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Recently Referred Formulae

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)
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& + & \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]}
F_{EDL}=\frac{2\pi R}{\varepsilon_{m}\kappa}\left[\left(\sigma_t^2+\sigma_s^2\right)e^{-2\kappa d}+2\sigma_t \sigma_s\right]\frac{1}{1-e^{-2\kappa d}}
F_{vdw}=-\frac{A_HR}{6d^{2}}
\kappa^{-1}= \sqrt{\frac{\varepsilon_{m}k_{B}T}{2n_{ion}Z^{2}e^{2}}}
k_r \simeq F_0 + (1 - F_0)(1 - \cos\theta_i)^5 , F_0 = \frac{(\eta - 1)^2}{(\eta + 1)^2}