Boson models of quadrupole collective motion

The subject of the lecture is the low-lying excitations of even-even (e-e) spherical nuclei. The predominant role of the quadrupole mode, which determines the structure of spectra and transitions, is obvious on the background of shell periodicity and pair correlations. Typical E2-transitions are strengthened Ω ∼ A2/3 times in comparison with single particle evaluations. Together with the regularity of the whole picture it gives evidence about collectivization of quadrupole motion. The collective states are combined in bands, where the transition probability are especially great; frequencies ω of the strengthened transitions are small in comparison with pair separation energies of 2 E-bar ∼ 2 MeV. Thus, the description of low-lying excitations of spherical nuclei has to be based on three principles: collectivity (Ω >> 1), adiabaticity (τ ≡ ω/2E-bar << 1) and quadrupole symmetry