Analytical approach to the linear E circle times e Jahn-Teller problem - art. no. 195104

The E x e Jahn-Teller effect has been studied previously by many authors. T his system is important because, as well as providing results that are usef ul in their own right, such as for modeling experimental data, it is a rela tively simple system that can be used to test ideas before applying them to more complicated systems. The most notable feature of this system is that in linear coupling, the lowest adiabatic potential energy surface forms a t wo-dimensional trough. Vibrations across the trough and rotations around th e trough must both be taken into account. Previous analytical approaches to this system give results that differ by a factor of 2 from numerical resul ts in strong coupling. These approaches are also difficult to extend to mor e complicated systems. In this paper, we develop an analytical method that shows how the approach can be extended to other systems. We also eliminate the factor of 2 discrepancy by including coupling to the upper potential sh eet. Finally, we show that a reasonable approximation to the true linear co upling results can be obtained by including only those points on the trough that become minima when weak quadratic coupling is added to warp the troug h, as long as anisotropy in the resultant wells is taken into account.