Quadrupole Splitting Theoretical Background

In the case of resonance absorption of synchrotron radiation by an Fe nucleus in a polycrystalline sample, the frequency dependence of the electric field of the forward scattered radiation, R(oj), takes a Lorentzian lineshape. In order to gain information about the time dependence of the transmitted radiation, the expression for R(oj) has to be Fourier-transformed into R(t) [6]. 

With the two excited nuclear states Ei and 2 given in terms of the quadmpole 

Equation (9.1) documents that quadmpole splittings A q exhibit quantum-beat spectra with period H/IuAEq superimposed over the time dependence of the nuclear decay exp(—f/t) with mean decay time t = 141 ns for Fe. In Fig. 9.2, quadmpole splittings A q = 0 and 2 mm s in the energy domain (conventional MS) are compared with those in the time domain (MS using synchrotron radiation) [7]. The QBs in the time domain spectmm for A q = 2 mm s are the result of the interference between the radiation scattered by different nuclear resonances. Consequently, their frequencies correspond to the energetic differences between these resonances. 

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