Perturbed angular correlation: Difference between revisions

Revision as of 01:19, 6 December 2019

Revision as of 01:21, 6 December 2019

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[[File:Complexpacspectrum.png|thumb|right|Bottom: A complex PAC-spectrum, top: its Fourier transformation.]]

According to the number n of detectors, the number of individual spectra (z) results after z=n²-n, for n=4 therefore 12 and for n=6 thus 30. In order to obtain a PAC spectrum, the 90° and 180° single spectra are calculated in such a way that the exponential functions cancel each other out and, in addition, the different detector properties shorten themselves. The pure perturbation function remains, as shown in the example of a complex PAC spectrum. Its Fourier transform gives the transition frequencies as peaks.

<math>R(t)</math>, the count rate ratio, is obtained from the single spectra by using:

:<math>R(t)=2\frac{W(180^\circ,t)-W(90^\circ,t)}{W(180^\circ,t)+2W(90^\circ,t)}

</math>

Depending on the spin of the intermediate state, a different number of transition frequencies show up. For 5/2 spin, 3 transition frequencies can be observed with the ratio ω₁+ω₂=ω₃. As a rule, a different combination of 3 frequencies can be observed for each associated site in the unit cell.

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[[File:Energywiki.png|thumb|right|Energy spectrum of ¹⁴⁹Gd with energy windows for start and stop.]]

In the typical PAC spectrometer, a setup of four 90° and 180° planar arrayed detectors or six octahedral arrayed detectors are placed around the radioactive source sample. The detectors used are scintillation crystals of BaF₂ or NaI. For modern instruments today mainly LaBr₃:Ce or CeBr₃ are used. Photomultipliers convert the weak flashes of light into electrical signals generated in the scintillator by gamma radiation. In classical instruments these signals are amplified and processed in logical AND/OR circuits in combination with time windows the different detector combinations (for 4 detectors: 12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, 43) assigned and counted. Modern digital spectrometers use digitizer cards that directly use the signal and convert it into energy and time values and store them on hard drives. These are then searched by software for coincidences. Whereas in classical instruments, "windows" limiting the respective γ-energies must be set before processing, this is not necessary for the digital PAC during the recording of the measurement. The analysis only takes place in the second step. In the case of probes with complex cascades, this makes it makes it possible to perform a data optimization or to evaluate several cascades in parallel, as well as measuríng different probes simultaneously. The resulting data volumes can be between 60 and 300 GB per measurement.

<math>R(t)</math>, the count rate ratio, is obtained from the single spectra by using:

:<math>R(t)=2\frac{W(180^\circ,t)-W(90^\circ,t)}{W(180^\circ,t)+2W(90^\circ,t)}

</math>

This function normalizes the count rates W at 180° and 90° in order to eliminate the time effects of the exponential decay and to compensate the different detector efficiencies.

== Sample materials ==