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A new model for the description of incoherent peaks observed in energy-dispersive x-ray fluorescence spectra is proposed. The model was derived after a systematic study of peak shapes based on Monte Carlo simulations. The model consists of a Gaussian modified by two exponential tail functions. The model is implemented in a non-linear least-squares fitting procedure and tested on spectra measured with a 109 Cd excitation XRF setup using an HPGe detector.

Several algorithms to calculate the vector of regression coefficients and the Jacobian matrix for partial least squares regression have been published. Whereas many efficient algorithms to calculate the regression coefficients exist, algorithms to calculate the Jacobian matrix are inefficient. Here we introduce a new, efficient algorithm for the Jacobian matrix, thus making the calculation of prediction intervals via a local linearization of the PLS estimator more practicable.

The need for an accurate description of characteristic x-ray lines has led to the development of complex peak models that combine a Gauss, a shelf and a tail function. Via relationships that describe the shelf and tail parameters as a function of the energy, it is possible to reduce the number of fit parameters significantly. In this work, we carried out an experiment to study the shelf and tail parameters obtained with an HPGe detector. We observed a strong discontinuity in the shelf and tail parameters around the K-edge energy of Ge. This indicates that these parameters are strongly dependent on the mass-attenuation coefficient of the detector material. Therefore, we propose relationships that describe those parameters as a function of the energy and the mass-attenuation coefficient. The implementation of these relationships in a fitting procedure results in a more robust fitting procedure with a much smaller number of fitting parameters. Excellent fits for HPGe spectra can be obtained. Because the detector dependence seems to be fairly general, we could successfully apply the model to Si(Li) spectra also.

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