We consider a single state stochastically coupled to its stochastic background states. The fluctuation of the strength function of the single state is systematically studied for the first time. We find that the upper and lower deviations of the strength function only depend on the ratio of the spreading width over the decay width of the single state and on the ratio of the common decay width over the mean level spacing of the background states. Based on two fit formulae for the upper and lower deviations the uncertainties of the full width at half maximum (FWHM) and lifetime of a single state are estimated. They predict the experimental error bars of the FWHM and lifetime. A comparison of the uncertainties with the experimental error bars is made for nuclear giant dipole resonance, which illuminates our theoretical predictions.
The triaxial superdeformed bands in odd mass nuclei are analysed by applying the Holstein-Primakoff transformation both to the total angular momentum and to the single-particle angular momentum in the triaxial rotor model. The special attention is paid to the D_2 symmetry in the Hamiltonian. By comparing this algebraic expression with the numerical results from the exact diagonalization of the rotor Hamiltonian, the quantum numbers are assigned to each level.