Resonance absorption of y-rays Mossbauer effect

Assume that there are two samples with exactly the same structure and nuclei. This signifies that the positions of two energy levels in both samples are exactly equal. Assume further that there is a way to initiate the nuclei of the first sample to emit y quanta. The emitted spectral line E -Eq=AE will exhibit a frequency, co. One can evaluate the value of the natural width of this spectral line (i.e., the width as defined by quantum physics (refer to Chapter 7.2) but not by imperfection of the experimental equipment). The uncertainty principle gives  

If this radiation is directed onto a second quite similar sample, resonance should occur, i.e., the resonance absorption should be observed. Indeed, the y-quantum energy is precisely equal to the energy difference E -Eq. The absorption of the electromagnetic waves with y-quantum energy just equal to the energy difference in a sample is caused by the resonance absorption, i.e.  

However, there are at least two factors that destroy the resonance. The first factor is recoil, which obtains free nucleus when knitting the y quantum. Really, the law of momentum conservation requires that the total system momentum, being equal to zero before emitting the y quantum (0=p +pj, should be kept at zero after disintegration, so 

It can be seen that the y-quantum energy Ey is less than the ideal value - q on the value of nucleus recoil energy E (denoted usually as R). From eqs. (8.3.5) and (8.3.6), we can find values E =R. The energy of a photon is correlated with its momentum by the equation (see Chapter 1.6)  

Quite another picture is observed if both nuclei are confined in a crystal. In this case, the whole crystal needs to be considered as a closed system. The theory of this effect (at energies 

---

Fig. 2.1 Nuclear resonance absorption of y-rays (Mossbauer effect) for nuclei with Z protons and N neutrons. The top left part shows the population of the excited state of the emitter by the radioactive decay of a mother isotope (Z, N ) via a- or P-emission, or K-capture (depending on the isotope). The right part shows the de-excitation of the absorber by re-emission of a y-photon or by radiationless emission of a conversion electron (thin arrows labeled y and e , respectively)...

Figure 1. Schematic representation of nuclear resonance absorption of y-rays (MOssbauer effect) and nuclear resonance fluorescence...

---