NONVACUUM BOUNCES AND QUANTUM TUNNELING AT FINITE-ENERGY

A bouncelike solution with nonzero energy is used for the explicit cal culation of the decay rate of an excited state of the inverted double- well potential. Three negative eigenvalues are associated with the sec ond 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 additiona l negative eigenvalues do not present difficulties. In fact, it is sho wn explicitly that only one negative eigenvalue contributes to the tun neling. The calculated imaginary part of the energy of the excited sta te is in agreement with that of WKB calculations. The tunneling effect s are investigated for high and low energies compared with the barrier height. Finally the Bogomolny-Fateyev relation is established, thus c hecking our results.