Reformulation of Dyson's boson expansion theory

Abstract

Techniques, recently renovated to use for constructing the Hermitian form of the boson expansion theories, are used to reformulate the non-Hermitian boson expansion theory of Dyson. It is shown, in particular, that a combined use of the Usui operator method and the term-by-term bosonization method leads to a very natural rederivation of the Dyson expansions. The eigenvalue problem, including the derivation of separately normalized eigenbra and eigenket vectors, is also discussed. The results obtained here can be used to analyze both even-$A$ and odd-$A$ nuclei.NUCLEAR STRUCTURE Boson expansion theories, Hermitian, non-Hermitian, particle-pair representation, Tamm-Dancoff representation, Marumori-Yamamura-Tokunaga method, term-by-term bosonization method, even-$A$ nuclei, odd-$A$ nuclei, infinite expansions, finite expansions, minimal truncation, maximal truncation, nonorthonormal basis, Dyson theory, spin wave, kinematic origin of unharmonicity.