Energy+Calibration+of+Gamma-ray+Spectra+-+Laboratory+Preparation+Exercise

When measuring gamma radiation one usually use a spectrometer. A spectrometer is an apparatus which will sort the measured data into an histogram sorted according to gamma-ray energies. Thus, a picture of the intensity distribution of the absorbed energy in the detector is obtained. In such a picture, peaks from the photo electric absorption of the various gamma rays emitted from the source can easily be spotted and analysed. The area of each peak will be proportional to the intensity of the corresponding gamma ray. Such a spectrometer is usually referred to as a Multi Channel Analyser (MCA). Before an MCA can be used to measure gamma rays of unknown energies (i.e. unknown samples) it must be calibrated. This is something you will learn to do using real detector systems in the lab. The exercise presented here is intended as preparation for such hand-on laboratory exercises and will make it easier for you to perform the hands-on exercises with maximum learning outcome. Your task in this exercise is to perform such an energy calibration and identify two unknown samples. You will get data from real measurements with a gamma-ray detectors similar to what you later on will encounter yourself.

Energy calibration of the detector system
Download ain September 2004 (using a detector in the detector lab of the Nuclear Chemistry Section at the University of Oslo). In this file you will find 6 calibration spectra obtained from measurements of 137Cs, 88Y, 60Co, 241Am, 54Mn, and 133Ba. The detector system is a "Multi-Channel Analyzer" (MCA) which generates a spectrum - a histogram - where registered radiation events are sorted according to energy. The MCA will count how many events of a given energy have been measured and store this number in the corresponding histogram column - or what we usually refer to as "channel". The channel numbers is simply the numbering of the bars in the spectrum histogram.

We use measurements of known nuclei to calculate the relationship between channel numbers and energy. Each of the calibration spectra has peaks corresponding to the distinct gamma-rays emitted from the given source. The spectra in the PDF-file has been labelled with the peak positions (centroids).

Do the following in order to obtain an energy calibration (relationship between gamma-ray energy and channel number):
 * 1) Use a gamma-ray energy database (e.g. the Berkeley/Lund database) or the NucWik list of gamma-ray calibration sources and find the gamma-ray energes emitted by the used calibration standards. Plot the relationship between the measured peak positions (centroids) in the spectra and the tabulated gamma-ray energies.
 * 2) Fit a straight line through the data points from (the best way to do this is by linear regression fitting, but you can also do it manually using plotting paper and a ruler). A good program for this is Origin, if you have access to it at your campus. What is the slope and y-intercept of the straight line?
 * 3) How good is the data represented by the straight line fitted above? Plot the deviation between values calculated from the coefficients of the straight line and the actual values. Is the deviations random? If not, suggest a better fitting function for the calibration!

Identify unknown elements in a sample from measured gamma-ray spectra
 * 1) Identify the sources used for the two spectra with unknown samples (from the PDF-file). The sources are two of the nuclei listed in the NucWik table of gamma-ray calibration sources. To do this you must use your calibration function calculate the energies of the peaks in the spectra. Then you can search for corresponding gamma lines in the table. Remember that there is some uncertainty in the measurements, so the energies will not match 100%!).