Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)An almost model-independent parametrization for the ratio of the total cross section to the elastic slope, as function of the center of mass energy, is introduced. The analytical result is based on the approximate relation of this quantity with the ratio R of the elastic to total cross section and empirical fits to the R data from proton proton scattering above 10 GeV, under the conditions of asymptotic unitarity and the black-disk limit. This parametrization may be useful in studies of extensive air showers and the determination of the proton-proton total cross section from proton-air production cross section in cosmic-ray experiments. (C) 2012 Elsevier B.V. All rights reserved.880111Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP [11/00505-0, 09/50180-0]