First of all - an admission... I bought WAY too much Cs-137. The photograph below shows my collection (0.01, 0.05, 0.1, 0.25, 0.5, 1, 2 and 5 uCi sealed samples). Why I think I have too much Cs can be seen from the following spectra collected for 5 minutes (300 seconds). I wanted to ensure that I had a wide spread of Cs-137 activities (amounts) to provide a good dose-response curve but am learning that one can't measure such a wide spread of activities using identical conditions and times and have the spectra be that useful for analytical purposes. In the previous figure showing all the spectra, the areas totaled are shown with gray shading (since I haven't learned how to do that in PRA it was done in Excel). Plotting the total counts in the shaded area vs. the activity of the calibration sources, and fitting those curves with either a linear (straight-line) and nonlinear (single-phase associative) fit yields the following data: The results are shown with both standard (linear) and logarithmic (base 10) axes to highlight how the linear fit really stinks at the lower activity levels. This would lead me to think that the nonlinear fit is more appropriate -but this could be wrong!
Averaging five independent spectra for each source for all of my sources (measured using identical GS-USB-PRO volume settings, analysis times and the like) gives the following data: Using the modified GS-STANDUP and holder allowed each sample to be presented to the shielded detector in a precise way each time resulting in such great statistics! Plotting the average total counts (in the areas of interest) against the activities resulted in the following figures (plotted with linear and logarithmic axes for my 'old-school' eyes): In the log-plot the background total counts are shown as the horizontal dash-dot-dash line.
A careful observer will notice that the graphs do not show the same number of points as I've disregarded the data from anything above 500 nCi when calculating the fit. [More accurately, when I let the fancy-schmancy graphing and statistics software calculate the fit.] I don't know if this is appropriate for gamma spectroscopy but I did it for the following reasons:
Using the statistical fit from the software indicates that the lowest detection limit for these conditions would be around 1-2 nCi (>68% confidence) or around 4 nCi (99.5% confidence). The logarithmic plot using the data from 10 - 500 nCi indicates that these results are not unreasonable. (Sorry, but I'm so old I remember curve fitting with calculators and graph paper so I am still prone to examining plots rather than just believe what some computer program told me the answer is...) I'm assuming that I can go lower (down in the pCi range) if I change the GS-USB-PRO settings and up the count times but I can't talk the guy at Spectrum Techniques to make me a source below 0.01 uCi (yet) so I can test it.
NOW FOR THE NEWBIE QUESTION: Is it already known that activity vs total counts fits a linear model or am I getting a nonlinear model due to my novice conditions? Any wisdom from experienced users or theoretical gurus would be welcome!