Inverting the Rayleigh-Schroedinger perturbation series: Application to atomic stabilization by intense light

We develop a method for calculating the (quasi)energy eigenvalue E(F) of a hydrogen atom in a nonperturbative ac field of strength F starting from a knowledge of the coefficients E(2m) of the Rayleigh-Schroedinger perturbation series E(F)=tsumm=0ME(2m)F2m. We first use the coefficients E(2m) (the unperturbed energy is E(0)) to construct the inverse series F2(E)=tsumm=1MF(m)(E-E(0))m. We resum the latter series using the Pade method, and solve the implicit equation F2(E)=bar F2 for E(bar F). The reconstructed function E(F) has the singularity structure appropriate to the true E(F). We are able to obtain good results for the lifetime of a hydrogen atom in a high-frequency field up to very high intensities, well into the (highly nonperturbative) stabilization regime