Elong-13-05-20

(1)

<math>\frac{N_{Pol}}{N_{u}} = \frac{ \mathcal{A} \left[ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z + \frac{1}{2}A_{zz}P_{zz}\right) \right] t_{Pol} }{ \mathcal{A} \left[ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) \right] t_u} </math>

(2)

<math>\frac{N_{Pol}}{N_{u}} = \left( \frac{t_{Pol}}{t_u} \right)\left[ \frac{ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z\right) }{ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } + \frac{\mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u} {\mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } \frac{1}{2}A_{zz}P_{zz}\right] </math>

If <math>t_{Pol} \approx t_u</math> and <math>f = \frac{\mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u} {\mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } </math>,

(3)

<math>\frac{N_{Pol}}{N_{u}} = \left[ \frac{ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z\right) }{ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } + f \frac{1}{2}A_{zz}P_{zz}\right] </math>

(4)

<math>\frac{N_{Pol}}{N_{u}} - \left[ \frac{ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z\right) }{ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) }\right]= f \frac{1}{2}A_{zz}P_{zz}</math>