Appendix A: ${\cal A_I}$, ${\cal A_Q}$ and ${\cal A_U}$ terms

The angular terms ${\cal A_I}$, ${\cal A_Q}$ and ${\cal A_U}$ are function of the angular coordinates $(\alpha, \beta)$ of an emmetting point on the solar disk; the angular coordinates $(\eta, \psi)$ of the magnetic field vector (or of the velocity field vector); the scattering angle $\theta$ and of $\gamma=\omega\,\tau$ (where $\omega$ is the Larmor angular frequency and $\tau$ is the lifetime of the upper level of the atomic transition considered). Their expressions are given by the following equations

$${\displaystyle {\cal A_L}=\sum_{i=0}^4\xi_i\,{\cal A_{L}}_i\;\;\;\;\mbox{with}\;\;\;\;{\cal{L}}={\cal{I}};{\cal{Q}};{\cal{U}} }$$ (A.1)

where

$$\begin{eqnarray*}\begin{array}{l} {\displaystyle \xi_0= {\varphi^\prime}^2_0(\alpha,\beta,\eta,\psi) }; \end{array}\end{eqnarray*}$$

$$\begin{array}{l} {\displaystyle \xi_1= \Re{\rm {e}}\left( \frac{ ... ...varphi^\prime}^2_1(\alpha,\beta,\eta,\psi) }{1+{i}\gamma}\right) }; \end{array}$$ (A.2)

$$\begin{eqnarray*}\begin{array}{l} {\displaystyle \xi_4= \Im{\rm {m}}\left( \frac... ...(\alpha,\beta,\eta,\psi) }{1+{i}2\,\gamma}\right) ; } \end{array}\end{eqnarray*}$$

and

$$\begin{array}{l} {\cal A_I}_0= d^2_{00}(-\theta)d^2_{00}(\eta)-2\... ...2\,d^2_{02}(-\theta)\big[d^2_{22}-d^2_{2-2}\big](\eta)\sin(2\psi) ; \end{array}$$ (A.3)

$$\begin{array}{l} {\cal A_Q}_0=d^2_{20}(-\theta)d^2_{00}(\eta)-\bi... ..._{2-2}\big](-\theta)\big[d^2_{22}-d^2_{2-2}\big](\eta)\sin(2\psi) ; \end{array}$$ (A.4)

$$\begin{array}{ll} {\cal A_U}_0=\big[d^2_{21}+d^2_{2-1}\big](-\the... ..._{2-2}\big](-\theta)\big[d^2_{22}-d^2_{2-2}\big](\eta)\cos(2\psi) . \end{array}$$ (A.5)

The coefficients $d^k_{qq^\prime}$ are given in Brink & Satchler (1962).