In terrestrial instruments for X-ray emission analysis (e.g. X-ray fluorescence, electron microprobe) the angle of excitation and the angle of characteristic X-ray emission by samples are typically well-defined. This is not the case for the Mars rovers’ alpha particle X-ray spectrometers, necessitating use of “effective” angles in any fundamental parameters approach to spectrum fitting and derivation of element concentrations. A new Monte Carlo computation of expected characteristic X-ray yields has enabled us to examine the choice of effective angles in detail and to compare with our previous estimates; the mean angles taken over all detected events appear to be the most satisfactory approximation. These were used in our GUAPX code to process APXS spectra from ten mono-mineralic geochemical reference materials. Agreement between our concentration values and those determined by the specialist company ActLabs was excellent. © 2019 Elsevier B.V.