Sodium beacon adaptive optics (AO) system has been proved to be a highly productive tool for improving the resolving power of large-aperture ground-based telescope imaging. The performance of the AO system is mainly limited by photon return of the sodium beacon, which is determined by the coupling efficiency that characterizes the interaction rate between sodium laser and sodium atoms. The interaction processing is strictly influenced by the collisions of sodium atoms with other molecules (N2, O2). Most of the existing collision kernels are assumed as the "memoryless" hard collision, which is completely velocity reset in a Maxwellian distribution of the sodium atoms after scattering. To be more realistic, we adopt a more practical "memory" Cusp weak collision kernel, considering the velocity distribution of sodium atoms after collisions are correlated with the velocity before collision. By solving the Bloch equations, the processing for the interaction between sodium laser and sodium atom with Cusp kernel is established, and the coupling efficiency of sodium beacon with different collision kernel by analyzing the population is obtained. The researching results show that, for "memoryless" kernel, comparing to Cusp kernel with shaping parameter (s) of 100, the coupling efficiency is larger than 56% at best case; for sodium laser with 12% power detuned to D2b line and at a power density ranges from 10 to 100 W/m2, the coupling efficiency of "memoryless" kernel is nearly the same as "memory" Cusp kernel with s of 10, 100 and 3 Cusp kernel.