Full angular distributions of the polarization parameter in elastic K+p scattering at 1.37, 1.45, 1.60, 1.71, 1.80, 1.89, 2.11, and 2.31 GeV/c are presented. These data were obtained in an experiment at the Zero Gradient Synchrotron using a polarized proton target with arrays of scintillation and Čerenkov counters to detect the scattered particles.
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The polarization parameter for K + p elastic scattering has been measured at 1.60, 1.80, 2.11 and 3.31 GeV/ c incident momenta over the entire angular range with an emphasis on the backward region. The results in the extreme backward region appear to be small and consistent with zero.
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Differential cross sections for p−p elastic scattering are presented with scattering angles in the center-of-mass system greater than 35° to 50°. The data were obtained at incident laboratory momenta 0.857, 1.091, 1.210, 1.374, 1.405, and 1.501 GeV/c. This spans the region of the onset of Δ(1236) production and where a possible spin-singlet D-wave resonance is indicated in an analysis of earlier data.
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We report here the results from an experiment to obtain differential cross sections for K−p elastic scattering in the laboratory momentum region from 1.4 to 1.9 GeV/c. These data span the region of a bump in the K−p total cross section at an energy of 2.05 GeV. Approximately 20000 elastic events were obtained at each of four momenta with an angular coverage of 0.9≥cosθc.m.≥−0.9. The data are intended to aid in phase-shift analyses of the resonances causing the bump in the total cross section and to study dip structures at constant values of the Mandelstam variables t and u.
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LEGENDRE POLYNOMIAL COEFFICIENTS.
FROM INTEGRATING LEGENDRE POLYNOMIAL FIT TO D(SIG)/DOMEGA. QUOTED ERRORS INCLUDE NORMALIZATION AND FITTING UNCERTAINTIES.
Differential cross sections for π+p elastic scattering in the momentum region 1.2 to 2.3 GeV/c are presented for the center-of-mass angular range 0.9>cosθ>−0.9. Typically, 50 000 events were obtained at each of 16 momenta using magnetostrictive-readout wire spark chambers to detect the particles scattered from a liquid hydrogen target. The results are compared to those of the CERN-71 phase-shift analysis. The well-known dips at t≅−0.7 (GeV/c)2 and at u′=−0.2 (GeV/c)2 are observed. In addition, structure is seen at constant u′=−1.3 (GeV/c)2. The results of a pion attenuation study in iron are also presented.
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We report on an experiment to obtain differential cross sections for K+p elastic scattering in the vicinity of the possible exotic baryon, the Z1*(1900). The differential cross sections are based on typically 70 000 selected events in the angular region −0.9≤cosθc.m.≤0.9 at each of 22 momenta from 0.865 to 2.125 GeV/c. The data are intended for use in partial-wave analysis to search for the Z1*.
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The analyzing power, A, was measured in proton-proton elastic scattering with use of a polarized proton target and 28-GeV/c primary protons from the alternating-gradient synchrotron. Over the P⊥2 range of 0.5 to 2.8 (GeV/c)2, the data show interesting structure. There is a rather sharp dip at P⊥2=0.8 (GeV/c)2 corresponding to the break in the elastic differential cross section at the end of the diffraction peak.
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We measured dσdt for p+p→p+p at 11.75 GeV/c using the zero-gradient synchrotron 70% polarized-proton beam and a 65% polarized-proton target. We obtained the spin-orbit asymmetry parameter A and the spin-spin correlation parameter Cm out to P⊥2=4.2 (GeV/c)2. We found that A drops smoothly towards zero, but that Cnn increases abruptly near P⊥2=3.6 (GeV/c)2, where the exp(−1.4P⊥2) component of elastic scattering becomes dominant. This suggests that large-P⊥2 "hard" elastic scattering may occur mostly when the two proton spins are parallel.
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Accelerating polarized protons to 22 GeV/c at the Brookhaven Alternating Gradient Synchro- tron required both extensive hardware modifications and a difficult commissioning process. We had to overcome 45 strong depolarizing resonances to maintain polarization up to 22 GeV/c in this strong-focusing synchrotron. At 18.5 GeV/c we measured the analyzing power A and the spin-spin correlation parameter Ann in large- P⊥2 proton-proton elastic scattering, using the polarized proton beam and a polarized proton target. We also obtained a high-precision measurement of A at P⊥2=0.3 (GeV/c)2 at 13.3 GeV/c. At 18.5 GeV/c we found that Ann=(-2±16)% at P⊥2=4.7 (GeV/c)2, where it was about 60% near 12 GeV at the Argonne Zero Gradient Synchrotron. This sharp change suggests that spin-spin forces may have a strong and unexpected energy dependence at high P⊥2.
