Schwinger's variational principle in its fractional form is applied to the study of vibrational excitations in collinear atomhyphen;harmonic oscillator collisions. Trial wavefunctions used are those of distorted waves derived from distortion potentials based on (a) a free molecule approximation, (b) an internal average, and (c) an optical potential recently proposed by Roberts. It is found that for nearest neighbor transitions in most of the systems studied a simple variational treatment yields transition probabilities superior to those of a perturbation expansion such as the distortedhyphen;wave Born series.
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