Theoretical analysis of the nonlinear susceptibility of hydrogen atom

The nonlinear refractive index of air and other gases plays an important role in the understanding of the propagation of intense laser pulses in the atmosphere. Using a numerical basis state method $[1]$ we have performed accurate calculations of the nonlinear susceptibility in hydrogen atom. Currently, models of filamentation mainly use perturbative approaches to determine the nonlinear susceptibility. We compare our results from ab-initio calculations of the nonlinear susceptibity with those from a perturbative calculation. The comparison allows us to determine an intensity at which perturbation theory breaks down for these kinds of calculations. \\[0pt] [1] S.H. Chen et al., Phys. Rev. A {\bf 86}, 013410 (2012)