Nuclear Forward Scattering

Only oscillators with their axis parallel to 
Dm = 0  dipole oscillator 
along 


Dm = +1  a right hand 
about  
Dm =  1  a left hand circular oscillator 
For simplicity let us consider a single crystal with pure electric hyperfine interactions. The excited state is split into two levels and the groundstate remains degenerated. This leads to two transitions R_{1} and R_{2} from the excited to the ground state
( DE(R_{1}) < DE(R_{2}) for V_{zz} > 0 ):
R_{1}   3/2, ± 1/2ñ ®   3/2, ± 1/2ñ  Dm = 0  
 3/2, ± 1/2ñ ®   3/2, ± 1/2ñ  Dm = ±1  
R_{2}   3/2, ± 1/2ñ ®   3/2, ± 1/2ñ  Dm = ±1 . 
From conventional Mössbauer spectroscopy we know that for single crystals the intensity ratio of the two transition lines is depending on the angle between the quantization axis (V_{zz} of the EFG in this case) and the direction of the incident radiation. The two extreme cases lead to a ratio of
Figure 4: The figure compares nuclear time response and nuclear absorption for different polarizations of the incident radiation and for three scattering geometries.
The scattering geometries of row (1), (2) and (3) are sketched on the left side. V_{zz}, the main axis of the electric field gradient (EFG) represents the quantization axis of the system. The weight of the nuclear transitions is indicated in the spectra.
In case of NFS (column (a)) additionally the polarization has to be taken into account: The synchrotron radiation incident on the sample is linearly polarized in the plane of the electron orbit in the storage ring. Due to the radiation characteristics of the relevant multipole radiation only certain transitions can be excited for certain geometries.
In all other cases the polarization of the incoming beam has to be decomposed into parts perpendicular and parallel to the projection of the quantization axis to a plane normal to the incoming beam and for each part the scattering has to be regarded separately.
The following figure shows the intensity of an airon foil
Nuclear forward scattering by a 5mm thick airon foil, 80% enriched in ^{57}Fe. The applied field was 0.2 Tesla, the direction relative to the incident beam is indicated in the figure
From the minimum of the dynamical beat at 85 ns the effective thickness of each of the two symmetric lines can be estimated to t_{eff }/line=25. This result is in perfect agreement with the 5mm thick airon foil which was used for the measurement: the weight of one Dm=0 transition in this geometry is a fraction of [ 4/(3+4+1+1+4+3)]=[ 1/4] of the sum of all (theoretically possible) transitions. The effective thickness of the whole sample is then 4·25 = 100 which corresponds to the 5mm thick foil.