  The characteristic polynomial of the effective Hamiltonian for a general
model has been discussed. It is found that, compared with the associated energy
eigenvalues, this characteristic polynomial generally has better analytical
properties and larger convergence radius when being expanded in powers of the
interaction parameter, and hence is more suitable for a perturbation
calculation. A form of effective Hamiltonian which has the same singularities
(branch points) as such characteristic polynomial has also been constructed.
