  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
$E^{[2+\epsilon]}$ 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 $E^{[2+\epsilon]}$ method is valid.
