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 $\alpha_{{\rm FS}}^{3}$ 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.