Semiclassical approximations of photoabsorption cross sections beyond the continuum threshold

We develop semiclassical approximations for calculating photoabsorption cross sections beyond the continuum threshold in quantum many-body systems. These approximations use the fully quantum-mechanical Wigner function of the ground state and semiclassical expansions only for the part of the cross section depending on the continuum states, thus avoiding the difficult explicit calculation of the continuum states. Even though the approach is general, we test it in electronic-structure theory for the photoionization cross sections of the hydrogen and helium atoms. The results suggest that these semiclassical approximations can be used to obtain good estimates of cross sections at high energy.

Automated summary

We propose a semiclassical approximation method for calculating photoabsorption cross sections beyond the continuum threshold in quantum many-body systems. The method makes use of the fully quantum-mechanical Wigner function of the ground state and employs semiclassical expansions only for the part of the cross section that depends on the continuum states, avoiding the explicit calculation of these states. The results of testing the method in electronic-structure theory for the photoionization cross sections of hydrogen and helium atoms indicate that these semiclassical approximations can provide good estimates of cross sections at high energy.