if the coupling effect or the dynamical anharmonicity effect is neglected, this theory turns to the wellknown boson expansion theory for only the collective phonons under a suitable quantization procedure.Then, it enables us to construct a new type of "dynamical boson expansion theory" which incorporates the dynamical anharmonicity as well as the kinematical one originating from the Pauli principle.This new dynamical boson theory is expected to provide us a powerful method for investigating the nuclear structure problems full-microscopically.The original version of the see method corresponds, roughly speaking, to the Holstein-Primakoff type boson theory.6),7)Quite recently we have shown in Ref. 2) (from now on referred to as 1) that there exists another version corresponding to the Dyson-type boson theory; namely, a "non-unitary realization" of the see method, so to speak.Although both the types of boson theory are strictly equivalent to each other, the Dyson theory is more convenient for realistic applications, since a method of hermitian treatment of the theory is established.3 ) Therefore the newly proposed Dyson version of the see method can be superior for the purpose of investigating the dynamical coupling effect, because the kinematical anharmonicity is evaluated without any approximation such as truncation of the expansion.In other words, the "zero-th order collective subspace" is constructed without any ambiguities.*) The see method itself has a wide range of applicabilities, e.g., to heavy ion reactions, spontaneous fissions and rotational motions.lO)However, we are mainly concerned, in this paper, with an application to the boson description of low-lying collective states.