In a special run of the LHC with β⋆=2.5
km, proton–proton elastic-scattering events were recorded at s√=13
TeV with an integrated luminosity of 340 μb−1
using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam t variable in the range from −t=2.5⋅10−4
GeV2
to −t=0.46
GeV2
using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section σtot
, parameters of the nuclear slope, and the ρ
-parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit t→0
. These parameters are determined from a fit to the differential elastic cross section using the optical theorem and different parameterizations of the t-dependence. The results for σtot
and ρ
are

σtot(pp→X)=104.7±1.1 mb ,ρ=0.098±0.011.
The uncertainty in σtot
is dominated by the luminosity measurement, and in ρ
by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.