Application of the Bohr Hamiltonian of the even–even nuclei with quadrupole and octupole deformations

The general theory of quadrupole and octupole excitation of even–even nuclei is described by using the Hamilton operator. The exact form of the total Hamiltonian of an even–even nucleus with quadrupole and octupole deformation contains seven dynamical variables [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. A general analytical solution of the Schrödinger equation with this Hamiltonian has not yet been found. Therefore, the study of collective excitations of even–even nuclei is carried out by introducing simplifying assumptions. The most significant approximations arising from these simplifications are discussed. Calculations of the energies of collective states of even–even nuclei are performed within the approximations of effective nonaxiality, axial symmetry and rigid nonaxial rotator. The obtained results are in good agreement with the corresponding experimental data.