A_H & \approx & \frac{3k_BT}{4}\left(\frac{\varepsilon_s(0)-\varepsilon_m(0)}{\varepsilon_s(0)+\varepsilon_m(0)}\right)\left(\frac{\varepsilon_t(0)-\varepsilon_m(0)}{\varepsilon_t(0)+\varepsilon_m(0)}\right)
\\
& + & \frac{\hbar\omega_e}{
8\sqrt{2}}\frac{\left(n_s^2-n_m^2\right)\left(n_s^2-n_m^2\right)}{\left(n_s^2+n_m^2\right)^{1/2}\left(n_s^2+n_m^2\right)^{1/2}\left[\left(n_s^2+n_m^2\right)^{1/2}+\left(n_s^2+n_m^2\right)^{1/2}\right]}
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