Q-phonon scheme in the collective nuclear model

The Q-phonon scheme developed in the framework of the algebraic collective nuclear model is discussed. It is shown that in the framework of this scheme the low-lying collective states of the even-even nuclei can be presented with an accuracy better than 90% of the norm using one or maximum two components of the Q-phonon basis constructed by an action of the fixed number of the quadrupole operators Q on the exact ground state of the system. Different applications of this approximate scheme are discussed. It is shown that using this scheme the relations between several E2-transition probabilities or between the energies of the collective states can be derived. It is shown also that the Q-phonon scheme can be used to extract an information about the equilibrium shapes of nuclei and their fluctuations from the data on the E2-transition probabilities