Date

Small Angle Elastic p p Scattering at 30-GeV, 50-GeV, and 70-GeV

Geshkov, I.M. ; Ikov, N.L. ; Markov, P.K. ; et al.
Phys.Rev.D 13 (1976) 1846-1850, 1976.
Inspire Record 113910 DOI 10.17182/hepdata.24790

A thin polyethylene target was exposed to the internal proton beam of the Serpukhov accelerator at 30, 50, and 70 GeV. The wide-angle recoil protons were registered by photoemulsion stacks and the differential cross sections of the elastic p−p scattering in the range of four-momentum transfer squared 0.0025≤|t|≤0.12 (GeV/c)2 were measured. The ratio of the real to the imaginary part of the forward nuclear amplitude α, the slope parameter of the diffraction peak b, and the total elastic cross section σel were found to be as follows: at 30 GeV, α=−0.183±0.051, b=10.61±0.27 (GeV/c)−2, σel=7.7±0.2 mb; at 50 GeV, α=−0.068±0.040, b=11.25±0.28 (GeV/c)−2, σel=7.0±0.2 mb; at 70 GeV, α=−0.104±0.065, b=11.21±0.40 (GeV/c)−2, σel=7.1±0.2 mb.

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Measurements of Elastic Scattering in $\alpha^- \alpha$ and $\alpha$ - Proton Collisions at the {CERN} Intersecting Storage Rings

The CERN-Naples-Pisa-Stony Brook collaboration Ambrosio, M. ; Anzivino, G. ; Barbarino, G. ; et al.
Phys.Lett.B 113 (1982) 347-352, 1982.
Inspire Record 176959 DOI 10.17182/hepdata.30919

We measured the elastic scattering of αα at s = 126 GeV and of α p at s = 89 GeV . For αα , the differential cross section d σ /d t has a diffractive pattern minima at | t | = 0.10 and 0.38 GeV 2 . At small | t | = 0.05−0.07 GeV 2 , this cross section behaves like exp[(100 ± 10) t ]. Extrapolating a fit to the data to the optical point, we obtained for the total cross section α tot ( αα ) = 250 ± 50 mb and an integrated elastic cross section σ e1 ( αα ) = 45 ± mb. Another method of estimating σ tot ( αα ), based on measuring the interaction rate, yielded 295 ± 40 mb. For α p, d σ /d t has aminimum at | t | = 0.20 GeV 2 , and for 0.05 < | t | < 0.18 GeV 2 behaves like exp[(41 ± 2) t ]. Extrapolating this slope to | t | = 0, we found σ tot ( α p) = 130 ± 20 and σ e1 ( α p) = 20 ± 4mb. Results on pp elastic scattering at s = 63 GeV agree with previous ISR experiments.

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Elastic $pp$ scattering at 1.45 BeV

Kruchinin, S.P. ; Mukhin, K.N. ; Romantseva, A.S. ; et al.
Sov.J.Nucl.Phys. 1 (1965) 225-229, 1965.
Inspire Record 1392861 DOI 10.17182/hepdata.54964

None

2 data tables match query

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Proton-Proton Interactions at 5.5 GeV/c

Alexander, G. ; Benary, O. ; Czapek, G. ; et al.
Phys.Rev. 154 (1967) 1284-1304, 1967.
Inspire Record 52243 DOI 10.17182/hepdata.55119

This report is based on about 10 500 pp collision events produced in the 81-cm Saclay hydrogen bubble chamber at CERN. Cross-section values for the different identified final states and resonances are given. The isobars N*1238, N*1420, N*1518, N*1688, N*1920, and N*2360 were identified and their production cross-section values were found via a best-fit analysis of different invariant-mass histograms. About 70% of the isobars are connected with the quasi-two-body reactions pp→N*N and pp→N*N*. The reaction pp→nN*1238(pπ+) with a cross section of 3.25±0.16 mb was analyzed in terms of a peripheral absorption model, which was found to be in good agreement with the data. Various decay modes of the N*1518 and N*1688 isobars were observed and their branching ratios determined. The branching ratio of nπ+ to pπ+π− was found to be 0.77±0.45 for N*1518 and 0.67±0.40 for N*1688. The branching ratio of N*1238(pπ+)π− to pπ+π− of N*1688 was estimated to be 0.74±0.14. Pion production turned out to be mainly due to decay of isobars. Production of meson resonances turned out to be less important; the reaction pp→ppω0→ppπ+π−π0 was identified with a cross-section value of 0.11±0.02 mb. Finally, the production of neutral strange particles with a cross section of 0.45±0.04 mb is descussed. Strong formation of Y*1385 is observed.

