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Communications in Theoretical Physics

Independent Descriptions of the collective Degrees of Freedom of Nuclei (I)

Lu DaHai, Yang LiMing

Published Mar 15, 2000• 0 citations
Publisher

Abstract

The present paper attempts to give independent descriptions of the collective degrees of freedom of nuclei such as the monopole and quadrupole ones in order to avoid the seniority mixing problem. This is done by the operatorized Bogoliubov transformation (OBT) which separates the degree of freedom from the rest described by the seniority particle operator which is not coupling to the pairs, and in terms of which the independent pair is composed. The OBT is derived in such a way that it can be generalized easily to include a new kind of “seniority particle operator” neither coupling to the nor to the pairs. In terms of this new particle operator the independent pair or the independent odd particle in odd nuclei is constructed.

DOI
10.1088/0253-6102/33/2/227

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The present paper attempts to give independent descriptions of the collective degrees of freedom of nuclei such as the monopole and quadrupole ones in order to avoid the seniority mixing problem. This is done by the operatorized Bogoliubov transformation (OBT) which separates the degree of freedom from the rest described by the seniority particle operator which is not coupling to the pairs, and in terms of which the independent pair is composed. The OBT is derived in such a way that it can be generalized easily to include a new kind of “seniority particle operator” neither coupling to the nor to the pairs. In terms of this new particle operator the independent pair or the independent odd particle in odd nuclei is constructed.
Introduction In many cases in physics, one has to deal simultaneously with collective and single-particle excitations of the system. The collective excitations are usually bosonic in nature while the single-particle excitations are often fermionic. One is therefore led to consider a system which includes bosons and fermions. In this book we discuss applications of a general algebraic theory of mixed Bose- Fermi systems to atomic nuclei. The collective degrees of freedom here can be described in terms of a system of interacting bosons as discussed in a previous book (Iachello and Arima, 1987), henceforth referred to as Volume 1. The single-particle degrees of freedom represent the motion of individual nucleons in the average nuclear field. They are described in terms of a system of interacting fermions. The coupling of fermions and bosons leads to the interacting boson-fermion model which has been used extensively in recent years to discuss the properties of nuclei with an odd number of nucleons. The interacting boson-fermion model was introduced by Arima and one of us in 1975 (Arima and Iachello, 1975). It was subsequently expanded by Iachello and Scholten (1979) and cast into a form more readily amenable to calculations. As in the corresponding case of even-mass systems, the algebra of creation and annihilation operators can be realized in several ways. One of these is the Hoistein-Primakoff realization which leads to a slightly different version of the interacting boson-fermion model called the truncated quadrupole phonon-fermion model (Paar, 1980; Paar and Brant, 1981), based on the boson realization introduced by Janssen, Jolos and Donau in 1974 and discussed in Sect. 1.4.6 of Volume 1.
A new method treating the interplay of pairing and intrinsic modes of excitation is proposed. In this method, the pairing mode associated with the J = 0-coupled nucleon pairs is represented by pairing bosons and the intrinsic mode characterized by the seniority quantum number is explicitly treated by ideal quasi-particle operators. We obtain a closed expression of the single-nucleon operator in terms of pairing bosons and ideal quasi-particles. As a simple illustration, the superconducting system is treated by introducing the coherent state of pairing bosons and the relation to the Bogoliubov transformation is discussed. The relation between this method and the canonical transformation method with auxiliary variables is also clarified.
We discuss the construction of ideal space seniority images of single fermion operators which proceeds via the generalized Dyson mapping and a subsequent similarity transformation. Particular attention is paid to the implications of a consistent treatment of single-particle and collective degrees of freedom. The results are compared with expressions for the mapped single fermion operators previously obtained, respectively, within the Otsuka-Arima-Iachello framework and by using the prescriptions of nuclear field theory. We point out certain inconsistencies in existing constructions of interacting-boson-fermion model operators in general and the interacting-boson-fermion model quadrupole operator in particular.
Abstract A generalization of the quantum mechanical representation transformation is presented, in this paper. It is shown that, as an important example, the Boson-expansion method, commonly employed in nuclear physics, corresponds to such a generalized transformation. Using this generalization, we were able to construct a special representation called the “Composite Particle Representation”. In the composite, particle representation, the composite particle degrees of freedom are included, as well as the original particle degrees of freedom. The former is introduced in order that the motion of certain particle clusters can be described as separate entities in a many-body system. This representation is shown to be exactly equivalent to the usual quantum mechanical representation which includes only the original particle degrees of freedom. Many applications of this theory are expected, in particular in the study of hadrons from the quark point of view and the Interacting Boson Model in nuclei.