An algebraic treatment of the nuclear quadrupole degree of freedom

The collective quadrupole degree of freedom is described by a SU(6) algebra, generated by five generalized coordinates and conjugated momenta and their commutators. On this basis a collective Hamiltonian is derived where the parameters of the realistic nuclear Hamiltonian (single particle energies, matrix elements of the interaction) appear in terms of a few constants. The algebraic properties of the collective variables lead to a new quantum number N which restricts the maximal number of phonons contained in the collective states. The collective Hamiltonian is applied to the transitional nuclei ¹⁵²Gd and ^{150, 152}Sm. The transformation into the intrinsic frame of reference yields explicit formulae for the potential energy, the mass coefficients and the moments of inertia in terms of the intrinsic deformation parameters.