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Isobar production and elastic scattering in p p interactions from 6-GeV/c to 30-GeV/c

Edelstein, R.M. ; Carrigan, Richard A., Jr. ; Hien, N.C. ; et al.
Phys.Rev.D 5 (1972) 1073-1096, 1972.
Inspire Record 67297 DOI 10.17182/hepdata.22467

Differential cross sections have been measured for nucleon-isobar production and elastic scattering in p−p interactions from 6.2 to 29.7 GeVc in the laboratory angle range 8<θsc<265 mrad. N*' s at 1236, 1410, 1500, 1690, and 2190 MeV were observed. Computer fits to the mass spectra under varying assumptions of resonance and background shapes show that conclusions on t and s dependence are only slightly affected despite typical variations in absolute normalization of ± 35%. Logarithmic t slopes in the small- |t| range are ∼15 (GeVc)−2 for the N*(1410), ∼5 (GeVc)−2 for the N*'s at 1500, 1690, and 2190 MeV, and ∼9 (GeVc)−2 for elastic scattering. Also for the small- |t| data, cross sections for N*'s at 1410, 1500, 1690, and 2190 MeV and for elastic scattering vary only slightly with Pinc consistent with the dominance of Pomeranchuk exchange and with diffraction dissociation. A fit of N*(1690) total cross sections to the form σ∝P−n gives n=0.34±0.06, while for elastic scattering n=0.20±0.05. For the N*(1690) the effective Regge trajectory has the slope αeff′(0)=0.38±0.17. When compared with N* production in π−, K−, and p¯ beams these data also agree with approximate factorization of the Pomeranchuk trajectory. N*(1236) cross sections are consistent with other measurements at similar momenta. For −t>1 (GeVc)−2, elastic scattering cross sections decrease approximately as Pinc−2, and they and N*(1500)− and N*(1690)− production cross sections have t slopes consistent with 1.6 (GeVc)−2.

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Analysis of two-prong events in proton proton interactions at 6.6 gev/c

Colton, E. ; Ming, Ma.Z. ; Smith, G.A. ; et al.
Phys.Rev.D 7 (1972) 3267-3295, 1972.
Inspire Record 82060 DOI 10.17182/hepdata.22134

A detailed analysis is presented of the reactions pp→pp,pp→ppπ0 and pp→pπ+n. The production cross sections are found to be 11.47 ± 0.33 mb, 2.54 ± 0.16 mb, and 5.73 ± 0.35 mb, respectively. The t dependence of elastic scattering can be described by the form e7.9t over the range 0.05<−t<0.50 GeV2. The single-particle distributions for the single-pion production processes are presented. Further detailed analyses are presented which demonstrate that pion-exchange phenomenology, both elementary and Reggeized, can account for the gross features of the peripheral pp→pπ+n data for M(pπ+)<2.4 GeV. Isospin-12 isobars are produced by some other processes in the channel pp→pN*+, especially when the invariant mass of the pion with the unrelated proton is large. We discuss the properties of these isobars.

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FITTED OVER 0.05 < -T < 0.5 GEV**2.

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Proton-proton small angle scattering and total cross section of 10.0 GeV⧸c

Bellettini, G. ; Cocconi, G. ; Diddens, A.N. ; et al.
Phys.Lett. 19 (1966) 705-705, 1966.
Inspire Record 1389783 DOI 10.17182/hepdata.782

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Total cross-sections of protons, anti-protons, and pi and K mesons on hydrogen and deuterium in the momentum range 6-GeV/c to 22-GeV/c

Galbraith, W. ; Jenkins, E.W. ; Kycia, T.F. ; et al.
Phys.Rev. 138 (1965) B913-B920, 1965.
Inspire Record 48756 DOI 10.17182/hepdata.5477

