Interactions between 4.15-Bev protons and the free hydrogen nuclei in nuclear emulsion are examined. The total elastic cross section from 27 events was determined to be 11.0±2.6 mb. On the basis of 113 interactions the total inelastic cross section was found to be 28.1±3.1 mb. The partial cross sections corresponding to inelastic collisions having two, four, six, and eight secondary particles were found to be respectively 16.3±2.4, 11.5±1.8, 0.2±0.1, and 0.1±0.1 mb. While the total inelastic cross section varies slowly with energy, the partial inelastic cross sections were found to be strongly energy dependent. The observed angular distribution of elastically scattered protons in the center-of-mass system was sharply peaked in the forward and backward directions, in fair agreement with calculations based on a simple optical model applicable for energies between 2 and 10 Bev. Particles produced in inelastic collisions were identified as pions or protons by measurements of energy loss and multiple scattering. For those particles identified, center-of-mass system distributions of energy, angle, and transverse momentum are presented.
In a special run of the LHC with $\beta^\star = 2.5~$km, proton-proton elastic-scattering events were recorded at $\sqrt{s} = 13~$TeV with an integrated luminosity of $340~\mu \textrm{b}^{-1}$ using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam $t$ variable in the range from $-t = 2.5 \cdot 10^{-4}~$GeV$^{2}$ to $-t = 0.46~$GeV$^{2}$ using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section $\sigma_{\textrm{tot}}$, parameters of the nuclear slope, and the $\rho$-parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit $t \rightarrow 0$. 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 $\sigma_{\textrm{tot}}$ 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 uncertainty in $\sigma_{\textrm{tot}}$ is dominated by the luminosity measurement, and in $\rho$ by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.
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