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.

This Letter presents a measurement of the inelastic proton-proton cross section using 60 $\mu$b$^{-1}$ of $pp$ collisions at a center-of-mass energy $\sqrt{s}$ of $13$ TeV with the ATLAS detector at the LHC. Inelastic interactions are selected using rings of plastic scintillators in the forward region ($2.07<|\eta|<3.86$) of the detector. A cross section of $68.1\pm 1.4$ mb is measured in the fiducial region $\xi=M_X^2/s>10^{-6}$, where $M_X$ is the larger invariant mass of the two hadronic systems separated by the largest rapidity gap in the event. In this $\xi$ range the scintillators are highly efficient. For diffractive events this corresponds to cases where at least one proton dissociates to a system with $M_X>13$ GeV. The measured cross section is compared with a range of theoretical predictions. When extrapolated to the full phase space, a cross-section of $78.1 \pm 2.9$ mb is measured, consistent with the inelastic cross section increasing with center-of-mass energy.

A measurement is presented of the inelastic proton-proton cross section at a centre-of-mass energy of sqrt(s) = 7 TeV. Using the CMS detector at the LHC, the inelastic cross section is measured through two independent methods based on information from (i) forward calorimetry (for pseudorapidity 3 < abs(eta) < 5), in collisions where at least one proton loses more than 5E-6 of its longitudinal momentum, and (ii) the central tracker (abs(eta) < 2.4), in collisions containing an interaction vertex with more than 1, 2, or 3 tracks with transverse momenta pT > 200 MeV. The measurements cover a large fraction of the inelastic cross section for particle production over about 9 units of pseudorapidity and down to small transverse momenta. The results are compared with those of other experiments, and with models used to describe high-energy hadronic interactions.

Pseudorapidity gap distributions in proton-proton collisions at sqrt(s) = 7 TeV are studied using a minimum bias data sample with an integrated luminosity of 7.1 inverse microbarns. Cross sections are measured differentially in terms of Delta eta F, the larger of the pseudorapidity regions extending to the limits of the ATLAS sensitivity, at eta = +/- 4.9, in which no final state particles are produced above a transverse momentum threshold p_T Cut. The measurements span the region 0 < Delta eta F < 8 for 200 < p_T Cut < 800 MeV. At small Delta eta F, the data test the reliability of hadronisation models in describing rapidity and transverse momentum fluctuations in final state particle production. The measurements at larger gap sizes are dominated by contributions from the single diffractive dissociation process (pp -> Xp), enhanced by double dissociation (pp -> XY) where the invariant mass of the lighter of the two dissociation systems satisfies M_Y <~ 7 GeV. The resulting cross section is d sigma / d Delta eta F ~ 1 mb for Delta eta F >~ 3. The large rapidity gap data are used to constrain the value of the pomeron intercept appropriate to triple Regge models of soft diffraction. The cross section integrated over all gap sizes is compared with other LHC inelastic cross section measurements.

A first measurement of the inelastic cross-section is presented for proton-proton collisions at a center of mass energy sqrt{s}=7 TeV using the ATLAS detector at the Large Hadron Collider. In a dataset corresponding to an integrated luminosity of 20 mub-1, events are selected by requiring hits on scintillation counters mounted in the forward region of the detector. An inelastic cross-section of $60.3 +/- 2.1 mb is measured for xi > 5x10^-6, where xi=M_X^2/s is calculated from the invariant mass, M_X, of hadrons selected using the largest rapidity gap in the event. For diffractive events this corresponds to requiring at least one of the dissociation masses to be larger than 15.7 GeV.

The highest-energy measurement of ΔσL(pp) and the first ever measurement of ΔσL(p¯p), the differences between proton-proton and antiproton-proton total cross sections for pure longitudinal spin states, are described. Data were taken using 200-GeV/c polarized beams incident on a polarized-proton target. The results are measured to be ΔσL(pp)=−42±48(stat)±53(syst) μb and ΔσL(p¯p)=−256±124(stat)±109(syst) μb. Many tests of systematic effects were investigated and are described, and a comparison to theoretical predictions is also given. Measurements of parity nonconservation at 200 GeV/c in proton scattering and the first ever of antiproton scattering have also been derived from these data. The values are consistent with zero at the 10−5 level.

Based on an analysis of the extensive air shower data accumulated over the last ten years at Akeno Cosmic Ray Observatory, the value of the proton-air nuclei inelastic cross section (σinp−air) has been determined assuming the validity of quasi-Feynman scaling of particle production in the fragmentation region. The energy dependence of σinp−air can be represented as 290(E/1 TeV)0.052 mb in the energy interval 1016.2–1017.6 eV, where E is the incident proton energy. The total p-p cross section (σtotp−p), derived using the nuclear distribution function obtained from the shell model, increases with energy as 38.5+1.37 ln2(√s /10 GeV) mb.

