Cosmic radiation

[lodovico]

Yes, right. It is not the "stopping power" but rather the "detection efficiency".
Lodovico

[toand]

With Pieters set-up, we measured muon lifetime in 156 oscilloscope images, that is, time between doublets. The expected lifetime is about 2.1 microseconds (2.2 in free space, but somewhat lower in a scintillator). Since the oscilloscope was set with a maximum delay of 9 microseconds between pulses, the distribution is cut (truncated) and the observed median/mean will be biased. Some kind of analysis is needed. The usual method is to apply a log-linear regression. This means binning (grouping) the observed values. This is tricky for a small number of observations. Here statistical methods may be more appropriate, for example maximum likelihood estimation.

The figures below illustrate the results of log-linear regression analysis and maximum likelihood estimation. In all cases, we are not far from 2.1 microseconds, but the statistical method appears more appropriate and gives the best estimate. With rough binning (left), the regression is marked by large uncertainty (broad confidence intervals). With more dense binning (figure in middle), the bins representing larger values are marked by random variation, forcing the "arbitrary" exclusion of bins. Maximum likelihood (right) appears more "safe" (robust).

[Sesselmann]

Nice analysis, which confirms the muon decay very accurately..

Can you explain for me why binning the interval times into 4-5 bins gives a statistically better result that simply sorting the intervals by delay in descending order and plotting it?

[toand]

Okay. If we order the intervals one after the other, the count will be 1 (one) for each interval. It will give us a single frequency of one for each lifetime value, that is a flat frequency (probability) function. Each value will be unique, which gives us no information on the expected lifetime. Binning is necessary to allow the density and shape of the frequency function to emerge.

[Sesselmann]

Ah yes, I see what you have done now..

Thanks for clarifying..

[Gar Wood]

I need to know if this will work to identify isotopes in PRA. After the calibration of Cs137 and the regions of interest are highlighted. Run the sample to be tested for a given amount of hours. 5 hrs for example. Then take every frequency in every single bin in the right peak (ROI) and add them all together. Divide by 5 for counts per Hr then by 60 for CPM. Then do the same for back round in the ROI and subtract it from that for a net total.