SU(3) Shell Model in a Deformed Harmonic Oscillator Basis

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Abstract
The SU(3) shell model is studied for the nucleus in an axially symmetric deformed harmonic oscillator well. The intrinsic state of the SU(3) shell model in a deformed well is given by the boson Bogolyubov transformation on the corresponding one in a spherical well. By investigating the SU(3) irreducible tensor character of the generators of this transformation, a set of rules about the reduction of this deformed intrinsic state to physically interesting states of the ordinary SU(3) shell model is formulated. When the deformation of the harmonic oscillator well is small, a concrete form of the deformed intrinsic state is given. Furthermore, formulae of electric quadrupole moment and E2 transition probabilities are obtained for an arbitrary irreducible representation (λµ) with λ>µ. As an example, these physical quantities in the ground rotational band of 20Ne are calculated numerically.

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