Norm operator method for boson expansions

We propose a new boson expansion theory, without using the closed-algebra approximation indispensable for their formulations until now, as an extension of the conventional practical boson expansion methods that have tried to elucidate nuclear collective motion. The limitation of both the number of phonon excitations and the sorts of phonon excitation modes results in proper boson expansions and allows the use of ideal boson state vectors. The norm operator plays a crucial role and makes it possible to perform boson expansions without the closed-algebra approximation. The treatment of the norm operator determines whether the type of mapping is Hermitian or not, while the boson expansions become infinite expansions regardless of the types of mapping. The closed-algebra approximation, which closes the commutation relations among selected phonons, becomes effective only when including too many sorts of phonon excitations that the small parameter expansions become impossible and the ideal boson state vectors include the spurious components. Its application to the small parameter expansions causes neglecting the terms of the next-to-leading order of magnitude. The conventional practical boson expansion methods, which use the closed-algebra approximation, should be replaced by those that do not use the closed-algebra approximation.Comment: 37 pages, submitted to PTE