Microscopic derivation of the generalized collective Hamiltonian

The nucleus in the center-of-mass frame is described by 3A-3 independent coordinates, including three Euler angles and three variables rho, beta, and gamma to describe orientation, size, and shape of the nuclear inertia ellipsoid as well as 3A-9 generalized Euler angles to describe internal motion of the nucleons. Based on the idea that the incompressible nucleus has constant density, we suggest a definition of the deformation parameter beta. It allows us to derive the Hamiltonian, which describes large-amplitude collective motions. At beta << 1 it reduces to a sum of the Bohr Hamiltonian and the Hamiltonian of monopole rho vibrations. As a result of straightforward calculations we obtain explicit expressions for all the inertial parameters as functions of the variables rho, beta, and gamma.