AN UPDATE ON THE THEORY OF ROTATIONAL ENERGY SURFACES

\begin{wrapfigure}{l}{0pt} \includegraphics[scale=0.3]{IcosaRES.eps} \end{wrapfigure} In Springer's \textit{Handbook for Atomic, Molecular, and Optical Physics}, William Harter gives a semiclassical theory of Hamiltonian Rotational Energy Surfaces. Therein accurate spectral estimates follow from classical precession integrals, real and complex. An analogy between the phase plane and the phase sphere suggests that integrals along a rotational energy surface can be known to the same precision as familiar standards such as the complete elliptic integral of the first kind. Newly developing integral-differential algorithms allow us to refine calculations on both domains. We will showcase a few results with high symmetry, and explain how they fit into a fully Riemannian perspective, which also improves upon the picture of tunneling phenomena