the Hartmann-Hahn Condition is:

\sqrt{ (\gamma_e H - \omega_{\mu w})^2 + P_{\mu w} \gamma_e^2 } = \gamma_p H

since we fixed the microwave power and frequency, the only parameter to change is the magnetic field. the solution of the magnetic field.

since, changing the magnetic field will also change the Larmor frequency of the proton and affect the pulse frequency of the NMR system. Thus, when changing the magnetic field, we have to find out the corresponding Larmor frequency to determine the NMR pulse frequency.

we first, measure the proton in water, since the proton can be regarded as free proton, and the Larmor frequency can be measured in high precision. the method we are used,

  1. set the NMR frequency in 12.2MHz, 12.4 MHz, etc.
  2. change the magnetic field such that the NMR signal is pure decay without any oscillation.

after acquire the data, we set the magnetic field and NMR frequency on crystal sample polarization.   there is only 1 magnetic field satisfy the Hartmann-Hahn condition and get a maximum polarization and NMR signal.

Note, the crystal field will broaden the peak of Larmor frequency, but the broadening is not shifting the center.