First-principles calculation of the frequency-dependent dipole polarizability of argon

Abstract

In this work we report state-of-the-art theoretical calculations of the dipole polarizability of the argon atom. Frequency dependence of the polarizability is taken into account by means of the dispersion coefficients (Cauchy coefficients) which is sufficient for experimentally relevant wavelengths below the first resonant frequency. In the proposed theoretical framework, all known physical effects including the relativistic, quantum electrodynamics, finite nuclear mass, and finite nuclear size corrections are accounted for. We obtained $\alpha_0=11.0763(19)$ for the static polarizability and $\alpha_2=27.976(15)$ and $\alpha_4=95.02(11)$ for the second and fourth dispersion coefficients, respectively. The result obtained for the static polarizability agrees (within the estimated uncertainty) with the most recent experimental data [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)], but is less accurate. The dispersion coefficients determined in this work appear to be most accurate in the literature, improving by more than an order of magnitude upon previous estimates. By combining the experimentally determined value of the static polarizability with the dispersion coefficients from our calculations, the polarizability of argon can be calculated with accuracy of around $10\,$ppm for wavelengths above roughly $450\,$nm. This result is important from the point of view of quantum metrology, especially for a new pressure standard based on thermophysical properties of gaseous argon. Additionally, in this work we calculate the static magnetic susceptibility of argon which relates the refractive index of dilute argon gas with its pressure. While our results for this quantity are less accurate than in the case of the polarizability, they can provide, via Lorenz-Lorentz formula, the best available theoretical estimate of the refractive index of argon.