Error in the determination of Gaussian peak centroids

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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, s(b)≈0.412fa 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).

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Maître de Recherches au Fonds National de la Recherche Scientifique.

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