Measurement of the hyperpolarizability ratioXyyyy(−2ω;0,ω,ω)Xyyxx(−2ω;0,ω,ω)for the inert gases

The ratio of dc electric-field-induced optical second-harmonic coefficients $R\equiv \frac{X_{\mathrm{yyyy}}(-2\mathrm{}\omega ;0,\omega ,\omega )}{X_{\mathrm{yyxx}}(-2\mathrm{}\omega ;0,\omega ,\omega )}$ has been measured for each of the inert gases. The results at $\omega =0.066\mathrm{}$ a.u. (the ruby-laser frequency) are: helium, 2.97 ± 0.03; neon, 3.01 ± 0.05; argon, 2.99 ± 0.04; krypton, 2.96 ± 0.04; and xenon, 3.03 ± 0.04. In the limit $\omega =0\mathrm{}$, symmetry considerations require $R=3\mathrm{}$. A theoretical estimate of $R$ at $\omega =0.066\mathrm{}$ a.u. predicts deviations from 3 which are significantly larger than those observed experimentally.