The rotational hyperpolarizability of a homonuclear diatomic molecule is calculated for all off-resonance third-order nonlinear optical processes. The treatment of rotations is fully quantum mechanical. The classical limit of the expression obtained for the dc Kerr effect agrees with the classical calculation in the static limit, but differs by a factor of (3/4 at optical frequencies.
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David P. Shelton (1987) studied this question.
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