Time-resolved pile-up compensation in PIXE analysis with list-mode collected data

Abstract

In order to improve the accuracy of the PIXE analysis with respect to the pile-up problem, a technique to analyse PIXE spectrums suffering from pile-up has been developed. It is based on the well-known relationship Na·Nb·τ=N, where Na and Nb are the count rates in two primary peaks, τ is the pile-up interval and N is the count rate in the resulting pile-up peak. This relationship, however, only holds for a constant count rate, a condition rarely encountered in practice. In order to compensate the spectrum for the pile-up effects despite a varying count rate, the X-ray energy signal together with the current are collected in list-mode event-by-event, grouped in time steps, enabling a time-resolved analysis of the spectrum. The above relationship can then be applied at every time step, here 10 ms, during which the count rate is considered constant. A formula to determine a compensation factor, (1+C), is inferred, that enables compensation for pile-up in the final spectrum. Also a simplified technique is proposed, where only the beam current is multiscaled for the duration of the experiment. The dependence of τ on the X-ray energy was determined by pulse generator experiments as well as by beam for a number of elements. Examples of the method are demonstrated for various degrees of instability in the beam, and with and without a beam deflection system.