Calculation of the correlation coefficients between the numbers of counts (peak areas and backgrounds) obtained from gamma-ray spectra

• The correlation coefficients between areas of closely spaced peaks are assessed.
• For isolated peaks the correlation arises from the common continuous background.
• If peaks overlap the correlation coefficient depends on how much they overlap.
• If peaks overlap also the background height affects the correlation coefficient.
• The correlation coefficient between the peak area and its background is −1.

Two simple methods for calculating the correlations between peaks appearing in gamma-ray spectra are described. We show how the areas are correlated when the peaks do not overlap, but the spectral regions used for the calculation of the background below the peaks do. When the peaks overlap, the correlation can be stronger than in the case of the non-overlapping peaks. The methods presented are simplified to the extent of allowing their implementation with manual calculations. They are intended for practitioners as additional tools to be used when the correlations between the areas of the peaks in the gamma-ray spectra are to be calculated. Also, the correlation coefficient between the number of counts in the peak and the number of counts in the continuous background below the peak is derived.