Microscopic derivation of the generalized collective Hamiltonian

Abstract

The nucleus in the center-of-mass frame is described by 3A−3 independent coordinates, including three Euler angles and three variables ρ,β,andγ 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 β. It allows us to derive the Hamiltonian, which describes large-amplitude collective motions. At β≪1 it reduces to a sum of the Bohr Hamiltonian and the Hamiltonian of monopole ρ vibrations. As a result of straightforward calculations we obtain explicit expressions for all the inertial parameters as functions of the variables ρ,β,andγ. Published by the American Physical Society 2024