A microscopic derivation of nuclear collective rotation-vibration model, axially symmetric case

摘要

We derive a microscopic version of the successful phenomenologicalhydrodynamic model of Bohr-Davydov-Faessler-Greiner for collectiverotation-vibration motion of an axially symmetric deformed nucleus. Thederivation is not limited to small oscillation amplitude. The nuclearSchrodinger equation is canonically transformed the to collective co-ordinates,which is then linearized using a constrained variational method. The associatedconstraints are imposed on the wavefunction rather than on the particleco-ordinates. The approach yields three self-consistent, time-reversalinvariant, cranking-type Schrodinger equations for the rotation-vibration andintrinsic motions, and a self-consistency equation. For harmonic oscillatormean-field potentials, these equations are solved in closed forms and appliedto the ground-state rotational bands in some axially-symmetric nuclei. Theresults are compared with the measured data.