Bohr Hamiltonian of the Even–Even Nuclei with Quadrupole and Octupole Deformations

Quantization of the kinetic energy of a nucleus with deformation in curvilinear coordinates in the presence of octupole vibrations of its surface is performed. The obtained Hamiltonian differs from the previously known expression for quadrupole vibrations only in the coefficients before the differentiation operators \(∂ /∂ γ \) and \(∂ /∂ η \). This is due to the difference in the components of the moment of inertia tensor of the nucleus for quadrupole and octupole modes. An exact expression for the full Hamiltonian of an even–even nucleus is determined, taking into account both quadrupole and octupole deformations, including seven dynamic variables. Some fields of application of the proposed Hamiltonian are discussed. Abstract Published by the Jagiellonian University 2025 authors