Semiclassical features of rotational ground bands

A time dependent variational principle is used to dequantize a second order quadrupole boson Hamiltonian. The classical equations for the generalized coordinate and the constraint for angular momentum are quantized and then analytically solved. A generalized Holmberg-Lipas formula for energies is obtained. A similar $J(J+1)$ dependence is provided by the coherent state model (CSM) in the large deformation regime, by using an expansion in powers of $1/x$ for energies, with $x$ denoting a deformation parameter squared. A simple compact expression is also possible for the near vibrational regime. These three expressions have been used for 44 nuclei covering regions characterized by different dynamic symmetries or in other words belonging to the all known nuclear phases. Nuclei satisfying the specific symmetries of the critical point in the phase transitions $O(6)\to SU(3)$, $SU(5)\to SU(3)$ have been also considered. The agreement between the results and the corresponding experimental data is very good. This is reflected in very small r.m.s. values of deviations.