Jahn-Teller systems as displaced para-Bose oscillators

It is shown that the E-e and Γ8−τ2g Jahn-Teller systems are respectively the infinite direct sums of the integer and half-integer (with the exclusion of the pure Bose case) irreducible displaced para-Bose oscillators. The energy spectrum of an arbitrary displaced para-Bose oscillator is considered. The ground state energy is calculated variationally by use of the para-Bose coherent states. The oscillatory behavior of the excited states is discussed. The results are applied to the E-e and Γ8−τ2g systems.