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Imaging and analyzing gunshot residue (GSR) particles using the scanning electron microscope equipped with an energy dispersive X-ray spectrometer (SEM-EDS) is a standard technique that can provide important forensic evidence, but the discrimination power of this technique is limited due to low sensitivity to trace elements and difficulties in obtaining quantitative results from small particles. A new, faster method using a scanning proton microbeam and Particle Induced X-ray Emission (m-PIXE), together with Elastic Backscattering Spectrometry (EBS) is presented for the non-destructive, quantitative analysis of the elemental composition of single GSR particles. In this study, the GSR particles were all Pb, Ba, Sb. The precision of the method is assessed. The grouping behaviour of different makes of ammunition is determined using multivariate analysis. The protocol correctly groups the cartridges studied here, with a confidence >99%, irrespective of the firearm or population of particles selected.

The charge density near the ends of the tube must must approximate that near the edge of a semi-infinite plane. This requires a singularity of the form o-!, where 0 is the distance from the edge. At 25th order the Fourier series does begin to develop this singularity, as may be seen in Fig. 1, which shows the charge density on a cylinder with hla=257r.An estimate of the accuracy of the solution is found by examining Eq. (14) at 25th order:The sum on 1n was run to 1n= 24, which introduces some error in the calculation of (eVa). Numerical results were 0.9996 at the equator and 0.8062 at the ends for hla=257r, compared to the assumed unity. The coefficients (in were calculated at both 24th and 25th order for the thick cylinder with hi a= 5, and for the thin cylinder with hI a= 257r. Each coefficient becomes increasingly stable with the addition of higher-order terms. The leading coefficient is then the most stable.The capacitance is found by integration of Eq. (14) over the cylinder to find the total charge, and division by V,. The orthogonality of the expansion terms leaves the capacitance in terms of the leading coefficient:Since (iO changes by no more than 0.02% from 24th to 25th order for all the hi a ratios considered, the capacitances are likewise accurate. If one desired only the capacitance and not the charge distribution, the sequence of values of (iO at much lower orders could be extrapolated to obtain the same accuracy.