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.
The measured total cross section. The systematic uncertainty includes experimental and theoretical uncerainties.
The measured total cross section. The systematic uncertainty includes experimental and theoretical uncerainties.
The rho-parameter, i.e. the ratio of the real to imaginary part of the elastic scattering amplitude extrapolated to t=0. The systematic uncertainty includes experimental and theoretical uncerainties.
A measurement of the total $pp$ cross section at the LHC at $\sqrt{s}=8$ TeV is presented. An integrated luminosity of $500$ $\mu$b$^{-1}$ was accumulated in a special run with high-$\beta^{\star}$ beam optics to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable $t$. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the $-t$ range from $0.014$ GeV$^2$ to $0.1$ GeV$^2$ to extrapolate $t\rightarrow 0$, the total cross section, $\sigma_{\mathrm{tot}}(pp\rightarrow X)$, is measured via the optical theorem to be: $\sigma_{\mathrm{tot}}(pp\rightarrow X) = {96.07} \; \pm 0.18 \; ({{stat.}}) \pm 0.85 \; ({{exp.}}) \pm 0.31 \; ({extr.}) \; {mb} \;,$ where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation $t\rightarrow 0$. In addition, the slope of the exponential function describing the elastic cross section at small $t$ is determined to be $B = 19.74 \pm 0.05 \; ({{stat.}}) \pm 0.23 \; ({{syst.}}) \; {GeV}^{-2}$.
The measured total cross section, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The nuclear slope of the differential eslastic cross section at small |t|, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The total elastic cross section and the observed elastic cross section within the fiducial volume.
A measurement of the total $pp$ cross section at the LHC at $\sqrt{s}=7$ TeV is presented. In a special run with high-$\beta^{\star}$ beam optics, an integrated luminosity of 80 $\mu$b$^{-1}$ was accumulated in order to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable $t$. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the $|t|$ range from 0.01 GeV$^2$ to 0.1 GeV$^2$ to extrapolate to $|t|\rightarrow 0$, the total cross section, $\sigma_{\mathrm{tot}}(pp\rightarrow X)$, is measured via the optical theorem to be: $$\sigma_{\mathrm{tot}}(pp\rightarrow X) = 95.35 \; \pm 0.38 \; ({\mbox{stat.}}) \pm 1.25 \; ({\mbox{exp.}}) \pm 0.37 \; (\mbox{extr.}) \; \mbox{mb},$$ where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation to $|t|\rightarrow 0$. In addition, the slope of the elastic cross section at small $|t|$ is determined to be $B = 19.73 \pm 0.14 \; ({\mbox{stat.}}) \pm 0.26 \; ({\mbox{syst.}}) \; \mbox{GeV}^{-2}$.
The measured total cross section, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The nuclear slope of the differential eslastic cross section at small |t|, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The Optical Point dsigma/(elastic)/dt(t-->0), the total elastic cross section and the observed elastic cross section within the fiducial volume. The first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
We have measured the asymmetry of elastic pp scattering at small scattering angles (30–100 mrad) in the Coulomb-nuclear interference region, using the polarized proton beam of Saturne II, a segmented scintillator active target, and two telescopes of multiwire proportional chambers. Results are given at four energies — 940, 1000, 1320 and 2440 MeV-and are compared with phase-shift calculations.
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Interactions of 781-MeV π+ mesons with protons were investigated using the Brookhaven National Laboratory 14-in. hydrogen bubble chamber. A total of 2305 events was observed. The data were normalized to a total cross section of 22.2 mb, giving partial cross sections σ(π+p→π+p)=9.5±0.5 mb, σ(π+p→π+pπ0)=9.3±0.5 mb, σ(π+p→π+π+n)=2.15±0.17 mb, and a multiple-pion-production cross section of 1.15±0.17 mb. The elastic angular distribution was obtained and is dσdω=(0.25±0.03)+(0.90±0.11)cosθc.m.+(2.57±0.24)cos2θc.m.+(0.19±0.22)cos3θc.m.−(1.73±0.34)cos4c.m.. The kinetic-energy and angular distributions of the outgoing particles in single-pion production are given. The data are compared with other experiments in this energy region and their relevance to the shoulder in the π+p total cross section near 830 MeV is discussed.
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Results are presented onK+p elastic scattering and on the reactionK+p→K+pπ+π− at 70 GeV/c. For the
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INTEGRATION OVER RANGE OF ABS(T) FROM 0 TO 1 GEV.
ELASTIC DIFFERENTIAL CROSS SECTION AT T=0 DERIVED FROM THE OPTICAL THEOREM.
500 MeV p→+p elastic and quasielastic, and p→+n quasielastic, analyzing powers (Ay) and spin-rotation-depolarization parameters (DSS, DSL, DLS, DLL, DNN) were determined for center-of-momentum angular ranges 6.8°–55.4° (elastic) and 22.4°–55.4° (quasielastic); liquid hydrogen and deuterium targets were used. The p→+p elastic and quasielastic results are in good agreement; both the p→+p and p→+n parameters are well described by current phase shift solutions.
The elastic P P analysing power at 500 MeV incident proton energy. There is an additional overall normalization uncertainty of 1 PCT.
The spin depolarization and spin rotation parameters in 500 MeV P P elastic interactions. Additional normalization uncertainty of 1 PCT (2 PCT for DLL and DLS).
The elastic P P analysing power at 500 MeV incident proton energy. There is an additional overall normalization uncertainty of 1 PCT.
The spin correlation parameter A00NN for 497.5 MeV proton + proton elastic scattering was determined over the center-of-momentum scattering angle region 23.1°–64.9 °. The new A00NN extend to more forward angles than existing A00NN and have significantly smaller statistical errors (±0.01–0.04). The A00NN are qualitatively described by recent phase shift analyses, but a quantitative shape and normalization discrepancy remains in the forward angle region. These new data provide important constraints for nucleon-nucleon spin-dependent amplitudes at forward angles which are used in theoretical models of nucleon-nucleus scattering.
Errors include statistical and systematic uncertainties.
The spin-rotation parameters A and R and the related spin-rotation angle β have been measured for π+p and π−p elastic scattering using protons polarized in the scattering plane. The pion-beam momenta are 427, 471, 547, 625, and 657 MeV/c and the angular range is −0.9≤cosΘc.m.≤0.3. The scattered pion and recoil proton were detected in coincidence, using a scintillator hodoscope for the pions, and the Large Acceptance Spectrometer combined with the JANUS polarimeter for the recoil protons. The results are compared with the four recent πN partial wave analyses (PWA's). Our data show that the major features of these PWA's are correct. The A and R measurements complete our program of pion-nucleon experiments, providing full data sets at three of the above beam momenta. Such sets can be used to test the constraints in the PWA's or to obtain a model-independent set of πN scattering amplitudes.
BETA is the spin-rotation angle.
BETA is the spin-rotation angle.
BETA is the spin-rotation angle.
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