The full CR72 2-site CPMG model

This is the model for 2-site exchange on most times scales (with the constraint that p_A > p_B), named after Carver and Richards (1972). It is selected by setting the model to `CR72 full'. The equation is

R_2eff = $\displaystyle {\frac{{1}}{{2}}}$ $\displaystyle \Big($ R_2A⁰ + R_2B⁰ + k_ex -2ν_CPMGcosh^-1 $\displaystyle \big($ D₊cosh(η₊) - D_-cos(η_-) $\displaystyle \big)$ $\displaystyle \Big)$ ,

(11.22)

D_±	= $\displaystyle {\frac{{1}}{{2}}}$ $\displaystyle \left(\vphantom{ \pm1 + \frac{\Psi + 2\Delta\omega ^2}{\sqrt{\Psi^2 + \zeta^2}} }\right.$ ±1 + $\displaystyle {\frac{{\Psi + 2\Delta\omega ^2}}{{\sqrt{\Psi^2 + \zeta^2}}}}$ $\displaystyle \left.\vphantom{ \pm1 + \frac{\Psi + 2\Delta\omega ^2}{\sqrt{\Psi^2 + \zeta^2}} }\right)$ ,	(11.23)
η_±	= 2 $\displaystyle {\frac{{1}}{{\nu_{\textrm{CPMG}}}}}$ $\displaystyle \left(\vphantom{ \pm\Psi + \sqrt{\Psi^2 + \zeta^2} }\right.$ ±Ψ + $\displaystyle \sqrt{{\Psi^2 + \zeta^2}}$ $\displaystyle \left.\vphantom{ \pm\Psi + \sqrt{\Psi^2 + \zeta^2} }\right)^{{\frac{1}{2}}}_{}$ ,	(11.24)
Ψ	= $\displaystyle \left(\vphantom{ \mathrm{R}_{\mathrm{2A}}^0- \mathrm{R}_{\mathrm{... ...trm{A}}\textrm{k}_{\textrm{ex}}+ p_{\textrm{B}}\textrm{k}_{\textrm{ex}}}\right.$ R_2A⁰ - R_2B⁰ - p_Ak_ex + p_Bk_ex $\displaystyle \left.\vphantom{ \mathrm{R}_{\mathrm{2A}}^0- \mathrm{R}_{\mathrm{... ...\textrm{k}_{\textrm{ex}}+ p_{\textrm{B}}\textrm{k}_{\textrm{ex}}}\right)^{2}_{}$ - Δω² +4p_Ap_Bk_ex²,	(11.25)
ζ	= 2Δω $\displaystyle \left(\vphantom{ \mathrm{R}_{\mathrm{2A}}^0- \mathrm{R}_{\mathrm{... ...trm{A}}\textrm{k}_{\textrm{ex}}+ p_{\textrm{B}}\textrm{k}_{\textrm{ex}}}\right.$ R_2A⁰ - R_2B⁰ - p_Ak_ex + p_Bk_ex $\displaystyle \left.\vphantom{ \mathrm{R}_{\mathrm{2A}}^0- \mathrm{R}_{\mathrm{... ...trm{A}}\textrm{k}_{\textrm{ex}}+ p_{\textrm{B}}\textrm{k}_{\textrm{ex}}}\right)$ .	(11.26)

Note that these equations use the numerically simplified form derived in the appendix of Davis et al. (1994).

This model is not accurate when the motional process is very slow. In that case, the `TSMFK01' model in Section 11.3.6 on page

should be used instead.