Rotating Wave Approximation to Nuclear Magnetic Resonance for Arbitrary Spins

To probe the magnetic dipole transitions between substates m and m’ in an arbitrary nucleus of spin I, a constant magnetic field H­₀ and a weaker field H₁(t) that is normal to H₀ with an oscillatory angular frequency ω, H₁(t) = H₁[ x cos(ωt) + y sin(ωt)]. The problem can be solved exactly by using the rotating wave approximation. Plots of the t dependencies of the substate m occupation probabilities for 1/2≤ I ≤9/2 using two different initial conditions plus a third initial condition for integral 1 ≤ I ≤ 4 values at near resonance are provided. The dynamic and geometric phases for arbitrary m are found in the adiabatic limit. The plots for the average occupation probability of each substate m over one period vs. the angular frequency ω for I = 1/2 to I = 5/2 at near resonance are also included.