Shift Of 2s1/2 Hyperfine Splittings Due To Blackbody Radiation

Frequency shifts of hyperfine splittings of $^{2}S_{\frac{1}{2}}$ states due to the blackbody radiation 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 shift at 300 K is large enough to be significant in primary Cs atomic beam 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-Segr\`e formula for determining the contact hyperfine matrix elements. It is applied to ${\mathrm{Ba}}^{+}$ and ${\mathrm{Hg}}^{+}$, for which no experimental data are yet available, and which are currently of interest for frequency standards.