Changes

= Intro = The Carver and Richards 1972 2-site relaxation dispersion model for [[SQ CPMG-type data]] for most time scales whereby the simplification $R_{2A{:R2Azero}}^0$ = $R_{2B{:R2Bzero}}^0$ is assumed. This model is labelled as '''CR72''' in [[Relaxation dispersion citation for relax|relax]].

R_{2,\textrm{eff}} = \frac{R_2^A+R_2^B+k_{\textrm{EX}}}{2} - \nu_{\textrm{cpmg}} \cosh^{-1} (D_+\cosh(\eta_+) - D_-\cos(\eta_-))\\\phantom{R_{2,\textrm{eff}}} = R_2 + \frac{k_{\textrm{EX}}}{2} - \nu_{\textrm{cpmg}} \cosh^{-1} (D_+\cosh(\eta_+) - D_-\cos(\eta_-))

\zeta = 2 \Delta \omega \, (R_2^A - R_2^B - p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}}) \\\phantom{\zeta} = - 2 \Delta \omega \, ( p_A k_{\textrm{EX}} - p_B k_{\textrm{EX}}) \\\phantom{\zeta} = - 2 \Delta \omega \, ( k_{\textrm{BA}} - k_{\textrm{AB}}) \\\phantom{\zeta} = - 2 \Delta \omega \, k_{\textrm{EX}} ( 2p_A - 1) \\\Psi = (- p_A p_B k_{\textrm{EX}} + p_B - p_A k_{\textrm{EX}})^2 - \Delta \omega^2 + 4 p_A p_B k_{\textrm{ex}}^2- \Delta \omega^2 \\\phantom{\Psi} = ( p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}} )^2 - \Delta \omega^2 \\= ( k_\phantom{\textrm{BAPsi}} + = k_{\textrm{ABex}} )^2 - \Delta \omega^2 \\

<math>k_{\textrm{EX:kex}}</math> is the chemical exchange rate constant, <math>p_A</math> {{:pA}} and <math>p_B</math> {{:pB}} are the populations of states A and B, and <math>\Delta \omega</math> {{:Deltaomega}} is the chemical shift difference between the two states in ppm.

== Code Parameters ==

httpThe CR72 model has the parameters {{{://svnR2zero}}, .gna.org/viewcvs/*checkout*/relax/trunk/lib/dispersion/cr72.py?revision=HEAD, {{:pA}}, {{:Deltaomega}}, {{:kex}}}.

== Parameters Code ==

The CR72 model has the parameters library code: {$R_2^0$, ${relax url|path=lib/dispersion/cr72...$, $p_A$, $\Delta\omega$, $k_{expy}$}.

* Carver, J. and Richards, R. (1972). General 2-site solution for chemical exchange produced dependence of T2 upon Carr-Purcell pulse separation. ''J. Magn. Reson.'', '''6'''(1), 89-105. ([http{{#lst://dx.doi.org/10.1016/0022-2364(72)90090-X 10.1016/0022-2364(72)90090-X]).Citations|CarverRichards72}}

* [http://www.nmr-relax.com/manual/reduced_CR72_2_site_CPMG_modelThe_reduced_CR72_2_site_CPMG_model.html relax manual],

[[Category:Models]][[Category:Dispersion models]][[Category:Relaxation_dispersionanalysis]]