The total cross sections σT of p, p¯, π±, and K± on hydrogen and deuterium have been measured between 6 and 22 GeVc at intervals of 2GeVc to an accuracy greater than previously reported. The method utilized was a conventional good-geometry transmission experiment with scintillation counters subtending various solid angles at targets of liquid H2 and D2. With the increase in statistical accuracy of the data, it was found that a previously adopted procedure of linearly extrapolating to zero solid angle the partial cross sections measured at finite solid angles was not a sufficiently accurate procedure from which to deduce σT. The particle-neutron cross sections are derived by applying the Glauber screening correction to the difference between the particle-deuteron and particle-proton cross sections. The cross sections σT(π+d) and σT(π−d) are equal at all measured momenta, which confirms the validity of charge symmetry up to 20GeVc. Results are presented showing the variation of cross sections with momentum; evidence is presented for a small but significant decrease in σT(pp) [and σT(pn)] in the momentum region above 12GeVc.

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Hadron - Nucleus Scattering at 70-GeV/c, 125-GeV/c and 175-GeV/c and a High Statistics Study of Hadron - Proton Elastic Scattering at 200-GeV/c

Schiz, Alan M. ; Sandweiss, Jack ;
FERMILAB-THESIS-1979-17, 1979.
Inspire Record 147258 DOI 10.17182/hepdata.155

Results of two studies of small angle elastic scattering are presented. The first experiment measured hadron-nucleus elastic scattering at 70, 125, 175 GeV/c incident momentum. The second experiment is a high statistics study of hadron-proton elastic scattering at 200 GeV/c incident momentum. Hadron-nucleus elastic scattering was measured for $\mu^{\pm}$, $K^{\pm}$, $p$, and $\bar{p}$ scatterinq from Be, C, Al, Cu, Sn, and Pb targets at .incident beam momenta of 70 and 175 GeV/c and for $\mu^+$, $K^+$, and $p$ scattering from Be, Al, and Pb targets at an incident beam momentum of 125 GeV/c. In all cases the minimum -t is 0.001 $(GeV/c)^2$ ; the maximum -t is 0.07, 0.16. 0.30 ($GeV/c)^2$ for incident beam momenta of 70, 125, 175 GeV/c respectively. Parameterizations of the differential cross section, $d\sigma/dt$, in the forward direction are presented....

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X ERROR D(P)/P = 0.1000 PCT.


K+ p, K- p AND anti-p p ELASTIC SCATTERING AT 32.1-GeV/c

The French-Soviet & CERN-Soviet collaborations Lewin, C. ; Denegri, D. ; Givernaud, A. ; et al.
SACLAY-DPhPE-79-19, 1979.
Inspire Record 144202 DOI 10.17182/hepdata.43800

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THESE DATA ARE TABULATED IN THE RECORD OF THE PUBLISHED VERSION.

FROM QUADRATIC EXPONENTIAL FITS TO D(SIG)/DT FOR -T = 0 TO 1.4 GEV**2. SYSTEMATIC ERRORS INCLUDED.


Measurement of proton-proton elastic scattering and total cross-section at S**(1/2) = 7-TeV

The TOTEM collaboration Antchev, G. ; Aspell, P. ; Atanassov, I. ; et al.
EPL 101 (2013) 21002, 2013.
Inspire Record 1220862 DOI 10.17182/hepdata.66456

At the LHC energy of $\sqrt s = 7\,{\mathrm { TeV}}$ , under various beam and background conditions, luminosities, and Roman Pot positions, TOTEM has measured the differential cross-section for proton-proton elastic scattering as a function of the four-momentum transfer squared t. The results of the different analyses are in excellent agreement demonstrating no sizeable dependence on the beam conditions. Due to the very close approach of the Roman Pot detectors to the beam center (≈5σ(beam)) in a dedicated run with β* = 90 m, |t|-values down to 5·10(−)(3) GeV(2) were reached. The exponential slope of the differential elastic cross-section in this newly explored |t|-region remained unchanged and thus an exponential fit with only one constant B = (19.9 ± 0.3) GeV(−)(2) over the large |t|-range from 0.005 to 0.2 GeV(2) describes the differential distribution well. The high precision of the measurement and the large fit range lead to an error on the slope parameter B which is remarkably small compared to previous experiments. It allows a precise extrapolation over the non-visible cross-section (only 9%) to t = 0. With the luminosity from CMS, the elastic cross-section was determined to be (25.4 ± 1.1) mb, and using in addition the optical theorem, the total pp cross-section was derived to be (98.6 ± 2.2) mb. For model comparisons the t-distributions are tabulated including the large |t|-range of the previous measurement (TOTEM Collaboration (Antchev G. et al), EPL, 95 (2011) 41001).

