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== Theory ==
The first <math>\gamma</math>-quantum (<math>\gamma_1, k_1</math>) will be emitted isotopically. Detecting this quantum in a detector selects a subset with an orientation of the many possible directions that has a given. The second <math>\gamma</math>-quantum (<math>\gamma_2, k_2</math>) has an anisotropic emisison and shows the effect of the angle correlation. The goal is to measure the relative probability <math>W(\Theta)\textrm{d}(\Omega)</math> with the detection of <math>\gamma_2</math> at the fixed angle <math>\Theta</math> in relation to <math>\gamma_1</math>. The probability is given with the angle correlation:
:<math>W(\Theta)=\sum^{k_{max}}_{k}A_{kk}P_{k}cos(\Theta)
</math>
For a <math>\gamma</math>-<math>\gamma</math>-cascade, <math>k</math> is due to the preservation of [[parity_(physics)|parity]]:
:<math>0<k<\textrm{min}(2I_S, I_i+I'_i)
</math>
Where <math>I_S</math> is the spin of the intermediate state and <math>I_i</math> with <math>i=1;2</math> the [[polarity_(physics)|multipolarity]] of the two transitions. For pure multipole transitions, is <math>I_i=I'_i</ math>.
<math>A_ {kk}</math> is the anisotropy coefficient that depends on the [[angular momentum]] of the intermediate state and the multipolarities of the transition.
The radioactive nucleus is built into the sample material and emits two <math>\gamma</math>-quanta upon decay. During the lifetime of the intermediate state, ie the time between <math>\gamma_1</math> and <math>\gamma_2</math>, the core experiences a disturbance due to the [[hyperfine interaction]] through its electrical and magnetic environment. This disturbance changes the angular correlation to:
:<math>W(\Theta)=\sum^{k_{max}}_{k}A_{kk}G_{kk}
</math>
<math>G_{kk}</math> is the perturbation factor. Due to the electrical and magnetic interaction, the angular momentum of the intermediate state <math>I_i</math> experiences a torque about its axis of symmetry. Quantum-mechanically, this means that the interaction leads to transitions between the M states. The second <math>\gamma</math>-quantum (<math>\gamma_2</math>) is then sent from the intermediate level. This population change is the reason for the attenuation of the correlation.
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>.
=== General theory ===
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