Theoretical investigation of Black-body Zeeman Shifts in Microwave Atomic Clock

With the development of microwave atomic clocks, black-body radiation Zeeman shifts need to be considered carefully. In this Letter, the frequency shifts of hyperfine splitting of ground state due to black-body magnetic field are investigated. The relative frequency shifts of different alkali atoms and alkali-like ions which could be candidates of microwave atomic clocks are calculated, and results are from -0.977E-17[T(K)/300]\textasciicircum 2 to 1.947E-17[T(K)/300]\textasciicircum 2 for different atoms. These results are consistent with previous works but with more precision, detailed derivations and clear physical pictures.