QED calculation of the dipole polarizability of helium atom

Abstract

The QED contribution to the dipole polarizability of the $^{4}\mathrm{He}$ 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 ${\ensuremath{\alpha}}^{3}$ in the fine-structure constant $\ensuremath{\alpha}$ amounts to $30.6671(1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, including the $0.1822\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ contribution from the electric-field derivative of the Bethe logarithm and the $0.011\phantom{\rule{0.16em}{0ex}}12(1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ correction for the finite nuclear mass, with all values in atomic units. The resulting theoretical value of the molar polarizability of helium-4 is $0.517\phantom{\rule{0.16em}{0ex}}254\phantom{\rule{0.16em}{0ex}}08(5)\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{3}/\text{mol}$ with the error estimate dominated by the uncertainty of the QED corrections of order ${\ensuremath{\alpha}}^{4}$ and higher. Our value is in agreement with but an order of magnitude more accurate than the result $0.517\phantom{\rule{0.16em}{0ex}}254\phantom{\rule{0.16em}{0ex}}4(10)\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{3}/\text{mol}$ of the most recent experimental determination [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)].