Application of a symmetry-adapted algebraic model to the vibratioinal spectrum of methane

Abstract

The stretching and bending vibrations of methane are studied in the framework of a symmetry-adapted algebraic model. The model is based on the realization of the one-dimensional Morse potential in terms of a $U(2)$ algebra. For the 44 observed energies we obtain a fit with a r.m.s. deviation of 1.16 cm${}^{-1}$ which is an order of magnitude more accurate than previous algebraic calculations.

5 pages, invited talk at ``21st International Colloquium on Group Theoretical Methods in Physics'', Goslar, Germany, July 15-20, 1996