A photoionisation cross-section quantifies the probability that an atom, ion, or molecule will absorb a photon and subsequently eject an electron, resulting in ionisation. It is a fundamental parameter in atomic, molecular, and optical physics, describing how strongly a particular species interacts with incident electromagnetic radiation at a given photon energy. The cross-section is typically measured in units of area (such as square centimeters, cm²), representing an effective target area for the photoionisation process.

The photoionization cross section is defined as the probability per unit area that a photon with a particular energy will ionize an atom or molecule. It is usually expressed in units of square centimeters (cm²).

Different orbitals and different elements all have varied σ(ω), and so the utilisation of a variable photon energy source (such as synchotron XPS) to assess, for example, band structure in solids results in markedly different lineshapes at different energies.(1)

Several computational approaches are used to determine photoionisation cross-sections:

• R-matrix method: This is a widely used technique for complex atoms and ions, allowing accurate treatment of electron correlation and resonance effects.

• Close-coupling approximation: Used to solve coupled integro-differential equations for bound and continuum states, often in conjunction with the R-matrix method.

• Stieltjes imaging technique: Applied for molecules, this method reconstructs continuum oscillator strength densities from discrete basis set calculations.

• Effective mass and finite element methods: Used in solid-state systems or nanostructures, especially for impurity-related photoionisation in quantum dots.

Recently, the Applied X-ray Spectroscopy team at UCL (headed by Dr. Anna Regoutz) undertook the incredibly useful task of digitising photoionisation cross sections of all elements from 1 ≤ Z ≤ 103 for a wide range of common excitation energies.

You can find this great resource here.

If you do use any of the work provided by the Regoutz group, be sure to cite the original paper:

J.J. Yeh, I. Lindau, Atomic subshell photoionization cross sections and asymmetry parameters: 1 ⩽ Z ⩽ 103, Atomic Data and Nuclear Data Tables, Volume 32, Issue 1, 1985, Pages 1-155, ISSN 0092-640X, https://doi.org/10.1016/0092-640X(85)90016-6.

Also, cite the digitised version to give credit to the amazingly useful work that the Regoutz team have put in to developing this fantastic resource!

C. Kalha, N. K. Fernando, C. Vigil Hernandez, E. E. Kurtulus, J. Li, Y. Zhou, A. Regoutz, Digitisation of Yeh and Lindau Photoionisation Cross Section Tabulated Data, 2020, figshare, Datase, https://doi.org/10.6084/m9.figshare.12389750.v2.

1. Green, J. C. and P. Decleva (2005). “Photoionization cross-sections: a guide to electronic structure.” Coordination chemistry reviews 249(1-2): 209-228. Read it online here.