The ALFA (Absolute Luminosity for ATLAS) Roman Pot detector system is part of the forward instrumentation of ATLAS located about 240 m away from the interaction point in the LHC tunnel in both directions. ALFA consists of a scintillating fiber tracker housed in vertical Roman Pots which enables the measurement of elastic proton-proton scattering at small scattering angles. In 2016 seven data-sets were recorded at a center-of-mass energy of $sqrt{s} = 13$ TeV during a fill with special beam optics of the LHC with $beta^{*} = 2.5$ km and parallel-to-point focusing in the vertical plane.The four-momentum transfer $t$ is measured for elastically scattered protons and used to extract the differential elastic cross section. In this work, the reconstruction efficiency for each of these seven data-sets is determined, which is needed for the correct normalization of the differential elastic cross section, in order to derive the the total cross section and the slope of the elastic cross section at small $|t|$, using the optical theorem. The $rho$-parameter, which is the ratio of the real to imaginary part of the forward scattering amplitude, is also measured at this given center of mass energy. The systematic uncertainties for the determination of these quantities as a result of the uncertainties from the determination of the reconstruction efficiency is investigated.
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