$\pi^- p$ Interactions at 205-GeV/c: Cross-Sections and Charged Particle Multiplicity.

Bogert, D. ; Hanft, R. ; Huson, F.R. ; et al.
Phys.Rev.Lett. 31 (1973) 1271-1274, 1973.
Inspire Record 81730 DOI 10.17182/hepdata.21380

Results are reported based on a study of 3114 π−p events at 205 GeV/c in the National Accelerator Laboratory 30-in. bubble chamber. The measured π−p total and elastic cross sections are 24.0 ± 0.5 and 3.0 ± 0.3 mb, respectively. The elastic differential cross section has a slope of 9.0 ± 0.7 GeV−2 for 0.03≤−t≤0.6 GeV2. The average charged-particle multiplicity for the inelastic events is 8.02 ± 0.12.

2 data tables match query

No description provided.

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$\pi^- p$ at 205 GeV/c: Multiplicities of Charged and Neutral Particles Production of Neutral Particles

Ljung, D. ; Bogert, D. ; Hanft, R. ; et al.
Phys.Rev.D 15 (1977) 3163, 1977.
Inspire Record 111665 DOI 10.17182/hepdata.24616

A study of 205-GeV/c π−p interactions has been made with a 48 800-picture exposure in the bare Fermilab 30-inch hydrogen bubble chamber. The average number of charged particles produced per inelastic interaction is 7.99±0.06. The elastic cross section is 3.18±0.13 mb and the total cross section is 24.19±0.44 mb. The inclusive cross sections for neutral-particle production are: σ(γ)=171.3±15.3 mb, σ(KS0)=3.64±0.61 mb (x<0.3), σ(Λ)=1.71±0.34 mb (x<0.3), and σ(Λ¯)=0.59±0.23 mb (x<0.1). The average number of π0's produced per inelastic collision is consistent with a linear rise with the number of charged particles, and about equal to the number of produced π− or π+. The average number of K0's, Λ's, and Λ¯'s is consistent with very little dependence on the number of charged particles. General characteristics of neutral-particle production are presented and compared with other experiments. For each topology the produced neutral energy is ∼13 of the incident energy.

2 data tables match query

THE ERRORS INCLUDE THOSE DUE TO VARIOUS CORRECTIONS.

No description provided.


$\pi^{\pm} p$, $K^{\pm} p$, $pp$ and $p\bar{p}$ Elastic Scattering from 50-GeV/c to 175-GeV/c

The Fermilab Single Arm Spectrometer Group collaboration Ayres, D.S. ; Diebold, R. ; Maclay, G.J. ; et al.
Phys.Rev.D 15 (1977) 3105, 1977.
Inspire Record 110409 DOI 10.17182/hepdata.24653

The differential cross sections for the elastic scattering of π+, π−, K+, K−, p, and p¯ on protons have been measured in the t interval -0.04 to -0.75 GeV2 at five momenta: 50, 70, 100, 140, and 175 GeV/c. The t distributions have been parametrized by the quadratic exponential form dσdt=Aexp(B|t|+C|t|2) and the energy dependence has been described in terms of a single-pole Regge model. The pp and K+p diffraction peaks are found to shrink with α′∼0.20 and ∼0.15 GeV−2, respectively. The p¯p diffraction peak is antishrinking while π±p and K−p are relatively energy-independent. Total elastic cross sections are calculated by integrating the differential cross sections. The rapid decline in σel observed at low energies has stopped and all six reactions approach relatively constant values of σel. The ratio of σelσtot approaches a constant value for all six reactions by 100 GeV, consistent with the predictions of the geometric-scaling hypothesis. This ratio is ∼0.18 for pp and p¯p, and ∼0.12-0.14 for π±p and K±p. A crossover is observed between K+p and K−p scattering at |t|∼0.19 GeV2, and between pp and p¯p at |t|∼0.11 GeV2. Inversion of the cross sections into impact-parameter space shows that protons are quite transparent to mesons even in head-on collisions. The probability for a meson to pass through a proton head-on without interaction inelastically is ∼20% while it is only ∼6% for an incident proton or antiproton. Finally, the results are compared with various quark-model predictions.

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$pp$ 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 $8.S0 \pm 0.12$.

2 data tables match query

QUOTED ERRORS INCLUDE EFFECTS OF CORRECTIONS.

No description provided.


201 GeV/c Proton Proton Elastic Scattering at Large Momentum Transfer

Hartmann, J.L. ; Orear, J. ; Vrieslander, J. ; et al.
Phys.Rev.Lett. 39 (1977) 975, 1977.
Inspire Record 120624 DOI 10.17182/hepdata.20930

Proton-proton elastic scattering has been measured in the region 4.9<|t|<12.1 GeV2 at a beam momentum of 201 GeV/c. If the form exp(At) is fitted to the data, the exponent A gradually changes from 1.5 to 0.9 GeV−2 over our t range. The data are consistent with the form exp(−6.6p⊥). A comparison with intersecting storage ring results shows that in this kinematical region the slopes are about the same, but dσdt at fixed t is still dropping with energy.