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The measured differential elastic cross section.

The measured differential elastic cross section in the high |T| region. where it originally appeared as a plot, but was not tabulated.

The fitted slope parameter for the elastic cross section fitted over 4 |T| ranges.

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Anti-p p and p p Forward Elastic Scattering Between 4-GeV/c and 10-GeV/c

Jenni, P. ; Baillon, P. ; Declais, Y. ; et al.
Nucl.Phys.B 129 (1977) 232-252, 1977.
Inspire Record 120467 DOI 10.17182/hepdata.35255

Differential cross sections have been measured in the region of small forward angles (between 0 and ∼40 mrad) for the elastic scattering reactions pp → pp at 4.2, 7.0 and 10.0 GeV /c and p p → p p at 4.2, 6.0, 8.0 and 10.0 GeV /c . The maximum momentum transfer is ∼0.025 GeV 2 at the lowest and ∼0.10 GeV/c at the highest incident momentum. Values of the slope and the real part of the forward scattering amplitude of the above reactions have been derived; the values obtained are in good agreement with dispersion relations.

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TABLE ALSO GIVES SIG, SLOPE AND T-RANGE USED IN FIT.


A bubble chamber study of proton-proton interactions at 4 GeV/c Part I—Elastic scattering, single-pion and deuteron production

Ooletti, S. ; Kidd, J. ; Mandelli, L. ; et al.
Nuovo Cim.A 49 (1967) 479-498, 1967.
Inspire Record 1185329 DOI 10.17182/hepdata.981

Elastic scattering, single-pion and deuteron production have been investigated. The cross-section for elastic scattering is σelastic = (13.5±0.3) mb. The angular distribution has been fitted to dσ/d|t|=(dσ/d|t|)0 e −bt in the region of low values oft. The best fit givesb=(6.7±0.5) (GeV/c)−2 and (dσ/d|t|)0=(91±5) mb(GeV/c)−2. The cross-sections for ppπ0, pnπ+ reactions are respectively (2.6±0.3) mb and (9.7±0.4) mb. These reactions are dominated by the (3/2, 3/2) nucleonpion isobar production and by forward backward collimation of the nucleons. The production rates for the isobars ++1238 , +1238 , +1500 have been estimated, taking into account the experimental peripheral behaviour of the interaction. In the pnπ+ reaction they are (50±2)%; (10±3)%; (4±3)%. In the ppπ+ reaction the production of ++1238 is estimated to be (45±10)%. The dπ+ and dπ+π+π- reaction cross-sections are respectively (0.03±0.01) mb, and (0.04±0.01) mb.

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Cross-Sections and Charged Particle Multiplicities at 102-GeV/c and 405-GeV/c.

Bromberg, C. ; Chaney, D. ; Cohen, Daniel H. ; et al.
Phys.Rev.Lett. 31 (1973) 1563-1566, 1973.
Inspire Record 81962 DOI 10.17182/hepdata.21360

We have measured the total inelastic cross section (σinel) and charged-particle multiplicities obtained in pp collisions at 405 GeV/c. The data are from a preliminary 12 000-picture bubble-chamber exposure. We find σinel=32.8±1.0 mb; the low moments of the multiplicity distribution for negative particles are 〈n−〉=3.50±0.07, D−=2.37±0.05, f2−=2.1±0.2, and f3−=0.1±0.9. We also present updated results at 102 GeV/c.

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SUPERCEDES PRELIMINARY RESULTS IN J. W. CHAPMAN ET AL., PRL 29, 1686 (1972).

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FIT TO ELASTIC DIFFERENTIAL CROSS SECTION FOR 0.05 < -T < 0.7 GEV**2.


