Effect of phase factor in kick approximation for super intense field ionization

Based on a simple consideration, the kick approximation used by Sundaram et al. in describing the interactions between super intense laser field and single atom is modified. Two different phase factors of the two kicks during one optical period are considered. It is found that we can introduce the factors in a very simple way and derive a new map which can be written in a closed form, and that to include these factors really improves the dynamical description of the system.