A Python-Based Framework for Computing Departure Coefficients of Radio Recombination Lines

Radio recombination lines (RRLs) diagnose electron density and temperature in ionized environments. However, current models fail to match observed RRL optical depths and line broadening, indicating unresolved discrepancies in existing theory. We develop a Python-based framework to compute RRL b_n departure coefficients as functions of electron density and temperature, focusing on cold, low-density H II regions where high principal quantum number (𝑛) transitions dominate. This approach incorporates dielectronic recombination and ℓ-mixing, refining hydrogenic b_n calculations to resolve discrepancies in optical depth and line broadening predictions. This unified computational model aims to reconcile inconsistencies across existing models. Once validated, it will support the training of machine learning algorithms for automated RRL spectral analysis and parameter estimation.