Energy calibration of NaI detectors

When measuring γ radiation one usually uses a spectrometer. A spectrometer is an apparatus which will sort the measured data into a histogram sorted according to γ-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 γ-rays emitted from the source can easily be spotted and analysed. The area of each peak will be proportional to the intensity of the correspondingγ-ray. Such a spectrometer is usually referred to as a Multi Channel Analyser (MCA). Before an MCA can be used to measure γ rays of unknown energies (i.e. unknown samples) it must be calibrated. Your task is to perform such an calibration and identify the two unknown samples. Energy calibration of the MCA: necessary spectra will be uploaded as soon as possible. You will find 6 calibration spectra obtained from measurements of 137Cs, 88Y, 60Co, 241Am, 54Mn, and 133Ba. The MCA associate the amount of light measured from the NaI crystal with channel numbers. 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 γ-rays emitted from the given source. The spectra have been labelled with the peak positions (centroids).

Step 1 – find the energy of the peaks
Use the table of γ-energy standards on page 15 in the booklet to the nuclear chart and the 6 calibration spectra to plot the relationship between the measured peak positions (centroids) in the spectra and the tabulated γ-ray energies.

Step 2 – Make the calibration plot
(Fit a straight line through the data points from a) (the best way to do this is by linear regression fitting, but you can also do it manually using plotting paper and a ruler). What is the slope and y-intercept of the straight line?

Step 3 – evaluation of calibration plot
How good is the data represented by the fitted straight line? Plot the deviation between the values calculated from the coefficients of the straight line and the actual values from the Nuclear Chart Table (page 15). Are the deviations random? If not, suggest a better fitting function!

Step 4 – unknown sources
Identify the sources used for the two spectra with unknown samples. The sources are two
of the nuclei listed in the page 15 table. (To do this you must use your calibration function to calculate the energies of the peaks in the spectra. Then you can search for corresponding γ lines in the table. Remember that there is some uncertainty in the measurements, so the energies will not match 100%!).

Step 5 – Second order calibration (if you have time)
Fit a second order polynomial to the data from a) and calculate the deviation between your
calibration and the tabulated γ-ray energies. How much did this improve your energy
calibration, if at all?