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As far as I understand, the basic principle of gamma spectrometer is simple - gamma ray hits scintillator, it generates number of photons which roughly proportional to gamma ray energy. Then we need to detect these secondary photons and plot a nice graph.

But as far as I see, scintillator size is typically too small to completely absorb gamma photon. Which also means that gamma photons coming from different angles will have different track lengths inside scintillator - and should generate different amount of light for the same gamma ray energy.

So, how can this work at all?

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A gamma photon does not release its energy travelling into the material but deposes it into a very local spot when it happens to interact by photoelectric, Compton scattering or pair production (other processes are very rare). The electron that emerges from these interactions typically travels few millimeters inside the material releasing all its energy (and a correlated amount of optical photons) into a single crystal.

The nasty interaction here is the Compton scattering in which also a secondary photon (of quite random energy) comes out. It may interact again into the same crystal but often it escapes taking some of the energy away.

To solve this problem you need the concept of coincidence. If you detect interactions in different crystals in a very narrow time windows you can assume that these comes from the same initial photon and rarely you will be wrong. So looking at coincidences you can reconstruct the energy of the initial gamma by summing all the energy deposed in the crystals. Or also you may go for an anti-Compton shielding which consist of a very heavy material (with high cross section) which surrounds the detector and allow to discard events in which a Compton scattered photon tried to leave the crystal but was stopped by the shielding.

Finally what matters is simply building up some statistics to get an energy spectrum in which every kind of event which is likely to happen will be signed by a nice peak while the unlucky "bad" events when some energy has escaped just fill up some noise background.

What said before is generally valid for gammas coming from nuclear decays/excitation whose energies are around the MeV. If we are talking about energy of GeV like the gammas generated by cosmic rays or by high-energy particle accelerators then the things are pretty different. After the first interaction the products will have enough energy to interact again and again creating a so called electromagnetic shower. You will need a pretty big and heavy (array of) crystal (=calorimeter) to contain all this cascade.

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  • $\begingroup$ +1 - the attenuation length may be long, but attenuation of individual photons happens in discrete steps $\endgroup$ – user10851 Nov 2 '13 at 0:58
  • $\begingroup$ I see, but why then segmented detectors needed, like it was mentioned in the previous answer by dmckee? To also track results of Compton scattering to lower noise floor? $\endgroup$ – BarsMonster Nov 2 '13 at 7:55
  • $\begingroup$ @BarsMonster A segmented detector like the AGATA Germanium array enables you to do gamma-ray tracking. Detecting multiple Compton interactions with high resolution in both energy (coming from the material) and position (coming from segmentation), you can reconstruct also the initial directions of the gammas. This also opens up a lot of possibilities in creating images with many medical and industrial applications. Still a lot of interesting investigation on nuclear structure has been done with bulky non-segmented detector in the last decades often with help of anti-Compton screening. $\endgroup$ – DarioP Nov 2 '13 at 10:37
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Well, it depends on the detector package, but you have three basic choices:

  • Restricted geometry You rig the detector such that only a very limited range of angles is possible. Generally with collimators and/or very limited interaction regions.

    Cheap and often easy, but almost always means very low acceptance.

  • Segmented detector You divide the active region into a sufficient number of individually instrumented pieces with the geometry arranged (crossing strips...) so that you can reconstruct the track by looking at what detector elements were hit, and that way you know the track length.

    Costs more because of all the instrumentation and you have to gain match all the segments; program the reconstruction; and deal with the ambiguity that can be caused by simultaneous hits.

    This is the workhorse of this business.

  • Calorimetry Make the detector deep enough to fully absorb the incident photons.

    You generally use leaded glass or other high-density scintillator for this.

As a practical matter we almost always use a combination of the above. Most detector packages have some collimation, and almost all use segmentation (even the calorimeters).

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