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