Measurement of Lorentzian linewidths

Abstract A new method is presented for the least-squares analysis of pulse height spectra from semiconductor detector-multichannel analyser systems, which does not involve the procedure of matching exponential tails onto Gaussian functions. We show that for a particular set of data taken at the Rutherford Laboratory the use of two Gaussian functions, one with a full width at half maximum approximately 3 times and amplitude 10–20% that of the first Gaussian, with the centroid of the wider Gaussian displaced slightly down in energy, gives a significantly better chi-square per degree of freedom than do matched exponential tails. The centroids obtained agree with those obtained from the exponential tails method. We then discuss the Voigt profile - the convolution of a Lorentzian with a Gaussian function - and show that by using the two-Gaussian approach to instrumental response it is quite simple to study Voigt profiles where the instrumental response is a distorted Gaussian and to extract the Lorentzian centre and linewidth.