  We present an approximative calculation of the ground-state energy for the
anisotropic anharmonic oscillator Using an instanton solution of the isotropic
action $\delta = 0$, we obtain the imaginary part of the ground-state energy
for small negative $g$ as a series expansion in the anisotropy parameter
$\delta$. From this, the large-order behavior of the $g$-expansions
accompanying each power of $\delta$ are obtained by means of a dispersion
relation in $g$. These $g$-expansions are summed by a Borel transformation,
yielding an approximation to the ground-state energy for the region near the
isotropic limit. This approximation is found to be excellent in a rather wide
region of $\delta$ around $\delta = 0$. Special attention is devoted to the
immediate vicinity of the isotropic point. Using a simple model integral we
show that the large-order behavior of an $\delta$-dependent series expansion in
$g$ undergoes a crossover from an isotropic to an anisotropic regime as the
order $k$ of the expansion coefficients passes the value $k_{{\rm cross} \sim
1/ |{\delta}|$.

Quantum Physics