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Here $R_{2}$ does not contain the $R_{ex}$ contribution. Also, $R_{\text{eff}}$ is absent of $R_{ex}$. <br>
But in Art's Protein Science paper (Ref [5]), the definition $R_{2} = R^{0}_2 + R_{ex}$ is used. The MP05 model reference also does not use Reff $R_{\text{eff}}$ [[MP05]]. The $R_{\text{eff}}$ parameter name is confusing and it seems to have been dropped from 2005 onwards. The $R_{\text{eff}}$ name appears to be specific to Art Palmer's group and as he himself has dropped it, then it would be best to avoid it too.
Ref [2], Equation 27. Here the calculated value is noted as: R_eff: $R_{\text{eff}} = R^{0}_2 + R_{ex} = R_{1\rho}' + R_{ex} = R_{1\rho} / \sin^2(\theta) - R_1 / \tan^2(\theta)$ <br>