QED calculation of the dipole polarizability of helium atom

TL;DR

This paper presents a highly precise QED calculation of helium-4's dipole polarizability, including finite nuclear mass effects, confirming previous results with improved accuracy and explaining discrepancies with earlier calculations.

Contribution

The study introduces a highly accurate QED-based computational method for helium's dipole polarizability, incorporating the electric-field derivative of the Bethe logarithm and finite nuclear mass effects.

Findings

Calculated the electric-field derivative of the Bethe logarithm as 0.0485572(14) a.u.

Total QED correction to polarizability is 30.6671(1) x 10^{-6} a.u.

Theoretical molar polarizability value is 0.51725408(5) cm^3/mol, matching experimental data.

Abstract

The QED contribution to the dipole polarizability of the $^4$He atom was computed, including the effect of finite nuclear mass. The computationally most challenging contribution of the second electric-field derivative of the Bethe logarithm was obtained using two different methods: the integral representation method of Schwartz and the sum-over-states approach of Goldman and Drake. The results of both calculations are consistent, although the former method turned out to be much more accurate. The obtained value of the electric-field derivative of the Bethe logarithm, equal to $0.048\,557\,2(14)$ in atomic units, confirms the small magnitude of this quantity found in the only previous calculation [G. {\L}ach, B. Jeziorski, and K. Szalewicz, Phys. Rev. Lett. 92, 233001 (2004)], but differs from it by about 5\%. The origin of this difference is explained. The total QED correction of the order of {\alpha} 3 in the fine-structure constant {\alpha} amounts to 30.6671(1)$\cdot 10^{-6}$, including the 0.1822$\cdot 10^{-6}$ contribution from the electric-field derivative of the Bethe logarithm and the 0.01112(1)$\cdot 10^{-6}$ correction for the finite nuclear mass, with all values in atomic units. The resulting theoretical value of the molar polarizability of helium-4 is $0.517\,254\,08(5)\,$cm$^3$/mol with the error estimate dominated by the uncertainty of the QED corrections of order $\alpha^4$ and higher. Our value is in agreement with but an order of magnitude more accurate than the result $0.517\, 254\, 4(10)\,$cm$^3$/mol of the most recent experimental determination [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)].