Approximate Formula for Superposition State of two Level Atom and Large Number of Counterpropagating Photons

An approximate formula describing the time evolution of the state of two level atom and large number of counterpropagating photons interacting with it is obtained. This formula is a natural generalization of the diffraction scattering amplitude formula in the resonant Kapitsa-Dirac effect in the Raman-Nath approximation. The applicability of derived formula assumes more than n1,2 ≈ 20 photons in each of the counterpropagating beams.