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 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.
The nuclear slope parameter B from a fit of the form exp(-Bt-Ct^2-Dt^3). The systematic uncertainty includes experimental and theoretical uncerainties.
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.
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.
As a part of our program to study p−p collisions at Cosmotron energies, the differential cross sections for elastic scattering were measured at five laboratory angles between 2.3° and 17° for each incident energy. Total elastic cross sections obtained by integration are 21.4±1.4, 17.0±0.8, and 14.7±0.7 mb at 1.35, 2.1, and 2.9 BeV, respectively. The angular distribution as a function of the momentum transfer, exhibits a forward diffraction peak, the width of which shrinks slightly as the incident energy increases. The experimental results were fitted by simple optical model calculations and also compared with the predictions of the composite particle theory of Chew and Frautschi.
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The differential cross section for π + p elastic scattering at 895, 945, 995 and 1040 MeV/ c has been measured in a hydrogen bubble chamber. The results are in good agreement with previous measurements using counter techniques except at extreme backward angles where significantly lower cross sections are obtained.
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The differential cross sections for K − p and p p elastic scattering have been measured over the range of four-momentum transfer squared 0.18<− t <3.3 (GeV/ c ) 2 . The K − p data decrease smoothly as a function of − t , whereas, the p p data shows a break at − t = 0.6 (GeV/ c ) 2 followed by a fast drop to − t ≅ 1.6 (GeV/ c ) 2 where the differential cross section levels off and stays constant out to − t = 3 (GeV/ c ) 2 .
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Total and differential cross sections are presented for the reactions K − p → K − p and K − p → K o n at 13 points in the c.m. energy range 1915–2168 MeV. An energy-dependent partial-wave analysis is carried out on these data together with the polarisation measurements of Daum et al. [1] and the total cross section measurements [2] within this energy range. The well known Σ(1915), Σ(2030) and Λ(2100) are observed and their resonance parameters measured. Structure is also found in the D 05 and F 07 waves. An SU(3) analysis of the 5 2 + octet, 7 2 + decuplet and 7 2 − singlet gives generally good agreement between theory and experiment except that the elasticity of the Σ(1915) is experimentally rather larger than predicted.
DETERMINED BY NORMALIZING AT ZERO DEG TO TOTAL CROSS SECTIONS VIA THE OPTICAL THEOREM.
THE MAXIMUM VALUE OF COS(THETA) VARIED BETWEEN 0.978 AND 0.988 (SEE TABLE 3).
We have measured π+p, π−p, and pp elastic scattering at an incident-beam momentum of 200 GeV/c in the region of −t, four-momentum transfer squared, from 0.021 to 0.665 (GeV/c)2. The data allow an investigation of the t dependence of the logarithmic forward slope parameter b≡(ddt)(lndσdt). In addition to standard parametrization, we use functional forms suggested by the additive quark model to fit the measured dσdt distributions. Within the context of this model we estimate the size of the clothed quark in the pion and proton. Limits on the elastic-scattering amplitude derived from unitarity bounds are checked, and no violations are observed.
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K + p elastic scattering has been measured over nearly the whole angular range at an incident momentum of 10 GeV/ c . The differential cross-section is found to decrease smoothly in the forward direction to - t ≈ 2 (GeV/ c ) 2 , where there is a change in slope, followed by a further decrease to - t ≈ 6 (GeV/ c ) 2 . Around 90° c.m. the cross-section is approximately 1 nb/(GeV/ c ) 2 , which is more than two orders of magnitude lower than at 5 GeV/ c . The backward peak has no structure.
THESE DATA ARE REPORTED MORE FULLY IN C. BAGLIN ET AL., NP B98, 365 (1975).
Measurements of the K - p and K + p elastic differential cross sections at 20 and 50 GeV/ c , respectively, have been made in the momentum transfer range 0.7 < ∥ t ∥ < 8.0 GeV/ c .
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