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The [[wikipedia:Chemical_shift | Chemical Shifts]] $\delta$ in ppm for nuclei of interest (ex. $^{15}$N and which have been loaded in with relax function [http://www.nmr-relax.com/manual/chemical_shift_read.html chemical_shift_read] from a [http://www.nmr-relax.com/manual/spectrum_read_intensities.html peak list formatted file]) is first converted to to the rad/s with the following function calls.<br>
$\bar{\omega}_{S,i} = 2\pi \cdot \delta_{S,i} \cdot B_0 \cdot \frac{\gamma_{^{15}N}}{\gamma_{^{1}H}}$
The spin lock field strength is converted to rad/s, with the following function call.<br>
$\omega_{S,1} = 2\pi \cdot \nu_{S,1}$
Fix for the symbols and maths - all $x$ usage has been replaced by parameter templates, <math> tags, or direct HTML conversion.
=== spin lock offset ===
In the literature, the values are often stated as "offset", "carrier offset", "offset of the spin-lock pulse" with values given in Hz, and can have values from 0-500 to 10-20.000 Hz.<br>
These values reflects offset frequencies to the carrier frequency, and in relax is noted as '''"Spin-lock offset, the frequency of of the rf field"''' : $\mathbf{\omega_{rf:omegarf}}$.
Relax needs input for $\mathbf{\omega_{rf:omegarf}}$ in ppm, and during calculations converts to the rad/s, with the following function call.
<source lang="python">
offsets[ei][si][mi][oi] = frequency_to_rad_per_s(frq=cdp.spin_lock_offset[id], B0=frq, isotope=spin.isotope)
'''Offset in the literature'''<br>
The offset is in the literature noted as $\Omega_S$Ω<sub>S</sub>, where $\Omega_S$ Ω<sub>S</sub> is the (Ex. $^{<sup>15}$</sup>N) resonance offset from the spin-lock carrier.
Note that $\Omega_S$ Ω<sub>S</sub> is dependent of the [[wikipedia:Chemical_shift | chemical shifts]] $\delta$ δ in ppm for the nuclei of interest. The [[wikipedia:Chemical_shift | Chemical Shifts]] δ in ppm for nuclei of interest (ex. <sup>15</sup>N and which have been loaded in with relax function [http://www.nmr-relax.com/manual/chemical_shift_read.html chemical_shift_read] from a [http://www.nmr-relax.com/manual/spectrum_read_intensities.html peak list formatted file]) is first converted to to the rad/s with the following function calls. <math>\bar{\omega}_{S,i} = 2\pi \cdot \delta_{S,i} \cdot B_0 \cdot \frac{\gamma_{^{15}N}}{\gamma_{^{1}H}}</math>
<source lang="python">
shifts[ei][si][mi] = frequency_to_rad_per_s(frq=shift, B0=frq, isotope=spin.isotope)
</source>
Then $\bar{\Omega}_S$ <span style="text-decoration: overline">Ω<sub>S</sub></span> is calculated with: $\bar{\Omega}_{<span style="text-decoration: overline">Ω<sub>S,i} </sub></span> = <span style= \bar{\omega}_{"text-decoration: overline">Ω<sub>S,i} </sub></span> - \omega_{rf{:omegarf}}$, where $\bar{\omega}$ <span style="text-decoration: overline">Ω</span> is the population averaged Larmor frequency of the spin and comes from the conversion of the [[wikipedia:Chemical_shift | Chemical Shifts]] $\delta_{δ<sub>S,i}$ </sub> to frequency $\bar{\omega}_{<span style="text-decoration: overline">Ω<sub>S,i}$</sub></span>.
<source lang="python">
Delta_omega = shifts[ei][si][mi] - offsets[ei][si][mi][oi]
=== spin lock field ===
The spin lock field strength is noted $\nu_1${{:nu1}}, and relax requires these to be provided in unit of '''Hz'''.<br> The spin lock field strength is converted to rad/s, with the following function call. <math>\omega_{S,1} = 2\pi \cdot \nu_{S,1}</math>
<source lang="python">
omega1 = point * 2.0 * pi
</source>
Then the Rotating frame tilt angle $\theta$ θ is calculated. <brmath>$\theta = \tan^{-1} \left( \frac{\omega_1}{\bar{\Omega}_{S,i}} \right)$</math>
<source lang="python">
