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

TL;DR

This paper derives a microscopic, self-consistent model for nuclear collective rotation-vibration motion in axially symmetric nuclei, extending previous phenomenological models without limiting oscillation amplitude.

Contribution

It introduces a novel microscopic derivation of the rotation-vibration model using a constrained variational approach and self-consistent equations applicable to arbitrary oscillation amplitudes.

Findings

Closed-form solutions for harmonic oscillator potentials

Application to ground-state rotational bands in nuclei

Comparison with experimental data shows good agreement

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 amplitude. The nuclear Schrodinger equation is canonically transformed the to collective co-ordinates, which is then linearized using a constrained variational method. The associated constraints are imposed on the wavefunction rather than on the particle co-ordinates. The approach yields three self-consistent, time-reversal invariant, cranking-type Schrodinger 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 the measured data.