Formal Relationship Between the Firearm “Memory Effect” and the Decay Time of the GSR Particles Present on the Shooter’s Hands

Background/Objectives: The Scanning Electron Microscope (SEM), combined with an Energy Dispersive Spectrometer (EDS), has been, for over fifty years of practical experience and research in the field, the analytical system of choice for the investigation and analysis of Gun Shot Residues (GSRs). However, the interpretation of analytical results has profoundly changed in recent decades. Specifically, the criteria for evaluating particles presumptive of contamination of a possible discharge have evolved, assessments regarding possible primary/secondary transfer phenomena have been refined, and the retention times of particulate matter on various types of surfaces involved during the discharge have been revalued. The purpose of this study is to provide a formal representation that links together the firearm memory effect, namely the formation of composite characteristic GSRs resulting from the use of the same Firearm but with ammunition having different metallic alloy constituents and different primer mixtures, and the decay time. Methods: The deduced mathematical model is based on experimental results reported in the scientific literature listed below, and it has been elaborated with a series of non-contradictory assumptions, each of which plays a specific role in the mathematical formalism used. Results and Conclusions: This model, although not yet validated through rigorous experimentation, represents a valuable tool in investigations related to the firearm memory effect when forensic specialists have collected GSR samples from the hands of the alleged shooter within four hours of the shooting.