Appendix C: Values of the hyperfine depolarizing rates

The variation of the hyperfine depolarizing rates with the temperature is very smooth and was found to increase as $T^\alpha$ and is given as follows for 200 K $\le$ $T \le 10~000$ K.

$$G_{0}(11,11)=0.6821\times10^{-8}n_{\rm H}\left(\frac{T}{5000}\right)^{0.388}(\mbox{s}^{-1})$$ J=1/2

$$G_{2}(11,11)=0.8867\times10^{-8}n_{\rm H}\left(\frac{T}{5000}\right)^{0.388}(\mbox{s}^{-1})$$

$$G_{4}(11,11)=0.0(\mbox{s}^{-1})$$

$$G_{0}(22,22)=0.4093\times10^{-8}n_{\rm H}\left(\frac{T}{5000}\right)^{0.388}(\mbox{s}^{-1})$$

$$G_{2}(22,22)=0.6139\times10^{-8}n_{\rm H}\left(\frac{T}{5000}\right)^{0.388}(\mbox{s}^{-1})$$

$$G_{4}(22,22)=1.0914\times10^{-8}n_{\rm H}\left(\frac{T}{5000}\right)^{0.388}(\mbox{s}^{-1})$$ (C.1)

$$G_0(00,00)= 1.0128\times10^{-8}n_{\rm H}\left(\frac{T}{5000}\right)^{0.410}(\mbox{s}^{-1})$$ J=3/2

$$G_2(00,00)=0.0(\mbox{s}^{-1})$$

$$G_4(00,00)=0.0(\mbox{s}^{-1})$$

$$G_0(11,11)= 8.6305\times10^{-9}n_{\rm H}\left(\frac{T}{5000}\right)^{0.417}(\mbox{s}^{-1})$$

$$G_2(11,11)=1.029\times10^{-8}n_{\rm H}\left(\frac{T}{5000}\right)^{0.414}(\mbox{s}^{-1})$$

$$G_{4}(11,11)=0.0(\mbox{s}^{-1})$$

$$G_0(22,22)= 7.6354\times10^{-9}n_{\rm H}\left(\frac{T}{5000}\right)^{0.391}(\mbox{s}^{-1})$$

$$G_2(22,22)=1.046\times10^{-8}n_{\rm H}\left(\frac{T}{5000}\right)^{0.399}(\mbox{s}^{-1})$$

$$G_4(22,22)=1.1088\times10^{-8}n_{\rm H}\left(\frac{T}{5000}\right)^{0.421}(\mbox{s}^{-1})$$

$$G_0(33,33)= 5.4956\times10^{-9}n_{\rm H}\left(\frac{T}{5000}\right)^{0.379}(\mbox{s}^{-1})$$

$$G_2(33,33)=8.0887\times10^{-9}n_{\rm H}\left(\frac{T}{5000}\right)^{0.383}(\mbox{s}^{-1})$$

$$G_4(33,33)=1.0839\times10^{-8}n_{\rm H}\left(\frac{T}{5000}\right)^{0.396}(\mbox{s}^{-1})$$ (C.2)

(J=1/2,J=3/2)

$$Q_0(11,11)=1.1761\times10^{-9}n_{\rm H}\left(\frac{T}{5000}\right)^{0.4}(\mbox{s}^{-1})$$

$$Q_2(11,11)=-4.1579\times10^{-10}n_{\rm H}\left(\frac{T}{5000}\right)^{0.414}(\mbox{s}^{-1})$$

$$Q_4(11,11)=0.0(\mbox{s}^{-1})$$

$$Q_0(22,22)=2.5429\times10^{-9}n_{\rm H}\left(\frac{T}{5000}\right)^{0.376}(\mbox{s}^{-1})$$

$$Q_2(22,22)=-0.1636\times10^{-9}n_{\rm H}\left(\frac{T}{5000}\right)^{0.302}(\mbox{s}^{-1})$$

$$Q_4(22,22)=0.2181\times10^{-9}n_{\rm H}\left(\frac{T}{5000}\right)^{0.302}(\mbox{s}^{-1}) .$$ (C.3)