  In this paper, we explore the metastable states of nonlinear Klein-Gordon
equations with potentials. These states come from the instability of a bound
state under a nonlinear Fermi's golden rule. In [16], Soffer and Weinstein
studied the instability mechanism and obtained an anomalously slow-decaying
rate $1/(1+t)^{\frac{1}{4}}$. Here we develop a new method to study the $L^2_x$
norm of solutions to Klein-Gordon equations. With this method, we prove the
first $H^1$ scattering result for Klein-Gordon equations with metastable
states. By exploring the oscillations, we also give another more robust and
more intuitive approach to derive the sharp decay rate $1/(1+t)^{\frac{1}{4}}$.
