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

Abstract

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.

Scattering Polarisation of the d-States of Ions and Solar Magnetic Field: Effects of Isotropic Collisions

“…Based on these tables, we used our Genetic Programming (GP) method of fitting in order to provide analytically general relationships between collisional rates, n * and E p . This method has been used successfully in Derouich et al (2015) and in Derouich (2017). The GP method minimises the summed square of the difference between the tabulated rates and rates obtained from the GP relationships.…”

“…Derouich et al 2015, Derouich et al 2003a. As done in most semi-classical collisional approaches, the approximation of the rectilinear trajectories is adopted in the collisional method of this work.…”

“…In this context, we developed an original collisional code which enables us to provide a large amount of the collisional depolarisation and polarisation transfer rates (e.g. Derouich et al 2015, Derouich et al 2003b). As done in most semi-classical collisional approaches, the approximation of the rectilinear trajectories is adopted in the collisional method of this work.…”

“…The study of the widths, shifts, and (de)polarisation of spectral lines under the influence of collisions with neutral perturbers has already been the subject of numerous studies (e.g. Lemaire, Chotin, & Rostas 1985;Baird, Eckart, & Sanderman 1979;Monteiro et al 1988;Chambaud & Lévy 1989;Anstee & O'Mara 1991;Spielfiedel et al 1991;Krsljanin & Peach 1993;Leininger, Gadéa, & Dickinson 2000;Derouich et al 2003b;Derouich, Radi, & Barklem 2015, see also Barklem 2016 and references therein). In addition, Anstee, Barklem and O'Mara (ABO) developed a powerful semi-classical theory during the 1990s for collisional line broadening by neutral hydrogen (Anstee & O'Mara 1991Anstee 1992;Anstee, O'Mara, & Ross 1997;; Barklem & O'Mara 1997;Barklem, Anstee, & O'Mara 1998).…”

Function mining for the < PT> -Nch correlations in pp and pp(bar) collisions based on symbolic regression

“…Many new physics results will be presented as a direct product from the successful application of different SR methods in different physics and science experiments to model and predict the experimental data; for example, Derouich et al [18] applied it in astronomy and astrophysics, Schmidt and Lipson [17] used it to rediscover the fundamental laws of nature, Cai [19] used it to model heat transfer correlations, Quade [20] investigated the prediction of dynamic systems using symbolic regression, Hills et al [21] discovered Lagrangians automatically from data based on SR, Kurse et al [22] studied the extrapolatable analytical functions using this technique, Yang [23] modeled oil production based on SR, Murari [24] investigated the derivation of confinement scaling laws, Golafshania [25] predicted the self-compacting concrete elastic modulus using two SR techniques, Guven and Aytek [26] built a new approach for modeling the stage-discharge relationship in hydrology, and Guven et al [27] empirically modeled evapotranspiration. The success of the SR methods in the abovementioned fields encourages us to use it in modeling and investigating the behavior of pp scattering.…”