Shape invariants in the multiple ''Q-excitation'' scheme

Simple relations are derived within the IBA which express the ground state expectation values of various multiples of the quadrupole operator in terms of a few E2 transition probabilities connecting low-lying collective states. A comparison with the exact IBA results for boson numbers N=6 and 12 reveals an accuracy better than 85% over the whole symmetry triangle. For the IBA parameter range physically important for the description of nuclear data the accuracy is better than 90%. Using these relations, the values of the cubic and fourth-order scalars and also the average value of the asymmetry parameter γ are determined for several nuclei. (orig.)