NONADIABATIC CORRECTIONS FOR COUPLED OSCILLATORS USING RAYLEIGH-SCHRODINGE PERTURBATION-THEORY OF VERY HIGH ORDERS

Prospects for higher order perturbation theory in evaluating nonadiabatic corrections to the adiabatic energy levels are investigated by performing calculations on a series of two-dimensional anharmonically coupled oscillators. The convergence properties of the perturbation series are demonstrated for different harmonic frequencies and magnitudes of perturbation. It is found that the perturbation series corresponding to the adiabatic levels which are away from any intersections can accurately be summed, by means of the Padé summation technique, even in the case of "giant" couplings. The proposed "nondegenerate" perturbation theory procedure may also provide accurate results, under certain conditions, even in the case of intersecting energy levels. It fails to converge only in the regions around the crossing points. Elsewhere, it converges safely (especially when using high-accuracy arithmetics) and provides the basis for relatively accurate interpolation over the crossing regions. © 1995 American Institute of Physics.