Counting Experiment: Analyzing Peaks & Error

[Jonny_trigonometry]

I'm doing a compton scattering experiment, and I'm ahving trouble finding a good analytical way of determining where the peak is with its associated error. Its a counting experiment, so we use Poisson statistics, and we have the output of counts per channel over a range of 512 channels, each corresponding to an energy. There is a peak in the sprectrum of channels, and the counts in each channel have error of sqrt(counts). So I know the y-error bars for each channel and everything, and I can find where the half-max is on each side of the peak to get a fairly good idea of which channel the peak correcponds to, and we can eyeball the error in that value, but my question is, how can we do this more analytically? We know y-errors, and we want to translate that into an x-error of the peak basically. This seems so simple, but yet I'm having trouble establishing a method.

 

[Jhero]

There are a few different approaches you can take to determining the peak and its associated error in your Compton scattering experiment. Here are a few suggestions:

1. Fitting a Gaussian curve to the data: One way to determine the peak and its associated error is to fit a Gaussian curve to your data. The peak of the curve will correspond to the peak of your spectrum, and the width of the curve will give you an estimate of the error in that peak. You can use a software program like Origin or Matlab to perform this curve fitting.

2. Using a peak finding algorithm: There are also algorithms designed specifically for finding peaks in data, such as the peakutils package in Python. These algorithms can take into account the y-error bars in your data and give you a more accurate determination of the peak and its associated error.

3. Calculating the centroid of the peak: Another approach is to calculate the centroid of the peak, which is the average of all the channel numbers weighted by the corresponding counts. This can be done using the following formula:

centroid = sum(channel * counts)/sum(counts)

The standard deviation of this centroid value can then be used as an estimate of the error in the peak location.

4. Using a statistical method: You mentioned that you are using Poisson statistics in your experiment. One way to approach this analytically is to use a statistical method, such as maximum likelihood estimation, to determine the peak and its associated error. This method takes into account the Poisson distribution of your data and can provide a more accurate estimate of the peak location and error.

Overall, the best method for determining the peak and its error will depend on the specific characteristics of your data and the level of accuracy you need. I would recommend consulting with a statistician or data analysis expert to determine the best approach for your particular experiment.