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Nonvacuum bounces and quantum tunneling at finite energy.

A bouncelike solution with nonzero energy is used for the explicit calculation of the decay rate of an excited state of the inverted double-well potential. Three negative eigenvalues are associated with the second variation of the action at the nonvacuum bounce which is different from the case of the vacuum bounce. The imaginary part of the energy results only from the symmetry of the bounce itself, and the additional negative eigenvalues do not present difficulties. In fact, it is shown explicitly that only one negative eigenvalue contributes to the tunneling. The calculated imaginary part of the energy of the excited state is in agreement with that of WKB calculations. The tunneling effects are investigated for high and low energies compared with the barrier height. Finally the Bogomolny-Fateyev relation is established, thus checking our results.