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

TL;DR

This paper derives an empirical value for the Boltzmann constant using spectroscopic data of HeH$^{+}$, achieving higher precision than previous methods by incorporating relativistic and QED effects in polarizability calculations.

Contribution

It introduces a novel empirical approach to determine the Boltzmann constant with unprecedented precision using molecular spectroscopy data.

Findings

Empirical Boltzmann constant value with higher precision.

Relativistic and QED effects are crucial for accurate polarizability.

Theoretical dipole and quadrupole polarizabilities for $^{3}$He with high precision.

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.