Reference efficiency curve (REC)

The reference efficiency curve (REC) is absolutely crucial, since the efficiency transfer (ET) principle applied in Angle is based upon it. All your actual detection efficiencies are calculated by comparison to it at corresponding energies. If the reference efficiency curve is not specified, these efficiencies will not (cannot) be calculated (only effective solid angles will be calculated in that case)!

Obtaining a reliable reference efficiency curve is thus essential for successful Angle utilization: all Angle results for a given detector will be relative to REC with an error propagation factor = 1 (that is to say 100% of the uncertainty in the REC is added to the uncertainty budget of the calculated efficiencies).

The investment of time and care in determining a reliable REC will always pay off!

We strongly recommend reading [1], [2] and [12] in the Literature to become more familiar with the subject.

Correct. Calibration sources should cover the gamma-energy region of analytical interest (e.g. 50-3000keV). It is suggested that calibrated sources with low certified uncertainties (not exceeding 1.5%-2.5%) are used to obtain as many calibration points (efficiencies vs. gamma-energies) as possible for the energy range mentioned. This non-negligible initial effort is largely paid back in future exploitation, since an accurate reference efficiency curve is fundamental for accurate Angle application.

The more experimental points you have, the better your REC will be. It is recommended to have at least 20 points for a good curve.

No. Simply select the data in your document, copy it, go to Angle and press “Paste from Clipboard”.

Angle interpolates the REC using the experimental points you defined. To make as good a fit as possible it is advisable do divide the REC in two or more regions, e.g. one where the REC is almost linear and the other one where it is not. For each region you can define the fitting polynomial order to be sure the final REC will follow the experimental points correctly. At joint points, the curve will be smoothened.

The regions should be well covered with experimental points. It is not a good idea to extrapolate the regions much beyond the area covered by experimental points. For example, if the lowest energy point is at 88 keV, one should not start the first region at 20 keV. Otherwise, the resulting efficiencies for low energies might not be accurate.

Yes. There are no limitations regarding the number of RECs in Angle. Once you define your REC you can save and use it anytime later. You can obtain different RECs for the same detector by varying calibration sources and/or counting distances.

Absolutely. The reference efficiencies for different detectors are not the same, even if they are the same type! Each detector should have its REC in order to obtain a correct calculation result. Data from one detector cannot be used for calculating the efficiencies of the other.

No. Any calibrated source(s) can serve to obtain a REC. However, when the quality (uncertainties) of output data is of great concern, it is advisable to have a REC which is produced from calibration source(s) geometrically not much different from the sample for which Angle calculations are performed. In doing so, error propagation will be reduced and the results will be more accurate.

One REC per detector is enough, in principle. It is recommended to construct it by counting the number of calibrated point sources at a large distance from the detector (e.g. 20-30 cm), avoiding true coincidences and matrix effects. In addition, absolutely calibrated point sources are often certified to a better accuracy than voluminous ones.

It is generally more prudent to use several single-nuclide sources, than a single multi-nuclide source.

However, in order to additionally exploit the ET error-compensation effect, one might consider constructing more RECs for the same detector. For instance, the same point source(s) counted at a large distance could also be counted on the detector top, yielding another REC. Calibrated cylindrical and Marinelli sources could produce additional RECs.

In an ideal case, using any of several RECs in εp calculations would produce the same result for the actual sample, i.e. the result should be independent of the choice of REC. However, given the fact that all input data (detector, source, geometry) are inaccurate to some extent, choosing a “likely” REC for the actual sample/geometry should eventually produce better (more accurate) results, due to larger ET error-compensation effect. In other words, if the REC sample/geometry is closer to the actual sample, the results will tend to be better.

This in itself is a measure of the accuracy of the various sample and detector parameter choices – if two RECs produce results which are close, the implication is that both sample/geometry and detector are well characterized.

Open the “Reference efficiency curve” dialog and click on the “Load saved curve” button. Choose the file with the name under which you saved the REC and click OK.

Another, more flexible way, to select a previously saved REC is using the pop-up menu, which you can open by clicking the “Reference efficiency curve” label in the “Additional parameters” group of the main window. Choose the option “Saved curves” and select the previously saved material from the sub-menu.

Yes. Open the “Reference efficiency curve” dialog and click on the “Import from GammaVision” button. Choose the EFT file which you saved from GammaVision and click OK. The interpolation parameters will also be imported, check them and modify, if you want.

Yes. Open the “Reference efficiency curve” dialog and click on the “Import from Canberra CAM file” button. Choose the CAM file which you saved from Genie 2000 and click OK.

No. Simply change whatever you want, enter the new name for the REC and click OK. You will be prompted if you would like to save the REC. It is a good tip to use this possibility when investigating/improving the quality of a REC by adding/removing/adjusting experimental points in the REC.

Definitely, any Marinelli standard would do it better than point ones for the REC in this case. This is because of the dominant contribution of the geometrical solid angle in the effective solid angle (the latter being directly related to the calculated efficiency).

If you do not have a Marinelli standard to hand, any large cylindrical standard, measured at the top of the detector, might still be a closer match to the gas Marinelli sample(s) than point ones.

To be well understood, there is nothing especially bad about neither the point sources, nor the Angle principles – it is all about the propagation of (inevitable) uncertainties in input data. Thus, point calibration sources would work as well if you do not have a better match.

You can stick to your experimental efficiencies at particular gamma-energies. Namely, in Angle 5 you can define a “discrete curve”. If you do not specify interpolation regions (i.e. if you enter “0” as the number of regions), interpolation will not be used. You will not be able to calculate efficiencies for energies defined by your REC’s experimental points, and their exact efficiency values will be used (leading to better accuracy for the given energies). This possibility may be particularly useful with NaI detectors.

Yes. In Angle 5 it is possible to see the calculated polynomial coefficients and other interpolation parameters. To see this, click on the “Interpolation data” button in the “Reference efficiency curve” window. You can select and copy parts of the data to another application, or click on the “Copy to Clipboard” button and copy all at once.

Also, Angle inserts calculated polynomial coefficients in the form of a comment in calculation parameters and calculation results files, so you can read them from other applications as well.

No, in that case you can use a reference calibration with whatever Cs-137 standard you have, thus at 661.6 keV energy only (“REC discretization”). This is a great practicality introduced in Angle 5.

For NaI detectors we recommend “REC discretization”, i.e. to have several calibration points at particular (“discrete”) energies of interest. Much better accuracy is achieved in that way. Of course, you will not be able to calculate efficiencies for any other energy than those few specified. Usually, this is not required with NaI.

Nevertheless, REC can be constructed the same way as for Ge detectors. Not so many experimental points can be considered though, since peaks are broad and tend to overlap. More single-nuclide (preferably single-gamma) calibration sources are advised rather than a single multi-nuclide or a multi-gamma source.

Apparently, one should not expect the same REC performance with NaI detectors as with Ge ones.