Large-dimensional shell-model calculation by using the Dyson boson mapping method

Kenjiro Takada, S Yasumoto

求 佐藤

Kosuke Takada

Kenjiro Takada, S. Tazaki, Seiichi Yasumoto

In order to truncate a high-dimensional Hilbert space for a many-nucleon shell model to a small collective subspace, we carry out a Dyson-type boson mapping and select a small number of collective bosons. In this way, we can divide the Dyson boson Hamiltonian into collective and non-collective parts; the latter includes the renormalization of the coupling effects between the collective and non-collective degrees of freedom. The boson Hamiltonian thus obtained is written in terms of the selected collective bosons only. Diagonalizing this boson Hamiltonian and comparing the numerical results with those obtained from exact shell-model calculations for some sd- and pf-shell nuclei, we find that our method gives a good approximation of the exact shell model. It is shown that the coupling effect between the collective and non-collective degrees of freedom plays an essential role. This method is also applied to some heavier pfg-shell nuclei for which it is unfeasible to carry out exact shell-model calculation because of the very large number of dimensions of the Hilbert space. Our numerical results are in very good agreement with experiment.

Takaharu Otsuka, Michio Honma, T. Mizusaki

P. Navrátil, J. Dobe

The shell-model fermion problem for systems of four protons and four neutrons in single-j shells is transformed into a boson problem using the generalized Dyson boson mapping. Exact boson calculations are performed. The spectrum of physical and nonphysical boson states and the effect of truncation in the boson space are studied. The necessity of transformation from the Dyson boson description to the seniority boson description is demonstrated within the truncated space.