Interaction with a radiofrequency field - the resonance phenomenon

3 INTERACTION WITH A RADIOFREQUENCY FIELD - THE RESONANCE PHENOMENON 

As one can see, this transition rate grows with the square of both, the gyromagnetic ratio of the nucleus and the magnitude of the RF magnetic field. Also, only magnetic fields Bi(r) perpendicular to Bo can induce such transitions, so as to give a non-vanishing value to the matrix element between the m, n states (as is the case of the operators H and ly). The selection rule for the transitions is also obtained from the properties of the H (or ly) operator Am = 1 [2]. 

A semiclassical interpretation for the excitation of the nuclear spins is obtained by considering the linearly polarized magnetic field Bi (t) as composed of two circularly polarized fields, both with the same frequency and amplitude Bi, but precessing around the z-axis in opposite directions  

For F2 = COL, i-C . on resonance, the field Bj (r) rotates around the z-axis coherently with the nuclear Larmor precession described by Equation (2.2.1), whereas B+ (r) rotates in the opposite sense. In a coordinate frame rotating around the z-axis with frequency SI = -f2k (named rotating frame), the field Bj (f) is stationary, as well as the nuclear spins, while B+ (t) rotates with twice the Larmor frequency. Therefore, only B] (t) will have an effective influence on the nuclear spins, provided that both fields have magnitude much smaller than that of the static field Bo 

The torque /t x Bj will cause each magnetic moment /i, which is stationary in the rotating frame, to process around the direction of the field B] . This direction is fixed in the rotating fl-ame (let us call it the x -direction) and rotates around the z-axis with the Larmor frequency in the laboratory reference frame. If the tfequency of the RF field S2 is not equal to col, i e., in the off-resonance case, the precession of the magnetic moments in the rotating frame is around an axis defined by an effective magnetic field given by  

---

Interaction with a radiofrequency field - the resonance phenomenon... 

---