Angular distribution in the two-quantum atomic photoeffect

Total and differential two-photon ionization cross sections are derived in the framework of perturbation theory, assuming a simple one-electron atomic model. It is shown that for an unpolarized target the angular distribution of the ejected electrons has the general form $\mathrm{a}+b{cos}^{2}\ensuremath{\theta}+c{cos}^{4}\ensuremath{\theta}$, whatever the quantum numbers $n$, $l$, of the initial energy level, and the state of polarization (linear or circular) of the incident radiation. The total transition rates for circularly and for linearly polarized light are quite different from each other. For an arbitrary $\mathrm{nl}$ state, the theoretically allowed maximum value of their ratio is $\frac{3}{2}$. Further analytical and numerical results are presented for hydrogen. The Appendix contains several useful summation formulas for spherical harmonics.