# Scattering polarization of the $d$-states of ions and solar magnetic field: Effects of isotropic collisions

## TL;DR

This paper develops simplified relationships for calculating collisional depolarization rates of ion d-states, enabling more accurate interpretation of solar magnetic field observations by reducing computational complexity.

## Contribution

It introduces new formulas based on atomic data for efficient calculation of collisional rates without detailed interaction potentials, aiding solar magnetic diagnostics.

## Key findings

- Achieved about 10% average error in collisional rate predictions.
- Validated relationships with complex and hyperfine-structured atoms.
- Provided a practical tool for solar magnetic field analysis.

## Abstract

Analysis of solar magnetic fields using observations as well as theoretical interpretations of the scattering polarization is commonly designated as a high priority area of the solar research. The interpretation of the observed polarization raises a serious theoretical challenge to the researchers involved in this field. In fact, realistic interpretations need detailed investigations of the depolarizing role of isotropic collisions with neutral hydrogen. The goal of this paper is to determine new relationships which allow the calculation of any collisional rates of the d-levels of ions by simply determining the value of n^* and $E_p$ without the need of determining the interaction potentials and treating the dynamics of collisions. The determination of n^* and E_p is easy and based on atomic data usually available online. Accurate collisional rates allow a reliable diagnostics of solar magnetic fields. In this work we applied our collisional FORTRAN code to a large number of cases involving complex and simple ions. After that, the results are utilized and injected in a genetic programming code developed with C-langugae in order to infer original relationships which will be of great help to solar applications. We discussed the accurarcy of our collisional rates in the cases of polarized complex atoms and atoms with hyperfine structure. The relationships are expressed on the tensorial basis and we explain how to include their contributions in the master equation giving the variation of the density matrix elements. As a test, we compared the results obtained through the general relationships provided in this work with the results obtained directly by running our code of collisions. These comparisons show a percentage of error of about 10% in the average value.