A SCALE TRANSFORMATION IN T-CIRCLE-TIMES-T(2) JAHN-TELLER SYSTEMS

The T x t Jahn-Teller (JT) system has been studied previously by many authors. It is well known that the potential energy surface for this s ystem contains four equivalent wells in strong coupling. The wells are not isotropic. In the strong coupling limit, the vibrational t-mode s plits into a(1)-mode of frequency omega(T) and an e-mode of frequency root(2/3)omega(T). However, it is difficult to incorporate this anisot ropic effect into analytical models. Previously, the current authors h ave used a unitary shift transformation and energy minimization proced ure to model many moderately to strongly coupled JT systems. However, the part of the Hamiltonian which produces the anisotropy was not trea ted fully. We now present a modification of this procedure for the T x t system in which a scale transformation is applied in addition to th e shift transformation. This is shown to introduce anisotropy automati cally into the problem. We show that the correct frequencies are obtai ned in the infinite coupling limit. Symmetry-adapted combinations of t he states associated with the wells are taken to obtain expressions fo r the T-1 ground state and A(2) inversion level. The inversion splitti ng between them is compared with existing results. We then discuss how the scale transformation method can be applied to other JT systems (f or which the limiting frequencies are unknown), such as those in the I -h symmetry which applies to the C-60 molecule.