Short half life nuclear homogenous or non homogenous Poisson?

[Beam me down]

I have completed an experiment to measure the decay rate of an isotope, and I am trying to estimate uncertainties. The half life is 40 seconds, with decays counted over a 15 second period (with many of these 10 second periods for a total of 6 minutes of recordings)

However in more detailed readings I think my set up may not model a Poisson distribution. As the rate of decay is clearly will drop off significantly over the measurement timeframe. So am I measuring a non-homogenous Poisson process or homogenous, or am I completely missing the understanding of non-homogenous Poisson?

Any advice would be greatly appreciated, my confusions are doing my head in.

 

[Bob S]

I believe that if you are counting thousands of events in each 15 second period, then the standard Gaussian error curve is sufficient. If you are counting less than say 10 events in each window, then Poisson error statistics are needed. I am aware of one experiment where there were estimated roughly 40 or 50 rare radioactive atoms created, so they not only had to use Poisson counting statistics, but also the binomial statistics as well because of the finite number of radioactive atoms..

 

[sir-pinski]

Based on your description, it seems like you may be measuring a non-homogenous Poisson process. This is because the decay rate is not constant over time, but instead drops off significantly over the measurement timeframe. A homogenous Poisson process assumes a constant rate of decay, so it may not accurately model your experiment.

In order to estimate uncertainties, it may be helpful to consider the non-homogenous nature of your data. This could involve adjusting your calculations to account for the changing decay rate over time. It may also be useful to consult with an expert or conduct further research on non-homogenous Poisson processes to better understand how they apply to your experiment.

Overall, it's important to carefully consider the assumptions and limitations of your experimental setup and data in order to accurately estimate uncertainties and draw conclusions from your results. I hope this helps and good luck with your research!