Absorbing nuclei

So far, we have discussed only the detection of y-rays transmitted through the Mossbauer absorber. However, the Mossbauer effect can also be established by recording scattered radiation that is emitted by the absorber nuclei upon de-excitation after resonant y-absorption. The decay of the excited nuclear state proceeds for Fe predominantly by internal conversion and emission of a conversion electron from the K-shell ( 90%). This event is followed by the emission of an additional (mostly Ka) X-ray or an Auger electron when the vacancy in the K shell is filled again. Alternatively, the direct transition of the resonantly excited nucleus causes re-emission of a y-photon (14.4 keV). 

The intensity of a Mossbauer spectrum depends not only on the recoil-free fractions of the source and the absorber and on the number of absorbing nuclei, but also on the linewidth of the absorption lines and on whether or not saturation effects occur. The following approximate expression is valid for relatively thin absorbers [17] ... 

We might imagine that we could prepare a system that physically moves the source of the radiation toward the absorbing nuclei with sufficient speed that the Doppler shift compensates for the energy difference. Restricting the motion... 

Since the signal intensity is proportional to the number of absorbing nuclei, HR NMR can also be used as a quantitative tool, e.g. in polymer end group determinations. 

Integration (Section 14.5) The area under an NMR signal that is proportional to the number of absorbing nuclei that give rise to the signal. 

It should not be forgotten that the excited absorber nuclei re-emit the y-ray within 10 s. However, if the internal conversion coefficient is high, correspondingly fewer y-rays will be emitted. More important, however, the re-emission is not directional but takes place over the full 4.-r solid angle. Consequently the number of secondary events recorded at the detector in a collimated transmission experiment are few and are usually neglected. 

Figure 1Z2 Shifts of the energy levels of the source and absorber nuclei...

The control rod calibration problem under study in the present discussion is concerned with a special situation where it is desired to calibrate a control rod during a xenon transient. What is meant by a xenon transient is explained briefly in what follows. When a reactor is in operation, certain nuclei with large neutron absorption cross sections are produced, so that they act as poisons. Of these poisons, xenon-135 is the most troublesome. In a reactor operating at power a balance is eventually achieved between rates of formation and loss of the absorbing nuclei, so that an equilibrium concentration is attained in the reactor. However, when a reactor operating at power is shut down, the xenon continues to increase [1, p. 335] without a sufficient neutron flux available to hum out the xenon, so to speak. Thus, the xenon will eventually disappear by radioactive decay, but not before it builds up to a maximum of substantial proportions. The maximum concentration will occur at about 12 hours after shut-down, the magnitude of the peak concentration depending on the power level before shut-down. This explains why, whenever it is necessary to be able to restart a reactor at any time after shutdown (e.g., a submarine reactor), the reactor must be sufficiently fueled so that it is possible to override maximum xenon at any time. 

In order to obtain resonant cdjsorption, the emitting and absorbing nuclei must be bound in solid lattices for which the lowest vibrational excitation energy is greater than the recoil energy. There will then be a fraction of the nuclei which will emit or cibsorb without any recoil at all. In order to obtain a... 

Before the discovery of the Mossbauer effect, many attempts had been made to improve the chances for y ray resonance absorption. The idea was to make the overlap between the emission and absorption lines larger by setting the emitter/absorber nuclei in motion (in order to compensate for the energy loss due to recoil) either mechanically (Moon 1950) or thermally (Malmfors 1953). 

The key problem, i.e., how to avoid recoil and Doppler broadening at the same time, has been solved by Rudolf Mossbauer (Mossbauer 1958a) when he discovered that y-ray emitting and absorbing nuclei if embedded in the lattice of a solid give rise to a recoilless line (the so-called Mossbauer line) at the energy Eq. 

In order to understand the interactions between the emitting/absorbing nuclei and the lattice, some basics of the Einstein model and the Debye model of solids are needed. 

Fig. 1.3. A schematic representation of Mossbauer spectroscopy with the simplest situation of source and absorber nuclei in identical environments and showing the resulting Mossbauer spectrum with an absorption tine at zero velocity.

Each of the original no neutrons will have a different history, but, on the average, a certain fraction of them will disappear as a result of processes (3) and (4). Only those absorbed in nuclei have a chance to produce additional neutrons a certain fraction of the absorbing nuclei... 

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