Unified numerical model of collisional depolarization and broadening rates that are due to hydrogen atom collisions

Context. Accounting for partial or complete frequency redistribution when interpreting solar polarization spectra requires data on various collisional processes. Data for depolarization and polarization transfer are needed, but are often lacking, while data for collisional broadening are usually more readily available. Recently it was concluded that despite underlying similarities in the physics of collisional broadening and depolarization processes, the relations between them cannot be derived purely analytically. Aims. We aim to derive accurate numerical relations between the collisional broadening rates and the collisional depolarization and polarization transfer rates that are due to hydrogen atom collisions. These relations would enable accurate and efficient estimates of collisional data for solar applications. Methods. Using earlier results for broadening and depolarization processes based on general (i.e., not specific to a given atom), semi-classical calculations that employ interaction potentials from perturbation theory, we used genetic programming (GP) to fit the available data and generate analytical functions describing the relations between them. The predicted relations from the GP-based model were compared with the original data to estimate the accuracy of the method. Results. We obtain strongly nonlinear relations between the collisional broadening rates and the depolarization and polarization transfer rates. They are shown to reproduce the original data with an accuracy of about 5%. Our results allow determining the depolarization and polarization transfer rates for hyperfine or fine-structure levels of simple and complex atoms. Conclusions. We show that by using a sophisticated numerical approach and a general collision theory, useful relations with sufficient accuracy for applications are possible.