Bounce in the valley: study of the extended structures from thick-wall to thin-wall vacuum bubbles

The valley structure associated with quantum metastability is examined. It is defined by the new valley equation, which enables a consistent evaluation of the imaginary-time path-integral. We study the structure of this new valley equation and solve it numerically. The valley is shown to contain the bounce solution, as well as other bubble structures. We find that even when the bubble solution has a thick wall, the outer region of the valley consists of a series of large-radius, thin-wall bubbles, whose interior is occupied by the true vacuum. Smaller bubbles, which contribute to the decay at higher energies, are also identified.