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3.2 Excitation of Magnetized Matter
With these assumptions the flip angle produced by a certain RF-pulse for a given
magnetization vector results in
α = ω 1 τ p = γB 1 τ p (3.16)
with ω 1 referring to the spin’s precession frequency. Figure 3.3 shows this coherences
in the rotating and the stationary coordinate frame.
Figure 3.3: The rotation of the magnetization vector in the rotation (left) and the
stationary coordinate frame (right). Image taken from [Liang1999]
Accordingly the magnetization vector rotates toward the y ′ -axis. In the laboratory
coordinate system (x, y, z) the movement describes a precession around the z-axis.
After τ p a signal called Free Induction Decay (FID) is detected with in B ⃗ 0 placed coils
and characterized by an exponential relaxation processes towards the equilibrium as
described in section 3.2.1.
3.2.1 Precession and Relaxation
The signal of a spin system which has been excited with a RF-pulse can only be detected
for some milli-seconds. The reason is that the spins are influenced by other
magnetic fields from their neighborhood as well. In short terms, the excitation energy
can be transferred to surrounding spins, which causes a dephasing of the magnetization
vector within the x ′ y ′ -plane referred as Spin-Spin-Relaxation or transversal relaxation
and additionally the rotated magnetization vector will tip backwards to its stationary
position parallel to the direction of the field B 0 which influences the amount of
signal for each repetition of the measurement. This is called longitudinal relaxation
or Spin-Grid-Relaxation. The latter can be phenomenologically interpreted as the
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