Frequency-dependent polarizability of helium including relativistic effects with nuclear recoil terms

TL;DR

This paper presents highly precise theoretical calculations of helium's frequency-dependent polarizability, including relativistic and nuclear recoil effects, to support future metrology standards with uncertainties below 0.2 ppm.

Contribution

It provides the first comprehensive calculation of helium's dynamic polarizability with relativistic effects and nuclear recoil, achieving unprecedented accuracy for metrology applications.

Findings

Polarizability at 632.9908 nm is 1.39181141 a.u.

Uncertainty of the calculated polarizability is 0.1 ppm.

Refractive index expansion of helium in powers of density was also obtained.

Abstract

Future metrology standards will be partly based on physical quantities computed from first principles rather than measured. In particular, a new pressure standard can be established if the dynamic polarizability of helium can be determined from theory with an uncertainty smaller than 0.2 ppm. We present calculations of the frequency-dependent part of this quantity including relativistic effects with full account of leading nuclear recoil terms and using highly optimized explicitly correlated basis sets. A particular emphasis is put on uncertainty estimates. At the He-Ne laser wavelength of 632.9908 nm, the computed polarizability value of 1.391 811 41 a.u. has uncertainty of 0.1 ppm that is two orders of magnitude smaller than those of the most accurate polarizability measurements. We also obtained an accurate expansion of the helium refractive index in powers of density.