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Using the coupled cluster method (CCM), we present a simple accurate calculation for the energies of the ground- and first excited states of the linear E x e Jahn-Teller and pseudo-Jahn-Teller Hamiltonians. From the solution of a single transcendental equation, we obtain results with a maximal error of 1.2%. These results are notably better than previous results obtained both via the CCM and other many-body approximations.

We compare the static approximation to the Hubbard-Stratonovich representation of the partition function with the order parameter representation based on the Landau theory of phase transitions and we find that the two expressions for the partition function are very similar if we choose the expectation value of the potential for the order parameter of the system. This choice for the order parameter has certain advantages above choosing the BCS energy gap for the order parameter in that it generalizes naturally for momentum-dependent pairing interactions and that it remains well defined in exact treatments. In a simple ${\mathit{i}}_{13/2}$-model calculation different choices for the order parameter are compared with the exact grand canonical and with the static path integral results.