RESUMMATION OF ANISOTROPIC QUARTIC OSCILLATOR - CROSSOVER FROM ANISOTROPIC TO ISOTROPIC LARGE-ORDER BEHAVIOR

We present an approximative calculation of the ground-state energy for the anisotropic oscillator with a potential 2)/2(x(2)+y(2))+g/4[x(4)2(1-delta)x(2)y(2)+y(4)]. Using an instanton solution for the isotropi c limit delta=0, we obtain the imaginary part of the ground-state ener gy for small negative g as a series expansion in the anisotropy parame ter delta. From this, the large-order behavior of the g expansions acc ompanying each power of delta are obtained by means of a dispersion re lation in g. The g expansions are summed by a Borel transformation, yi elding 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 devo ted to the immediate vicinity of the isotropy point. Using a simple mo del integral we show that the large-order behavior of a delta-dependen t series expansion in g undergoes. a crossover from an isotropic to an anisotropic regime as the order k of the expansion coefficients passe s the value k(cross)similar to 1/\delta\.