QED calculation of the dipole polarizability of helium atom

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 $0.0485572(14)$ in atomic units, confirms the small magnitude of this quantity found in the only previous calculation [G. Łach, 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 α 3 in the fine-structure constant α 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 $0.51725408(5)$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 $0.5172544(10)$cm${}^3$/mol of the most recent experimental determination [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)].

References in corpus (7)

• ${\alpha }^4$ Ry corrections to singlet states of helium
• Relativistic, QED, and finite nuclear mass corrections for low-lying states of Li and Be${}^{+}$
• Complete ${\alpha }^{6}m$ corrections to the ground state of H${}_2$
• Helium energy levels including $m{\alpha }^6$ corrections
• Frequency-dependent polarizability of helium including relativistic effects with nuclear recoil terms
• Nuclear Charge Radii of ${}^{10,11}$B
• Refractive index and generalized polarizability

Cited by in corpus (4)

• Precision Measurements in Few-Electron Molecules: The Ionization Energy of Metastable ${}^4$He${}_2$ and the First Rotational Interval of ${}^4$He${{}_2}^{+}$
• Path-integral calculation of the fourth virial coefficient of helium isotopes
• Relativistic treatment of diamagnetic susceptibility of helium
• Rotational state-changing collisions of C${}_2$H${}^{-}$ and C${}_2$N${}^{-}$ anions with He under interstellar and cold ion trap conditions: a computational comparison