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Hidden radian units

21 bytes removed, 12:42, 24 July 2013
Changed the sectioning again, and a few small edits.
<keywords content="diffusion rates, dimensionless units, hidden units, radian, relaxation rates, rotational correlation times, SI supplementary units, spherical harmonics" />
 == SI Supplementary Units - The dimensionless and hidden radian unit ==
Warning: If hard core NMR or physics theory is not to your taste, please do not read any further!
This post is mainly for later reference, but concept is quite important for understanding the relaxation equations in NMRor, in fact, and actually any rotational physical processin physics. It is important for understanding the model-free equations, for reduced spectral density mapping, for SRLS, and for relaxation dispersion. The reason is because R1 and R2 are measured in rad/s. As I describe in section 1, the radian unit can be dropped because it is plainly obvious that NMR and relaxation is an angular process and hence radian units are implied (that was sarcastic). Hence R2 can be said to be in units of 1/s, but never, ever Hz. Also note that because of the SI conventions described below, describing the correlation time in s units does not prove that there are no radian units. But reporting rates as Hz implies no radian units whereas reporting as 1/s instead often means radian units are present.
This is also a follow on from the [https://mail.gna.org/public/relax-devel/2007-06/msg00012.html comprehensive unit analysis of Abragam's relaxation equations].
== Source ==
This was [https://mail.gna.org/public/relax-users/2009-01/msg00000.html originally published] on the [https://mail.gna.org/listinfo/relax-users relax users mailing list].
== SI supplementary units ==
=== SI supplementary units (radian and steradian) ===
=== IUPAC report ===
This reference explains a bit more clearly why the radian unit is
== Spherical harmonics ==
The time dependent spherical harmonic can be written as
== Rotational correlation times ==
My opinion here is that the rotational correlation time is a
=== Book quotations ===
Title: Physical Properties of Lipids
== Relaxation rates ==
Here, my opinion is that the R1 and R2 The units for relaxation rates are in rad/s. The equationsfrom the book quotations hopefully show this conversion from Hz torad/s.
=== Book quotations ===
Title: Nuclear Spin Relaxation in Liquids: Theory, Experiments, and
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