G Wider/Progress in Nuclear Magnetic Resonance Spectroscopy 32(1998)193-275 described by the Bloch equations [30]. Because the In the rotating frame where b becomes static th spin is a quantum mechanical phenomenon this main magnetic field B. vanishes for nuclei with reso- description has a very limited scope, but it proves nance frequency vo. Hence, Eq(2)in this rotating ery useful for the description of single resonance frame contains only a transversecomponent hes under the action of radiofrequency(rf) pulses w=-y(B1, 0,0)with BI chosen along and thus for the characterization of the effect of RF Consequently M precesses by an angle p around the magnetic field B applied as a pulse for the short 2.1. Magnetization, precession and bloch equations In a classical description the macroscopic magneti- zation M created by the spins is described by a vector where B is called the flip angle of the pulse. The fip M parallel to the magnetic field vector Bo M is forced angle is often indicated in degrees, for example during move away from the direction of Bo by an a 90 pulse M can precess from the z axis to the x axis additional linearly polarized magnetic field BI per- The angle B depends on y and is negative for positive pendicular to Bo. BI must fulfil the resonance con- y values such as for protons(Table 1). For positive y ition and oscillate with the resonance frequency vo. values a magnetic field B pointing along the positive The magnetization vector M precesses about the x axis turns M towards the negative y axis. a B, field resulting magnetic field B=B.+BI with an angular along the +y axis turns M towards the +x axis velocity vector w pointing in the opposite direction [16, 31]. When applying an rF pulse with a frequency ind the components as described in Eq (2) differing from vo the action of the rf pulse becomes more complex as described in Appendix A, a situation r(2B, cos(2xv,(+6), 2B, sin(2 vol +o), B,) often referred to as non-ideal behaviour of the RF resonance The oscillating magnetic field 2B, coS(wRFt) used where w=(wr, Wy, Wo), B. is chosen along the z for excitation is linearly polarized in the laboratory ind o describes the angle between the x axis and B frame. The transformation into the rotating frame The magnetic field B is often applied only for short can best be followed when this is thought of as a time periods as RF pulses. The discussion of the superposition of two counter-rotating, circular polar motion of the magnetization vector M in space due zed fields with an amplitude B. When transforming to RF pulses is usually based on a rotating frame of into the rotating frame one component matches the reference which has the same z axis along the static Larmor frequency whereas the other oscillates at magnetic field B as the laboratory frame but rotates twice the Larmor frequency and does not fulfil the around the z axis with a frequency which is often resonance condition. Bloch and Siegert [32] calcu- hosen equal to the resonance frequency vo. In this lated the effect of the non-resonant field and found rotating frame of reference, the relevant component that it slightly shifts the frequency of the observed of the applied oscillating field B, appears static resonance lines away from the disturbing field by making the discussion and visualization much easier the small amount vB=(yB,)/Aw where y=Y/(2T) To fulfil the physical requirement that the magnetiza. and Av stands for twice the resonance frequency tion vector M returns to its equilibrium position in a The Bloch-Siegert shift is small and amounts, for finite period of time after a disturbance, a longitudinal example, to O5 Hz for a frequency of 600 MHz dur elaxation time T,(spin-lattice relaxation)is intro. ing an RF pulse with duration T of 10 us and a fip duced. The loss of coherent precession is described angle of 3(Eq (3)or 90. The shift disappears as by a transverse relaxation time T2(spin-spin relaxa- soon as b is switched off. An effect similar to the tion). The motion of the magnetization vector M Bloch-Siegert shift occurs whenever an RF field is under the action of the magnetic field B and hence applied with a frequency Av off-resonance for the under w can be described by the Bloch equations nuclear spins. Although first described by Ramsey [30]. These equations are presented in Appendix a [33] it is still very often referred to as the bloch- for further reference Siegert effect. To better distinguish it from the effect