Stark Effect in Ground-State Hyperfine Structure Calculated for Na and K Atoms

We have used perturbation theory to calculate the shift due to an electric field E in the frequency of the hfs transition (F=I+1/2,0)↔(F=I-1/2,0) for the ground states of the Na and K atoms. The frequency shift δf=-k×10^-6E²Hz(V/cm)², and we calculate k to be 0.111 and 0.061 for Na and K, respectively. Electron correlations are not included. The corresponding experimental values measured by Mowat are 0.124 ±{} 0.004 and 0.071 ±{} 0.002.