Observing Quantum Tunneling in Perturbation Series

It is well-known that the quantum tunneling makes conventional perturbation series non-Borel summable. We use this fact reversely and attempt to extract the decay width of the false-vacuum from the actual perturbation series of the vacuum energy density (vacuum bubble diagrams). It is confirmed that, at least in quantum mechanical examples, our proposal provides a complementary approach to the conventional instanton calculus in the strong coupling region.