A simplified method for calculating the ac Stark shift of hyperfine levels of alkali-metal atoms

• New method to calculate the ac Stark shift of hyperfine levels is proposed.
• Our method has a simple form and a high accuracy.
• Our method can easily incorporate theoretical and experimental atomic structure data.
• Our method calculates differential light shifts at a reasonable accuracy.

The ac Stark shift of hyperfine levels of neutral atoms can be calculated using the third order perturbation theory (TOPT), where the third order corrections are quadratic in the atom–photon interaction and linear in the hyperfine interaction. In this paper, we use Green's function to derive the E[2+ϵ]E[2+ϵ] method which can give close values to those of TOPT for the differential light shift between two hyperfine levels. It comes with a simple form and easy incorporation of theoretical and experimental atomic structure data. Furthermore, we analyze the order of approximation and give the condition under which E[2+ϵ]E[2+ϵ] method is valid.