Accurate calculation of pileup effects in PIXE spectra from first principles

Background subtraction in PIXE spectra has been a persistent problem in PIXE data analysis. Pile‐up represents an important contribution to the background, but its treatment in software codes handling PIXE spectra frequently suffers from strong or even incorrect approximations. This paper gives a short review of various studies and methods of pile‐up correction and applies an analytic calculation based on first principles for PIXE spectra pile‐up subtraction. No distinction between peak and continuum contributions is necessary. The only parameters required for the calculation are the collection time, the shaping time of the amplifier and the resolving time of the pile‐up rejection system, without any need for normalisation constants. Calculations are presented for a series of experimental PIXE spectra, for different count rates and amplifier shaping times and spectra collected with the pile‐up rejection system on and off. The agreement between calculated and observed pile‐up is excellent.