The paper discusses the concept ofQ‐phonons and its connection to the concept ofQ‐invariants and the shape parameters of nuclei. It will also discuss some useful relations betweenQ‐invariants and observables. These relations allow one to determine crucial nuclear observables such as the square of the quadrupole moment of the first 2+state from lifetime data of the gamma‐ and ground band which may have applications, in future measurements with rare isotopes beams. These concepts are discussed for the Barium, Xenon and Cerium nuclei with mass numbers aroundA= 130, because some of these concepts were either introduced or at least heavily used in the discussion of the nuclear structure of these nuclei. © 2002 American Institute of Physics