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Cosmic ray (CR) air showers, detected via the air fluorescence technique, arereconstructed in part using functions that parameterize the longitudinalprofile of each shower. The profile parameterization yields the position ofshower maximum, X_max, which is sensitive to the incident CR particle type:e.g. p, C/N/O, Fe or photons. The integral of the profile is directly relatedto the shower energy. The Pierre Auger fluorescence reconstruction uses theGaisser-Hillas 4-parameter form. The HiRes group has used both theGaisser-Hillas form and a 3-parameter Gaussian in Age form. Historicallyanalytic shower theory suggested yet other forms; the best known is a3-parameter form popularized by Greisen. Our work now uses the shower fullwidth half-maximum, "fwhm", and shower asymmetry parameter, "f", to unify theparameterization of all three profile functions. Furthermore shower profilesexpressed in terms of the new parameters: (fwhm, f) have correlations greatlyreduced over Gaisser-Hillas parameters (X_0, lambda). This allows showerprofile reconstructions to add constraints (if needed) on the mostlyuncorrelated parameters (fwhm, f).

A Parametrization of Cosmic Ray Shower Profiles Based on Shower Width