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The triaxial quadrupole collective Hamiltonian, based on relativistic energydensity functionals, is extended to include a pairing collective coordinate. Inaddition to triaxial shape vibrations and rotations, the model describespairing vibrations and the coupling between triaxial shape and pairing degreesof freedom. The parameters of the collective Hamiltonian are determined by acovariant energy density functional, with constraints on the intrinsic triaxialshape and pairing deformations. The effect of coupling between triaxial shapeand pairing degrees of freedom is analyzed in a study of low-lying spectra andtransition rates of $^{128}$Xe. When compared to results obtained with thestandard triaxial quadrupole collective Hamiltonian, the inclusion of dynamicalpairing compresses the low-lying spectra and improves interband transitions, inbetter agreement with data. The effect of zero-point energy (ZPE) correction onlow-lying excited spectra is also discussed.

Coupling shape and pairing vibrations in a collective Hamiltonian based  on nuclear energy density functionals (II): low-energy excitation spectra of  triaxial nuclei