Experimental determination of the dispersion in the mean linear dipole polarizability α(ω) of small hydrocarbons and evaluation of Cauchy moments between 325 nm and 633 nm

Abstract

The frequency dependent linear mean dipole polarizability α(ω) of the hydrocarbons CH4, C2H6, C3H8, n — C4H10, C(CH3)4 (neopentane), C2H4, C3H6, and cyclo — C3H6 has been determined by precise measurements of the refractive index in the frequency range between 0·07198116 a.u. (λ = 632·990 nm) and 0·1401389 a.u. (λ = 325·130 nm). This is the first experimental determination of α(ω) in the UV frequency region of neopentane and cyclopropane. It will be shown, that the uncertainty in the relative dispersion Δα(ω)/Δω of α(ω) is mostly determined by the uncertainty in the frequency of the radiation sources used. In addition, Cauchy moments S(-2), S(-4), S(-6), and S(-8) are calculated with an extended numerical procedure from the measured data sets, showing that a simple Gaussian least-squares fit of α(ω) in ω2 is not sufficient to obtain S(-2k). In addition, some data of the relative dispersion of the second refractivity virial coefficient of some of these gases are presented.