The ATLAS experiment with the ALFA sub-detector, provides a unique opportunity to measure elastic proton--proton scattering at the LHC at a centre-of-mass energy of sqrt{s} = 7 TeV, that has never been reached before.The ALFA detector is a tracking detector housed in Roman Pots, which makes it possible to measure elastically scattered protons down to very small scattering angles.From the proton tracks, measured during a LHC fill with special beta^* = 90 m beam optics, the differential elastic cross-section as a function of the four-momentum transfer squared t is determined, and the total hadronic cross-section sigma_{tot}, the nuclear slope parameter B and further derived quantities are extracted by utilizing the optical theorem.The total hadronic cross-section is a fundamental parameter of strong interaction depending on the centre-of-mass energy.It has been measured for more than 50 years at different energies and accelerators, where a rise with energy was observed.A newly developed fully data-driven method is used to determine the t-independent event reconstruction efficiency in the two spectrometer arms to be epsilon_{rec}(Arm 1368) = 0.8974 +- 0.0005 (stat.) +- 0.0061 (syst.) and epsilon_{rec}(Arm 2457) = 0.8800 +- 0.0005 (stat.) +- 0.0092 (syst.) by carefully selecting elastic-scattering events not reconstructed in the entire ALFA detector.Special care is also taken of other important aspects of the analysis like the determination of the luminosity and beam optics parameters.An integrated luminosity of L = 80 µb^{-1} is accumulated to measure the differential elastic cross-section from which the total hadronic cross-section is extracted from a fit in the range 0.01 GeV^2 <= -t <= 0.1 GeV^2 to be sigma_{tot} = 95.35 +- 0.38 (stat.) +- 1.25 (exp.) +- 0.37 (extr.) mb.In addition, the nuclear slope parameter at small |t| is determined to be B = 19.73 +- 0.14 (stat.) +- 0.26 (syst.) GeV^{-2}.
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