On the empirical dipole polarizability of He from spectroscopy of HeH${}^{+}$

Abstract

Using a long-range polarization potential for HeH${}^{+}$, we can obtain an empirical value for the Boltzmann constant $k_B$ with an order of magnitude greater precision than the previous best experimental value based on the dipole polarizability of ${}^4$He. We find that relativistic and QED effects of order ${\alpha }_{\mathrm{FS}}^3$ in the fine structure constant are crucial in the quadrupole polarizability in order to fit the dipole polarizbility with this precision using the polarization potential. By calculating finite-mass corrections for ${}^3$He, we also present theoretical values for the dipole and quadrupole polarizabilities of ${}^3$He with 9 and 7 digits of precision respectively.

We thank Krzystof Pachucki, Z-C. Yan, Stephen Lundeen, Richard Drachman, Anand Bhatia, Robert Le Roy, Grzegorz Lach, and Jim Mitroy for helpful discussions