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2.2 GeV point taken from Brown et al., PR D31(85) 3017.
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Measurement was made of dσdt for n↑+p↑→n+p at P⊥2=0.8 and 1.0 (GeV/c)2 at 6 GeV/c. The 6-GeV/c 53%-polarized neutrons from the 12-GeV/c polarized deuteron beam at the Argonne zero-gradient synchroton were scattered from our 75%-polarized proton target. Both spins were oriented perpendicular to the scattering plane. We found large unexpected spin-spin effects in n−p elastic scattering which are quite different from the p−p spin-spin effects.
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We measured the differential cross section for proton-proton elastic scattering at 6 GeV/c, with both initial spins oriented normal to the scattering plane. The analyzing power A shows significant structure with a large broad peak reaching about 24% near P⊥2=1.6 (GeV/c)2. The spin-spin correlation parameter Ann exhibits more dramatic structure, with a small but very sharp peak rising rapidly to about 13% at 90°c.m.. This sharp peak may be caused by particle-identity effects.
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The energy dependence of the spin-parallel and spin-antiparallel cross sections for p↑+p↑→p+p at 90°c.m. was measured for beam momenta between 6 and 12.75 GeV/c. The ratio (dσdt)parallel:(dσdt)antiparallel at 90° is about 1.2 up to 8 GeV/c and then increases rapidly to a value of almost 4 near 11 GeV/c. Our data indicate that this ratio may depend only on the variable P⊥2, and suggests that the ratio may reach a limiting value of about 4 for large P⊥2.
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Forward differential cross sections for π − p elastic scattering at 1.0, 1.5 and 2.0 GeV/ c show that the square of the imaginary parts of the nuclear scattering agrees with the optical theorem prediction within ±3%, when averaged over the three momenta.
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Cross sections are presented for the K + p interacttions with 2, 3, 4 and 5 particles in the final state for incident momenta between 2.1 and 2.7 GeV/c. The results are compared with those from other experiments at nearby momenta.
Axis error includes +- 0.0/0.0 contribution (?////).
A bubble chamber investigation of π−+p elastic scattering at 1 200 MeV (K.E.) is reported. The total and differential cross-sections are determined. By extrapolation of the angular distribution, the 0° cross-section is derived and compared with the results obtained with the help of the dispersion relations and the optical theorem. The forward peak is investigated in terms of diffraction scattering and a value for the optical radius is derived.
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Final results are presented of the analysis of the elastic channel in an exposure of 40 000 pictures at each of the four incident K + momenta 2.11, 2.31, 2.5 and 2.72 GeV/ c taken in the 1.5 m British National Hydrogen Bubble Chamber at the 8 GeV/ c proton synchrotron at the Rutherford High Energy Laboratory. Differential cross sections are presented and the results are compared with other published data. A Legendre polynomial analysis requires partial waves up to G wave at all momenta. For the backward peak, visible at each momentum, the slope and the intercept are calculated. A comparison of the forward peak is made with extrapolations from Regge models fitted at higher momenta.
RESULTS DIFFER SLIGHTLY FROM THOSE PREVIOUSLY REPORTED IN J. M. BRUNET ET AL., NP B36, 45 (1972).
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Measurements of polarization in π+p elastic scattering have been made at 1.60, 1.80, 2.11, and 2.31 GeVc. The data cover the entire angular range, with emphasis on the backward region. Comparisons have been made with both u-channel and t-channel models, as well as with predictions of phase-shift analyses. While the agreement is generally poor in all cases, the best agreement is with some t-channel predictions.
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We measured dσdt for p↑+p↑→p+p from P⊥2=4.50 to 5.09 (GeV/c)2 at 11.75 GeV/c. We used a 59%-polarized proton beam and a 71%-polarized proton target with both spins oriented perpendicular to the scattering plane. In these large-P⊥2 hard-scattering events, spin effects are very large and the ratio (dσdt)↑↑:(dσdt)↑↓ grows rapidly with increasing P⊥2, reaching a value of 4 at 90° (c.m.). Thus, hard elastic scattering, which is presumably due to the direct scattering of the protons' constituents, may only occur when the two incident protons' spins are parallel.
THE ERRORS INCLUDE STATISTICAL AND SYSTEMATIC ERRORS ADDED IN QUADRATURE. THE PARALLEL/ANTIPARALLEL SPIN CROSS SECTION RATIO IS (1+CNN)/(1-CNN).
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.
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.
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