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An analytical model for the Jahn - Teller system

The Jahn - Teller (JT) problem is investigated analytically using a unitary transformation method. Minimization of the adiabatic energy surface for this problem results in wells of either or symmetry, depending on the coupling strengths. The dynamic JT problem is then solved in the tunnelling regime using projection operators to find symmetrized combinations of the states associated with the wells. By analogy to other JT systems, the ground state would be expected to have the same degeneracy as the original orbital state, and thus to be an H-type quintet. However, it is found that there are a range of couplings strengths for the g and h modes for which the tunnelling ground state for the wells can be an A-type singlet. A similar result was recently found for the pure JT system. It is also found that for wells, the limiting value of the tunnelling splitting between the H and A states for a pure system tends to in weak coupling, whilst for a pure system it tends to . For systems coupled to both modes, the value of the tunnelling splitting strongly depends upon which of the two modes is dominant. Both the level ordering in strong coupling and the anomalous behaviour in weak coupling can be shown to be fundamental symmetry properties of these JT systems, and not consequences of the details of our model. The JT systems studied here are possible models for the ground state of the cation and for an excited state of the anion .