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3.1 Magnetic Field and Magnetization
Figure 3.2: Precession of the magnetic moment µ of an isolated spin around a magnetic
field B 0 with the Larmor-frequency ω 0 .
and especially considering the two states for a hydrogen nucleus by
E ↑ (m I = −1/2) = 1 2 γB 0 (3.11)
E ↓ (m I = 1/2 = − 1 2 γB 0.
The energy difference between these two states adds up to
∆E = E ↓ − E ↑ = γB 0 = ω 0 (3.12)
with the Larmor-frequency ω 0 . For the number of spins per unit volume can be assumed
with the two and all possible states N = N ↑ +N ↓ and therefore the distribution of these
states is given by a Bolzman distribution. That means if N ↑ refers to the spins parallel
to ⃗ B 0 and N ↓ define the spins anti-parallel the distribution is given by:
N ↑
= exp( ∆E
N ↓ kT = exp(γB 0
). (3.13)
kT
with the Bolzman constant k = 1.38 × 10 − 23J/K and T as the absolute temperature
of the spin system.
With a net-magnetization of M 0 = µ · (N ↑ − N ↓ ) and assuming that ∆E