$pp$ Interactions at 300-GeV/c: Measurement of the Charged Multiplicity, Total and Elastic Cross-Sections

Firestone, A. ; Davidson, V. ; Lam, D. ; et al.
Phys.Rev.D 10 (1974) 2080, 1974.
Inspire Record 1242 DOI 10.17182/hepdata.25012

In a 35 000-picture exposure of the 30-in. hydrogen bubble chamber to a 300-GeV/c proton beam at the Fermi National Accelerator Laboratory, 10054 interactions have been observed. The measured total cross section is $40.68 \pm 0.55$ mb, the elastic cross section is $7.89 \pm 0.52$ mb, and the average charged-particle multiplicity for inelastic events is $8.S0 \pm 0.12$.

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QUOTED ERRORS INCLUDE EFFECTS OF CORRECTIONS.

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Two-prong events in proton proton interactions at 8.1 gev/c

Ginestet, J. ; Manesse, D. ; Tran, Ha Anh ; et al.
Nucl.Phys.B 13 (1969) 283-293, 1969.
Inspire Record 56040 DOI 10.17182/hepdata.8347

About 10 000 two-prong events of 8.1 GeV/ c proton-proton interactions in the CERN 2 m. bubble chamber have been analyzed. We study elastic scattering and single-pion production reactions. We give cross sections for isobar production. We attempt to interpret the general features of the pp→pn π + reaction by the Deck mechanism. We compare the production and the decay of δ ++ (1236) with absorption or π Regge trajectory exchange models.

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Elastic scattering and single-pion production in proton proton interactions at 6.92 bev/c

Alexander, G. ; Carmel, Z. ; Eisenberg, Y. ; et al.
Phys.Rev. 173 (1968) 1322-1329, 1968.
Inspire Record 55956 DOI 10.17182/hepdata.5540

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.

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A Measurement of $\bar{p} p$ and $p p$ Elastic Scattering at {ISR} Energies

The AMES-BOLOGNA-CERN-DORTMUND-HEIDELBERG-WARSAW collaboration Breakstone, A. ; Campanini, R. ; Crawley, H.B. ; et al.
Nucl.Phys.B 248 (1984) 253-260, 1984.
Inspire Record 204422 DOI 10.17182/hepdata.33837

We have measured the differential cross section for pp and p̄p elastic scattering at √ s = 31, 53 and 62 GeV in the interval 0.05 < | t | < 0.85 GeV 2 at the CERN ISR using the Split Field Magnet detector. At 53 and 62 GeV, for 0.17 < | t | < 0.85 GeV 2 both pp and p̄p data show simple exponential behaviour in t ; at √ s = 31 GeV the data for 0.05 < | t | < 0.85 GeV 2 are consistent with a change in slope near | t | = 0.15 GeV 2 .

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ERRORS CONTAIN BOTH STATISTICAL AND T-DEPENDENT SYSYEMATIC ERRORS.

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LOCAL SLOPE PARAMETERS BASED ON QUADRATIC EXPONENTIAL FIT.

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Precise Measurements of Proton - Anti-proton and Proton Proton Total Cross-sections at the {CERN} Intersecting Storage Rings

Carboni, G. ; Lloyd Owen, D. ; Potter, K. ; et al.
Nucl.Phys.B 254 (1985) 697-736, 1985.
Inspire Record 207680 DOI 10.17182/hepdata.33833

A detailed account is given of high-precision measurements of the total hadronic cross sections of proton-antiproton and proton-proton interactions at centre-of-mass energies of 30.6, 52.8 and 62.7 GeV. The experiment was performed at the CERN Intersecting Storage Rings (ISR) using the total interaction-rate method, in which additive correction terms for trigger losses were held to less than 6% of the final result. An experimental determination of the vertical beam-displacement scale permitted luminosity-monitor calibrations to be made with high intrinsic accuracy. The overall precision (systematic and statistical errors combined) achieved in the total cross sections was ± 1.1% for proton-antiproton reactions and 0.7% for proton-proton reactions. In the proton-proton case the measurement was the most precise such measurement made at the ISR.

