Author: bugman
Date: Fri May 9 10:12:05 2014
New Revision: 23126
URL: http://svn.gna.org/viewcvs/relax?rev=23126&view=rev
Log:
Clean ups for the end of the B14 dispersion model section of the manual.
Here a number of 'v' were changed to \nu and the standard \kAB, \pA, and \pB
are now used.
Modified:
trunk/docs/latex/dispersion.tex
Modified: trunk/docs/latex/dispersion.tex
URL:
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/dispersion.tex?rev=23126&r1=23125&r2=23126&view=diff
==============================================================================
--- trunk/docs/latex/dispersion.tex (original)
+++ trunk/docs/latex/dispersion.tex Fri May 9 10:12:05 2014
@@ -636,13 +636,13 @@
It is interesting to consider the region of validity of the Carver and
Richards result. The two results are equal when the correction is zero, which
is true when
\begin{equation}
- \sqrt{v_{1c}^2-1} \approx v_2 + 2k_{\textrm{AB}}p_D .
-\end{equation}
-
-This occurs when $k_{\textrm{AB}}p_D$ tends to zero, and so $v_2=v_3$.
-Setting $k_{\textrm{AB}}p_D$ to zero amounts to neglecting magnetisation
that starts on the ground state ensemble and end on the excited state
ensemble and vice versa.
-This will be a good approximation when $p_A \gg p_B$.
-In practise, significant deviations from the Carver and Richards equation
can be incurred if $p_B > 1$\%.
+ \sqrt{\nu_{1c}^2-1} \approx \nu_2 + 2 \kAB p_D .
+\end{equation}
+
+This occurs when $\kAB p_D$ tends to zero, and so $\nu_2 = \nu_3$.
+Setting $\kAB p_D$ to zero amounts to neglecting magnetisation that starts
on the ground state ensemble and end on the excited state ensemble and vice
versa.
+This will be a good approximation when $\pA \gg \pB$.
+In practise, significant deviations from the Carver and Richards equation
can be incurred if $\pB > 1$\%.
Incorporation of the correction term results in an improved description of
the CPMG experiment over \citet{CarverRichards72}.
The reference for this equation is:
r23126 - /trunk/docs/latex/dispersion.tex