Semiempirical Formula for Nuclear Rotational Energies

Abstract

Using the theory of molecular spectra to obtain an estimate of the higher-order corrections to the energy levels of a nonrigid rotator, we sum the infinite power series in $I(I+1)$ to describe the energy levels in the ground-state rotational bands of deformed even-even nuclei by the expression $E(I)=A(I)I(I+1)$, where $A(I)=\frac{A[1+(N\ensuremath{-}1)(\frac{B}{A})I(I+1)]}{[1+N(\frac{B}{A})I(I+1)]},$ with $N=2.85\ensuremath{-}0.05I$. The predictions of this two-parameter formula show surprisingly good agreement with the experimentally observed energy levels in even-even nuclei in the rare-earth region, including Os isotopes and $N=90$ nuclei. Comparison with other relatively successful models advanced during the recent years, e.g., the Davydov-Chaban model as adopted by the Berkeley group, the cranking-model extension by Harris, the classical hydrodynamical model used by Moszkowski, the rotator-vibrator model, the asymmetric-rotator model, etc., reveals a distinctly greater success of our description when it is applied to such a wide range of nuclei.