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Comparison of p$ \Bar{$p$}$ and p p Elastic Scattering at $S^{(1/2)}=52$.8-{GeV}

Amos, Norman A. ; Block, M. ; Bobbink, G. ; et al.
Phys.Lett.B 120 (1983) 460-464, 1983.
Inspire Record 181387 DOI 10.17182/hepdata.30816

Proton-antiproton and proton-proton elastic scattering have been measured in the four-momentum transfer range 0.001⩽| t |⩽0.06 GeV 2 for center-of-mass energy 52.8 GeV at the CERN Intersecting Storage Rings (ISR). Using the known pp total cross section, a simultaneous fit to the pp̄ and pp differential cross sections yields the pp̄ total cross section; in addition, we obtain the ratio of the real-to-imaginary part of the forward nuclear-scattering amplitude and the nuclear-slope parameter for both pp̄ and pp. Our results show conclusively that the pp̄ total cross section is rising at ISR energies and lend support to conventional theories in which the difference between the pp̄ and pp total cross section vanishes at very high energy.

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Measurement of Small Angle anti-Proton - Proton and Proton Proton Elastic Scattering at the CERN Intersecting Storage Rings

Amos, Norman A. ; Block, M.M. ; Bobbink, G.J. ; et al.
Nucl.Phys.B 262 (1985) 689-714, 1985.
Inspire Record 214689 DOI 10.17182/hepdata.33711

Antiproton-proton and proton-proton small-angle elastic scattering was measured for centre-of-mass energies s =30.6, 52.8 and 62.3 GeV at the CERN Intersectung Storage Rings. In addition, proton-proton elastic scattering was measured at s =23.5 GeV . Using the optical theorem, total cross sections are obtained with an accuracy of about 0.5% for proton-proton scattering and about 1% for antiproton-proton scattering. The measurement of the interference of the Coulomb scattering and the hadronic scattering permits a determination of the ratio of the real-to-imaginary part of the forward hadronic scattering amplitude. Also presented are measurements of the hadronic slope parameter.

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Measurement of Elastic Scattering in Anti-proton - Proton Collisions at 52.8-{GeV} Center-of-mass Energy

The CERN-Naples-Pisa-Stony Brook collaboration Ambrosio, M. ; Anzivino, G. ; Barbarino, G. ; et al.
Phys.Lett.B 115 (1982) 495-502, 1982.
Inspire Record 178572 DOI 10.17182/hepdata.30888

We measured the differential cross section for p̄p and pp elastic scattering in the momentum-transfer range 0.01 <| t | < 1.0 GeV 2 at the CERN Intersecting Storage Rings with center-of-mass energy s = 52.8 GeV . Fitting the differential cross section with an exponential [ A exp ( bt )], we found b p p = 13.92 ± 0.59 GeV −2 for | t | < 0.05 GeV 2 , whilst for | t | > 0.09 GeV 2 , b p p = 10.68 ± 0.26 GeV −2 . Using the optical theorem, we obtained for the total cross section σ tot ( p p)= 44.86 ± 0.78 mb and, by integrating the differential cross section, we obtained for the total elastic cross section σ el ( p p) = 7.89 ± 0.28 mb . Calculations of σ tot combining elastic-rate and total-rate measurements are also given. All of these measurements were also performed for pp scattering at the same energy, and the results for both reactions are compared.

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NUMERICAL VALUES OF DATA ON FIGURES TAKEN FROM PREPRINT CERN-EP/82-65.

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Comparison of Small Angle p$ \Bar{$p$}$ and p p Elastic Scattering at the {CERN} Intersecting Storage Rings

Amos, Norman A. ; Block, M.M. ; Bobbink, G.J. ; et al.
Phys.Lett.B 128 (1983) 343-348, 1983.
Inspire Record 190335 DOI 10.17182/hepdata.30667

Antiproton-proton and proton-proton small-angle elastic scattering have been measured for centre-of-mass energies √ s = 30.7 and 62.5 GeV at the CERN Intersecting Storage Rings (ISR). Antiproton-proton and proton-proton total cross sections are obtained using the optical theorem. The measurement of the Coulomb scattering and its interference with the nuclear scattering allows a determination of the ratio of the real-to-imaginary part of the forward nuclear scattering amplitude. Also presented are measurements for the nuclear slope parameter at √ s = 62.5 GeV. Our new results reinforce the conclusions drawn recently from our measurements at √ s = 52.8 GeV. In particular, the pp̄ total cross section is rising at ISR energies and should continue to rise well beyond these energies.

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DATA REQUESTED FROM AUTHORS.

RESULTS OF FITS.

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