Abstract
When the Holstein-Primakoff (Hermitian)-type boson expansion theory is applied for nuclear structure calculations, truncation at the fourth-order expansion of the boson Hamil tonian is often used. The Dyson-type boson mapping has no difficulty concerning boson expansion, since the Dyson boson Hamiltonian is written in up to sixth-order boson oper ators, and we do not have to make any truncation of the boson expansion. In the present work, we propose a new clear-cut method to obtain the normal-ordered Holstein-Primakoff boson expansion. Using this method, we test whether or not the truncation of the boson expansion is good approximation in various cases. We show that truncation at the fourth order expansion of the normal-ordered Holstein-Primakoff boson Hamiltonian is a rather good approximation, but it is not sufficient for detailed analyses.
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