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The interaction occurs between the magnetic core dipole moment <math>\vec{\nu}</math> and the intermediate state <math>I_S</math> or/and an external magnetic field <math>\vec{B}</math>. The interaction also takes place between nuclear quadrupole moment and the off-core electric field gradient <math>V_{zz}</math>.
=== Magnetic dipole interaction ===
For the magnetic dipole interaction, the frequency of the [[precession]] of the [[nuclear spin]] around the axis of the magnetic field <math>\vec{B}</math> is given by:
:<math> \omega_L=\frac{g\cdot u_N\cdot B}{\hbar}
</math>
:<math>\Delta E=\hbar\cdot\omega_L=-g\cdot u_N\cdot B
</math>
<math>g</math> is the [[Landé_g-factor]] und <math>u_N</math> is the [[nuclear magneton]].
With <math>N=M-M'</math> follows:
:<math>E_{magn}(M)-E_{magn}(M')=-(M-M')g\mu_NB_z=N\hbar\omega_L
</math>
From the general theory we get:
:<math>G_{k_1k_2}^{NN}=\sqrt{(2k_1+1)(2k_2+1)}\cdot e^{-iN\omega_L
t}\times\sum_M\begin{pmatrix}
I&I&k_1\\
M'&-M&N\\
\end{pmatrix}\begin{pmatrix}
I&I&k_2\\
M'&-M&N\\
\end{pmatrix}
</math>
For the magnetic interaction follows:
:<math>G_{k_1k_2}^{NN}=e^{\left({-iN\omega_Lt}\right)}
</math>
=== General theory ===
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