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

Abstract

We derive a microscopic version of the successful phenomenological hydrodynamic model of Bohr–Davydov–Faessler–Greiner for collective rotation–vibration motion of an axially symmetric deformed nucleus. The derivation is not limited to small oscillation amplitudes. The nuclear Schrödinger equation is canonically transformed to collective coordinates, and then linearized using a constrained variational method. The associated constraints are imposed on the wavefunction rather than on the particle coordinates. This approach yields three self-consistent, time-reversal invariant, cranking-type Schrödinger equations for the rotation–vibration and intrinsic motions, and a self-consistency equation. For harmonic oscillator mean-field potentials, these equations are solved in closed forms and applied to the ground-state rotational bands in some axially symmetric nuclei. The results are compared with those of other models and related measured data.