Calculation of multiphoton-ionization Greens functions using the Wentzel-Kramers-Brillouin approximation

We present a uniform method for approximating the functions that appear in the N-photon radial matrix element. This matrix element is required for calculating multiphoton-ionization cross sections and angular distributions in lowest-order perturbation theory. The functions include the initial- and final-state radial wave functions, and the regular and irregular parts of the radial Greens function. We point out that all of these functions satisfy a differential equation of the same form, and differ only in their boundary conditions. The WKB method is then applied to this differential equation to obtain approximations to all of these functions. We then use these solutions to calculate two-photon-ionization cross sections of hydrogen for photon energies between 8.5 and 13.2 eV. Also presented are two-photon-ionization cross sections for Cs around the minimum near the 7p resonance and comparisons with previous work.