Introduction

What is Angle?

Angle is advanced quantitative gamma-spectrometry software. Angle has been in use for over 20 years in numerous gamma-spectrometry based analytical laboratories worldwide. Originally developed for semiconductor (Ge) detectors, Angle currently supports scintillation (NaI) devices as well. The vast majority of gamma-spectrometry systems in operation nowadays are built around these two detector types.

Angle allows for the accurate determination of the activities of gamma-spectroscopic samples, and thus is used for the quantification (i.e. spectrometry) of measurements. This is achieved by the calculation of detection efficiencies (see further), using the so-called “efficiency transfer” (ET) method. ET is a semi-empirical approach, which means that it is a combination of both experimental evidence and mathematical elaboration: detection efficiency for any “unknown” sample, and its activity can be determined by a calculation from the measurement of a standard source with a known activity (detector calibration). The two (standard and sample) do not need to match whatsoever – by shape, size, composition or positioning vs. the detector, etc. – offering practically unlimited flexibility and substantial cost reduction in application.

What is detection efficiency?

A spectroscopic measurement implies a radiation source and a radiation detector. In the context of the present software we deal primarily with radioactive (gamma-ray emitting) sources, as well as with sources emitting X-rays in a higher energy range. Appropriate photon detectors include both Germanium and Sodium-Iodide ones.

Only a fraction of the photons (gamma or X-rays) emitted by the source is captured by the nearby detector and hence recorded as a “spectrum” by the measurement device (multichannel analyzer), since:

  • Photons are emitted from the source in all directions, only some of which travel towards the detector (geometrical solid angle)
  • Out of those heading towards the detector, some are absorbed by the materials encountered on the way: the source itself, the container walls, the air layer between the source and the detector, detector cap, etc. (attenuation)
  • Finally, not all of those reaching the detector’s active body (the crystal) deposit their energy into it – some just pass through (detector response)

Some of the photons reaching the detector active body (the crystal) deposit only part of their energy into it. They do contribute to the spectrum, but are of no interest in this context. Rather, we are interested in those which deposit all their energy, forming a “full-energy peak” in the spectrum.

Full-energy detection efficiencyp) is then simply the ratio of the number of photons recorded in the full-energy peak (during the measurement, or “counting”) to the number of all the photons of that energy emitted from the source (during the same time). In other words, it is the probability that a photon emitted from the source will be recorded as such by the detector. Apparently, εp is a function of photon energy.

Why detection efficiency matters?

It is clear from the above that detection efficiency (εp) is essential for the determination of source activity (more precisely, the activity of a particular radionuclide), which is the goal of any gamma-spectrometric measurement. The total number of “counts” in the full-energy peak (“peak area”, Np) itself cannot provide this information. However, from the two combined (Np and εp), the source activity can be derived (see further).

In other words, in order to know the actual source activity, the measurement result (counts) itself is not enough to determine, or even to estimate the actual source activity – both detection efficiency and peak area have to be known to meet that aim.

Determining detection efficiency is, thus, the key to quantitative gamma-spectrometry. With this “gate open”, the remaining part is rather elementary, or even trivial – incorporating some basic experimental evidence.

How to determine detection efficiency?

There are, in principle, three approaches to detection efficiency determination: absolute, relative and semi-empirical.

Absolute methods, such as Monte Carlo, are essentially mathematical and thus highly exact. However, they require extensive knowledge of a large number of physical parameters that characterize the detection process. This approach often implies long computation times and poor accuracy (due to high error propagation factors).

Relative method is the spectrometry classic. A source of known activity is compared with an unknown one by employing identical counting arrangements. It is very accurate, but apparently not flexible at all to changing experimental conditions.

Semi-empirical methods combine the positive attributes of both the relative and absolute methodologies, simultaneously minimizing their drawbacks. Semi-empirical methods commonly consist of two parts: experimental (producing a reference efficiency characteristic of the detector – “calibration”) and a calculation of εp. There are numerous variations within this approach.

How do the different approaches to efficiency determination compare?

There are pros and cons for each of the abovementioned approaches, depending on the purpose. Laboratory practice, however, has demonstrated that the semi-empirical methods – as is the case with Angle – represent the best compromise between the absolute and relative ones: while requiring less input parameters than the former, they offer much more flexibility than the latter.

Semi-empirical methods are less affected by input errors (due to uncertainties in detector parameters, for example), as their relative/experimental “halves” tend to reduce, or even cancel out, these errors.