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A new measurement of elastic $pp$ scattering at $\sqrt{s} = 13$ TeV with theATLAS-ALFA detector is presented. The measurement was performed using datarecorded in a special run of the LHC with $\beta^\star = 2.5$ km. The elasticcross-section was measured differentially in the Mandelstam $t$ variable andfrom a fit to ${\textrm{d}}\sigma/\textrm{d}t$ the total cross section, the$\rho$-parameter and parameters of the nuclear slope are determined. Theresults for $\sigma_{\textrm{tot}}$ and $\rho$ are \begin{equation*}\sigma_{\textrm{tot}}(pp\rightarrow X) = \mbox{104.7} \; \pm 1.1 \; \mbox{mb} ,  \; \; \rho = \mbox{0.098} \; \pm 0.011 . \end{equation*} The energy evolutionof $\sigma_{\textrm{tot}}$ and $\rho$, connected through dispersion relations,is compared to several models. Furthermore, the total inelastic cross sectionis determined from the difference of the total and elastic cross section, andthe ratio of the elastic to total cross section is calculated.

Determination of the total cross section and $\rho$-parameter from  elastic scattering in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS  detector