SHIFT OF ²S_l/2 HYPERFINE SPLITTINGS DUE TO BLACKBODY RADIATION AND ITS INFLUENCE ON FREQUENCY STANDARDS

Abstract
Frequency shifts of hyperfine splittings of ²S_1/2 states due to the blackbody electric field are calculated. It is shown that they can be estimated from the dc hyperfine Stark shifts, which have previously been measured in the ground states of hydrogen and the alkali atoms. The shifts scale as T⁴. The fractional shift for Cs at 300 K is -1.7 x 10^-14, which is large enough to be significant in primary frequency standards, and should be measurable. A simple method of calculating the hyperfine Stark shifts is described, which is based on the Bates-Damgaard method for determining radial matrix elements and the Fermi-Segrè formula for determining the contact hyperfine matrix elements. It agrees with the experiment to within 12% for the entire alkali series. It is applied to Ba⁺ and Hg⁺, for which no experimental data are yet available, and which are currently of interest for frequency standards. At 300 K, the fractional shifts are -9.9 x 10^-17 and -2.4 x 10^-15 for Hg⁺ and Ba⁺, respectively. The shift due to the blackbody magnetic field is -1.3 x 10^-17 [T(K)/300]² for any ²S_1/2 state.