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For around 100 years, hydrogen spectral modelling has been based on Voigtprofile fitting. The semi-classical Voigt profile is based on a 2-level atomapproximation. Whilst the Voigt profile is excellent for many circumstances,the accuracy is insufficient for very high column density damped Lyman-$\alpha$absorption systems. We have adapted the quantum-mechanical Kramers-Heisenbergmodel to include thermal broadening, producing a new profile, the KHT profile.Interactions involving multiple discrete atomic levels and continuum terms, notaccounted for in the Voigt model, generate asymmetries in the Lyman line wings.If not modelled, this can lead to significant systematics in parameterestimation when modelling real data. There are important ramifications inparticular for measurements of the primordial deuterium abundance. However, theKHT model is complicated. We therefore present a simplified formulation basedon Taylor series expansions and look-up tables, quantifying the impact of theapproximations made. The KHT profile has been implemented within thewidely-used VPFIT code.

Quantum mechanics at high redshift -- Modelling Damped Lyman-$\alpha$ absorption systems