The pp total, elastic, and all the inelastic cross sections were measured at 11 momenta in the range 0.9–2.0 GeV/c. No clear structure was observed in their momentum dependences. The momentum dependence of the total cross section agrees quite well with the result of a phase-shift analysis by Arndt. Our measurement of the ppπ 0 and pnπ + cross sections served to normalize the earlier systematic but relative and extrapolated measurements of these cross sections over a narrower momentum range. Calculations by König and Kroll based on a pion exchange model including the effect of an I = 1 dibaryon did not fit the single-pion production cross sections.

The SATURNE II polarized proton beam and the Saclay frozen spin polarized proton target were used to measure the total cross section difference Δσ T = −2 σ 1 tot at 26 energies between 0.43 and 2.4 GeV. Here Δσ T is the total cross section difference for transverse beam and target spins parallel and antiparallel, respectively, and σ 1tot is one of spin-dependent terms in the total cross section σ tot . The energy dependence of Δσ T below 1 GeV shows similar structures as for Δσ L . An additional minimum appears at about 1.3 GeV, which involves a structure in singlet spin partial waves.

The Fermilab hybrid 30-in. bubble-chamber spectrometer was exposed to a tagged 147-GeV/c positive beam containing π+, K+, and p. A sample of 3003 K+p, 19410 pp, and 20745 π+p interactions is used to derive σn, 〈n〉, f2cc, and 〈nc〉D for each beam particle. These values are compared to values obtained at other, mostly lower, beam momenta. The overall dependence of 〈n〉 on Ea, the available center-of-mass energy, for these three reactions as well as π−p and pp interactions has been determined.

Elastic scattering and single-pion production in pp collisions at 6.92 BeVc were studied in the BNL 80-in. hydrogen bubble chamber. Partial cross sections for the different final states are given. The reaction pp→nN1238*(pπ+) with σ=1.9±0.3 mb is analyzed and is in agreement with the modified one-pion-exchange model. Single-pion production can be explained as due mainly to two channels: (a) pp→N1238*(pπ+)n, and (b) pp→p(nπ+) or pp→p(pπ0), where the (nπ+) and (pπ0) pairs are in an I=12 state.

We have measured the difference between the pp total cross sections for parallel and antiparallel longitudinal spin states at beam momenta of 1.0, 1.1, 1.30, 1.58, 1.71, 2.1, and 2.25 GeV/c in a transmission counter experiment. These results reveal new structure in the plab range of 1.0 to 2.5 GeV/c.

In an exposure of the chamber Mirabelle at the Serpukhov accelerator, 1 943 interactions at 50 GeV/ c and 8 959 at 69 GeV/ c have been observed. Topological cross sections and charged multiplicity distributions are presented. The average charged multiplicities found are respectively 5.32 ± 0.13 and 5.89 ± 0.07.

From 2728 events of 205-GeV pp interactions found in 15 000 pictures taken with the 30-in. hydrogen bubble chamber at the National Accelerator Laboratory, a total cross section of 39.5±1.1 mb was measured. The mean charged-particle multiplicity for inelastic pp collisions was measured to be 7.65±0.17. The prong distribution from 2 to 22 prongs is broader than a Poisson distribution and has a width parameter f2−=〈n−(n−−1)〉−〈n−〉2=0.95±0.21.

The charged-particle multiplicity distribution in 205−GeVc proton-proton interactions is presented. In addition, the total diffractive contributions to each charged multiplicity are estimated assuming a factorizable Pomeron.

We have measured the differential cross section for small angle p−p scattering from 25 to 200 GeV incident energy and in the momentum transfer range 0.015<|t|<0.080 (GeVc)2. We find that the slope of the forward diffraction peak, b(s), increases with energy and can be fitted by the form b(s)=b0+2α′ lns, where b0=8.3±1.3 and α′=0.28±0.13 (GeVc)−2. Such dependence is compatible with the data existing both at higher and lower energies. We have also obtained the energy dependence of the p−p total cross section in the energy range from 48 to 196 GeV. Within our errors which are ± 1.1 mb the total cross section remains constant.

We have measured the difference between the pp total cross-sections for parallel and anti-parallel longitudinal spin states at beam momenta of 3 and 6 GeV/ c . These results, combined with our previous measurements, at lower momenta, are useful in clarifying a striking structure appearing at around 1.5 GeV/ c . We have also measured for the first time, the spin-spin correlation parameter C LL ( t ) in pp elastic scattering at 6 GeV/ c . We observe evidence for an exchange with A 1 -like quantum-numbers.

We have measured the total cross-section difference for pp scattering in initial spin states parallel to the beam direction at beam momenta of 1.17, 1.47, 1.69, 1.97 and 2.49 GeV/ c . This measurement was done in a standard transmission experiment. A striking energy dependence is observed with a maximum difference of −16.9 mb at P lab = 1.47 GeV/ c .