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Nuclear Physics A

Boson-like expansions without bosons: Application to several exactly soluble shell models with collective features

Pranab K. Chattopadhyay, Abraham Klein, Franz R. Krejs

Published Sep 1, 1974• 9 citations
Publisher
DOI
10.1016/0375-9474(74)90667-8

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Progress of Theoretical Physics•Mar 1, 1989•2 citations
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.
The selfconsistent-collective-coordinate method is applied to anharmonic quadrupole vibrations in a degenerate many j-shell model with the pairing-plus-quadrupole force. By comparing the result obtained by this method with that obtained by the boson-expansion method, it is shown that 1) the selfconsistent-collective-coordinate method yields, after a suitable canonical quantization, the result that agrees to order (j + 1/2)-1 with that obtained by the boson-expansion method, in the limit that the time-dependent Hartree-Bogoliubov space is truncated to the multiphonon space built out of the 2+ phonons, and 2) the couplings between the RPA 2+ phonons and the other modes (the pairing rotations and the noncollective modes) considerably modify the fourth-order boson Hamiltonian obtained by the conventional boson-expansion method.