Multiphoton ionization rates for circular and linear polarization are calculated at threshold for various hydrogenic s states in the framework of ordinary perturbation theory. Circularly polarized light turns out to be more efficient in many cases.
The ratio ${\ensuremath{\mu}}_{N}$ of the cross section for circularly polarized light to that for linearly polarized is numerically investigated for N-photon ionization of atomic hydrogen. For N<4, it appears that the gain factor is greater than unity. For $N\ensuremath{\ge}4$, the ratio ${\ensuremath{\mu}}_{N}$ is generally smaller than unity and decreases when the multiphoton order N increases.