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The third-harmonic coefficient of an atom is obtained in terms of zeroth-, first-, and second-order wave functions. The results of an accurate variations calculation of the third-harmonic coefficient of helium is presented. The zero-frequency third-harmonic coefficient is 42. 8 a. u. which is identical to the static hyperpolarizability obtained by Grasso, Chung, and Hurst. The 1s²→1s2p transition wavelength is determined to be 582 {} compared with the experimental result of 584 {}.
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R. Klingbeil (1973) studied this question.
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