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Progress of Theoretical Physics

A New Type of Bosonization of Quasi-Particle Pair Modes

K. Taniguchi, Y. Miyanishi

Published Oct 1, 1990• 1 citation
Publisher

Abstract

By using a unitary operator which maps the fermion space to the boson-fermion space we give a new type of bosonization of the correlated pair modes exhibiting the nuclear collective oscillations approximately. The relation to the conventional boson expansion method is briefly discussed.
DOI
10.1143/ptp.84.568

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We propose a new method that transcribes the fermion system to the boson-fermion system by introducing a unitary operator defined in the whole boson-fermion space. We obtain the boson-fermion expansion of the fermion pair operators such that only the collective pair modes are transformed into boson operators while the non-collective modes are unchanged in the lowest order approximation. The odd- A system is treated in the same formalism as the even-even nuclear system. We briefly discuss the relation between our method and the conventional boson expansion theory.
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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.
The bosonization method developed in nuclear physics in the last 20 years is briefly reviewed. Introduction In the last 20 years, a considerable amount of work has gone into the development of bosonization methods for highly correlated finite fermion systems. This work has been stimulated by the phenomenological successes of the interacting boson model introduced in 1974 in which atomic nuclei composed of nucleons (fermions) are treated in terms of an interacting system of bosons (fermion pairs). In this article the logic scheme of the bosonization method in nuclear physics will be briefly reviewed. The purpose here is to provide the basic references upon which the review is built and sources where further references can be found. Bosonization methods were introduced much earlier than 1974 in connection with infinite Fermi systems. The method developed in nuclear physics has some similarities with those developed in other areas of physics, but it also has major differences. In nuclear physics one maps not only operators but also states and seeks a description not only of the ground state but also of the entire excitation spectrum. Furthermore, number projection plays a very important role contrary to the case of infinite systems where number projection is not relevant. These differences, and others, will be briefly remarked upon in this article. Strongly Interacting Finite Fermion Systems Fermions and the Shell Model Quite often in physics one has to deal with a system of interacting fermions.