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Photon scattering cross sections have proved essential in many applications, such as modelling opacities and radiative transport, studying the cooling of astrophysical plasma, analysing planetary atmospheres, and Raman spectroscopy.
In particular, Raman spectroscopy of H$_{2}$ plays an important in analysing hydrogen storage techniques, monitoring ortho-to-para conversion, and monitoring nuclear waste.
Atomic and molecular hydrogen are abundant in the interstellar medium, with H$_{2}^{+}$ being formed by the radiative association of protons and atomic hydrogen, and ionisation of H$_{2}$.
Hence, photon scattering cross sections for H$_{2}$ and its ion are of particular interest in astrophysics.
Photon--molecule scattering processes have been well understood to second order in perturbation theory since the development of the Kramers--Heisenberg--Waller (KHW) matrix element [1,2] in the mid-1920s.
We have calculated photoionisation cross sections for all bound vibrational levels of the 1s$\sigma_{g}$ ground electron state of H$_{2}^{+}$ and its isotopologues [3].
Rayleigh and Raman scattering cross sections have been calculated for transitions between all rovibrational levels of the $X\,{}^{1}\Sigma_{g}^{+}$ ground electronic state of H$_{2}$, resulting in a total of 9582 Rayleigh and Raman cross sections [4].
This work represents the most comprehensive study of photon scattering on molecular hydrogen, and extends of our approach to photon scattering on atoms to diatomic molecules.
Isotopologue effects have been investigated and were found to be small.
Thermally-averaged photoionisation, Rayleigh, and Raman scattering cross sections have been produced for a system in local thermodynamic equilibrium.
Fig. 1 Photoionisation cross sections for all bound vibrational levels of the 1s$\sigma_{\mathrm{g}}$ ground electronic state of H$_{2}^{+}$ by unpolarised light.
Fig. 2 Local thermodynamic equilibrium Rayleigh scattering cross sections for a gas of H$_{2}$ at temperatures of 90, 300, 3000, and 9000 K.]2
[ 1] H. A. Kramers and W. Heisenberg, Z. Phys. 31, 681 (1925).
[ 2] I. Waller, Z. Phys. 51, 213 (1928).
[3] A. J. C. Singor, L. H. Scarlett, M. C. Zammit, I. Bray, and D. V. Fursa, ApJS 269, 19 (2023).
[4] A. J. C. Singor, L. H. Scarlett, M. C. Zammit, I. Bray, and D. V. Fursa, J. Chem. Phys. 161, 244304 (2024).
