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A theoretical expression is derived for the Kerr constant of a gas at low pressures using a general expression for the energy of a molecule in a strong electric field. It is shown that the temperature independent part is closely related to the change of molecular polarizability with field strength. For spherically symmetric systems, the measured Kerr constant can be used to find the magnitude of this hyperpolarizability.
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Buckingham et al. (1955) studied this question.
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