Closed formulas for ground band energies of nuclei with various symmetries

Abstract

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 the 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 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 all the known nuclear phases. Nuclei satisfying the specific symmetries of the critical point in the phase transitions O(6) → SU(3), SU(5) → SU(3) have also been considered. The agreement between the results and the corresponding experimental data is very good. This is reflected in very small root mean square values of deviations.