The adiabatic approximation for magnetic resonance of spin 1 and 3/2 nuclei

The spin state of particles evolving in time during nuclear magnetic resonance (NMR) experiments is complex, because it involves both the magnitude and frequency of the applied magnetic field B(t)=B₀z+B₁[xcos(wt)+ysin(wt)]. Despite the complexity, the importance of understanding the spin properties of nuclei has been increasing, especially in order to characterize the pair spin state of exotic superconductors. Michael Berry in 1984 simplified the spin ½ problem in the adiabatic approximation for sufficiently low w values. However, to our knowledge, this has not previously been done for higher spin values. We have studied both the adiabatic and non-adiabatic limits for the magnetic resonance of spin 1 and 3/2 nuclei. These approximations should be useful for the interpretation of NMR experiments, especially those involving the Knight shift in superconductors.