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Nuclear Physics A

A microscopic boson model for collective transition nuclei: Schwinger representation of the SO(8) shell model algebra

U. Kaup, Peter A. Ring, R. S. Nikam

Published Apr 1, 1988• 8 citations
Publisher
DOI
10.1016/0375-9474(88)90395-8

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With the aim of applying to the Lipkin model in the case of open shell system, a possible form of the boson realization for the su(2)-algebra is proposed both in the Schwinger and the Holstein-Primakoff representation. The basic idea is borrowed from the Schwinger boson realization for the su(4)-algebra for many-quark system recently presented by the present authors. As the simplest approximation, a certain approximate form is given and the result is a natural generalization of the RPA result in the case of closed shell system.

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Explicit construction of Dyson, Holstein-Primakoff, and Schwinger representations for random-phase approximation phonon operators is given within Lie algebraic framework. It is shown that these representations emerge as exact boson realizations of quadrupole collective algebra, but the enforcement of SU(6) symmetry involves important constraints embodied in definite nonlinear conditions imposed on random-phase approximation phonon amplitudes. The constructed Schwinger representation could be employed to provide alternative approach to the interacting boson model parameters, avoiding standard procedures of mapping the shell-model SD subspace into the sd boson space.
With the aim of applying to the Lipkin model in the case of open shell system, a possible form of the boson realization for the su(2)-algebra is proposed both in the Schwinger and the Holstein-Primakoff representation. The basic idea is borrowed from the Schwinger boson realization for the su(4)-algebra for many-quark system recently presented by the present authors. As the simplest approximation, a certain approximate form is given and the result is a natural generalization of the RPA result in the case of closed shell system.