A Rigorous Least-Squares Analysis of Complex Gamma-Ray Spectra with Partial Compensation for Instrumental Instability
The least-squares method for analyzing multichannel gamma-ray spectra is one of great power and versatility, but its full potential is difficult to realize due to instrumental instabilities. For sources having low or moderate activities and for which the counting times range from a few minutes to several hours, the most important instabilities are long term drifts in zero-energy channel-intercept and gain. A computer routine based on the use of a special reference source is described, which can detect changes in zero-intercept of as little as 0.05 channels (for a 512 channel analyzer), and in gain of as little as 0.1%. By prior transformation of the data to compensate for these effects, and by the use of appropriate weighting factors in the least-squares analysis, the goodness of fit is dramatically improved. Often, the goodness of fit indicator "chi-squared over degrees of freedom" is reduced from a value in excess of three, to a value which does not differ significantly from unity. The weighting procedure described takes into account the statistical errors in both the complex spectrum which is to be analyzed, and in the reference spectra which are its components. These computer methods have been applied to the analysis of gamma-spectra from biological materials containing low activities of the natural series of radionuclides, and of atomic fallout products.