A Wentzel-Kramers-Brillouin (WKB) approach for calculating the lifetime of
the ground state of two coupled oscillators with the most probable escape p
ath along one of the coordinate axes is suggested. The WKB approximation of
the wave function in the neighborhood of this path is obtained by scaling
the corresponding variable. An analytic formula for the lifetime is derived
and numerically verified. The method is applied to the Henon-Heiles potent
ials. It is shown that the WKB method can be, in contrast to the numerical
ones, easily extended to the problems of an arbitrary number of spatial dim
ensions.