Example: Born model for the calculation of the atomic photoionization cross-section

Atomic photoionization is a fundamental radiative process playing important role in the physics of photon-matter interaction. In the perturbation regime when the radiation field is much weaker than the intra-atomic field the photoionization cross section can be calculated in one photon approximation in the first-order of perturbation theory.

Born model for the calculation of photoionization cross section is derived for the spectral region far from the ionization threshold of nl atomic subshell. In this case the wave function of ejected photoelectron can be described with reasonable accuracy as a plane wave. Then the photoionization cross section is expressed via Fourier transform of the radial wave function Pnl(r) of ionized electronic subshell. Function  Pnl(r) can be obtained as the serial decomposition of Hartree-Fock solution via Slater-type wave functions with the tabulated coefficients.

Sodium atom photoionization cross section calculated in the frame of Born model is presented in the figure. Note that the lower limit of the photon energy is taken equal to 50 eV. This value is much greater than the ionization potential of the ground state of the sodium atom ( I3s=5.139 eV) so Born model is applicable for considered spectral region.

Photoionization cross section of the ground state of sodium atom calculated in the Born approximation (I3s=5.139 eV)

Order the data