Quadrupole collective states within the Bohr collective Hamiltonian

The article reviews the general version of the Bohr collective model for the description of quadrupole collective states, including a detailed discussion of the model's kinematics. The quadrupole coordinates, momenta and angular momenta are defined and the structure of the isotropic tensor fields as functions of the tensor variables is investigated. After a comprehensive discussion of the quadrupole kinematics, the general form of the classical and quantum Bohr Hamiltonian is presented. The electric and magnetic multipole moment operators acting in the collective space are constructed and the collective sum rules are given. A discussion of the tensor structure of the collective wavefunctions and a review of various methods of solving the Bohr Hamiltonian eigenvalue equation are also presented. Next, the methods of derivation of the classical and quantum Bohr Hamiltonian from the microscopic many-body theory are recalled. Finally, the microscopic approach to the Bohr Hamiltonian is applied to interpret collective properties of 12 heavy even-even nuclei in the Hf-Hg region. Calculated energy levels and E2 transition probabilities are compared with experimental data.