Triaxiality and the determination of the cubic shape parameter K 3 from five observables

The absolute and the relative quadrupole shape invariants ${q}_{3}$ and ${K}_{3}$ provide a model independent measure of triaxiality for \ensuremath{\beta}-rigid nuclei. We will show that one can obtain approximate values of ${q}_{3}$ and ${K}_{3}$ by analytical formulas involving only few observables. These formulas allow one to get a---model independent---error for these approximate values. The approximations which are made will be shown to hold within a few percent both in the rigid triaxial rotor model and the interacting boson model. The shape parameter ${K}_{3}$ is given for an exemplary set of nuclei and is translated into effective values of the geometrical deformation parameters \ensuremath{\beta} and \ensuremath{\gamma}.