High-accuracy calculation of black-body radiation shift in $^{133}$Cs primary frequency standard

TL;DR

This paper presents high-precision relativistic calculations of the black-body radiation shift in $^{133}$Cs, resolving discrepancies among previous methods and achieving uncertainties suitable for next-generation atomic clocks.

Contribution

It provides the most accurate theoretical value of the BBR shift coefficient for $^{133}$Cs, identifying errors in prior semi-empirical calculations and supporting improved clock accuracy.

Findings

Calculated BBR coefficient $eta=-(1.708\pm0.006) imes 10^{-14}$ at 300K

Achieved 0.35% accuracy in the BBR shift value

Resolved a 10% discrepancy with recent semi-empirical calculations

Abstract

Black-body radiation (BBR) shift is an important systematic correction for the atomic frequency standards realizing the SI unit of time. Presently, there is a controversy over the value of the BBR shift for the primary $^{133}$Cs standard. At room temperatures the values from various groups differ at $3 \times 10^{-15}$ level, while the modern clocks are aiming at $10^{-16}$ accuracies. We carry out high-precision relativistic many-body calculations of the BBR shift. For the BBR coefficient $\beta$ at $T=300K$ we obtain $\beta=-(1.708\pm0.006) \times 10^{-14}$, implying $6 \times 10^{-17}$ fractional uncertainty. While in accord with the most accurate measurement, our 0.35%-accurate value is in a substantial, 10%, disagreement with recent semi-empirical calculations. We identify an oversight in those calculations.