Error in the determination of Gaussian peak centroids

Abstract

We have determined uncertainties s(b) in the estimates of peak centroids for Gaussian spectral lines. Peak centroids b were estimated by a least-squares method fitting Gaussian to peaks. A calculational method yields, in the case of a negligible background, $\text{s(b)≈0.412}\text{f}\text{a}$ where f and a denote the full width at half maximum and the amplitude of the peak, respectively. Monte Carlo calculations of synthetic peaks on a background Bg show that s(b) = K₁ + K₂ Bg where K₁ and K₂ depend on a, f, and k (number of data points used in the fitting). K₁ and K₂ have been determined in useful particular cases. Experimental errors in peak centroids are obtained by adjusting Gaussian to profiles of known lines recorded in beam-foil spectra. Good agreement is found between experimental and calculated errors s(b).