Unified Cranking-Model Description of Bohr and VMI Approache

TL;DR

The paper presents a unified cranking-model analysis showing that both the Bohr and Variable Moment of Inertia (VMI) descriptions are limiting cases of a single framework. By decomposing the angular momentum into static and dynamic parts, it derives $\Im_{total} = 3 B \beta^2 + \eta$, where $\eta$ encodes Coriolis effects, and obtains the energy expression $E = \frac{1}{2} C' (\Im - \Im_0)^2 + \frac{\hbar^2 I(I+1)}{2 \Im}$ with $\Im_0 = 3 B \beta_0^2 + \eta$ and $C' = \frac{C}{36 B^2 \beta_0^2}$. A second-order Taylor expansion in small centrifugal stretching bridges Bohr's quadratic inertia dependence with a linear approximation, and explicitly isolates the Coriolis contribution, resolving the apparent contradiction between the two approaches. The results offer a coherent description of rotational spectra across deformation regimes and connect to related analyses such as Okhunov's corrections.

Abstract

A unified analysis based on the cranking model is presented, demonstrating that both the Bohr and Variable Moment of Inertia (VMI) models arise as limiting cases of this framework. This result resolves the apparent contradiction between the two models by showing that they correspond to different physical limits of the same formalism. In addition, this analysis explicitly reveals the contribution of Coriolis effects to the rotational energy and moment of inertia.