  Variational perturbation theory is used to determine the decay rates of
metastable states across a cubic barrier of arbitrary height. For high
barriers, a variational resummation procedure is applied to the complex energy
eigenvalues obtained from a WKB expansion; for low barriers, the variational
resummation procedure converts the non-Borel-summable
Rayleigh-Schr\"o\-din\-ger expansion into an exponentially fast convergent one.
The results in the two regimes match and yield very accurate imaginary parts of
the energy eigenvalues. This is demonstrated by comparison with the complex
eigenvalues from solutions of the Schr\"odinger equation via the
complex-coordinate rotation method.

Quantum Physics