2 data tables match query

7904 ELASTIC EVENTS.

1030 ELASTIC EVENTS.


400 GeV/c pp Elastic Scattering: Energy and Angle Dependence at High Momentum Transfer

Conetti, S. ; Hojvat, C. ; Ryan, D.G. ; et al.
Phys.Rev.Lett. 41 (1978) 924, 1978.
Inspire Record 131549 DOI 10.17182/hepdata.20819

Proton-proton elastic scattering at 400 GeV/c has been measured in the region 5.4<−t<14.4 GeV2 with no sign of a second dip or "break." If the data are fitted by exp(At), the slope A decreases from 1.5±0.1 to 0.7±0.2 GeV−2 over the range. At fixed t the 400-GeV/c cross sections are about 0.6 times those at 200 GeV/c in this t range. At fixed θc.m.=15°, dσdt∝s−n where n=9.7±0.3.

2 data tables match query

No description provided.

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A Comparison of the Shapes of pi+ p and p p Diffraction Peaks from 50-GeV/c to 175-GeV/c

The Fermilab Single Arm Spectrometer Group collaboration Ayres, D.S. ; Diebold, Robert E. ; Maclay, G.J. ; et al.
Phys.Rev.Lett. 37 (1976) 548, 1976.
Inspire Record 108238 DOI 10.17182/hepdata.21073

The ratio of π+p to pp elastic scattering is found to be smoothly varying over the range −t=0.03 to 0.4 GeV2. It is well fitted by a single exponential, indicating the forward behavior must be quite similar for the two reactions.

1 data table match query

ACTUALLY THE DATA ARE THE EXPONENTIAL SLOPE OF THE RATIO OF D(SIG)/DT FOR THE TWO REACTIONS.


A High Statistics Study of pi+ p, pi- p, and p p Elastic Scattering at 200-GeV/c

Schiz, A. ; Fajardo, L.A. ; Majka, R. ; et al.
Phys.Rev.D 24 (1981) 26, 1981.
Inspire Record 143937 DOI 10.17182/hepdata.24037

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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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.

No description provided.

LOCAL SLOPE PARAMETERS BASED ON QUADRATIC EXPONENTIAL FIT.

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A Measurement of $\bar{p} p$ and $p p$ Elastic Scattering in the Dip Region at $\sqrt{s}=53$-{GeV}

Breakstone, A. ; Crawley, H.B. ; Dallavalle, G.M. ; et al.
Phys.Rev.Lett. 54 (1985) 2180, 1985.
Inspire Record 212895 DOI 10.17182/hepdata.20368

We have measured the differential cross section for p¯p and pp elastic scattering at s=53 GeV in the interval 0.5<|t|<4.0 (GeV/c)2 at the CERN intersecting storage rings using the split-field magnet detector. The shape of the differential cross section differs significantly between p¯p and pp scattering in the region 1.1<|t|<1.5 (GeV/c)2, with p¯p data showing a less pronounced dip structure than pp data.

1 data table match query

No description provided.


Analysis of Two Prong Events on p p Interactions at 205-GeV/c: Separation of Elastic and Inelastic Events.

Barish, S. ; Colley, D. ; Derrick, M. ; et al.
Phys.Rev.D 9 (1974) 1171-1179, 1974.
Inspire Record 93436 DOI 10.17182/hepdata.21998

We present results of complete measurements of the two-prong events observed in a 50 000-picture exposure of the 30-in. hydrogen bubble chamber to a 205−GeVc proton beam at the National Accelerator Laboratory. Using kinematic fitting, elastic and inelastic events are separated and cross sections are obtained. The total two-prong cross section is measured to be 9.77 ± 0.40 mb, of which 2.85 ± 0.26 mb represents the inelastic contribution. The total elastic cross section is measured to be 6.92 ± 0.44 mb. Our data are consistent with the break in dσdt at |t|∼0.1−0.2 (GeVc)2 observed at the CERN ISR. A prominent low-mass enhancement is observed in the distribution of missing mass squared from the slow proton for the inelastic events. An analysis based on the missing-mass spectrum and the particle rapidities shows that this low-mass enhancement accounts for about 77% of the total inelastic two-prong cross section. The diffractive cross section in the two-prong events is 2.20 ± 0.25 mb, in agreement with certain two-component models.

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USING A TOTAL CROSS SECTION OF 39.0 +- 1.0 MB.

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Analyzing Power Measurements of Coulomb Nuclear Interference With the Polarized Proton and Anti-proton Beams at 185 GeV/c

The E581/704 collaboration Akchurin, N. ; Carey, David C. ; Coleman, R. ; et al.
Phys.Lett.B 229 (1989) 299-303, 1989.
Inspire Record 280476 DOI 10.17182/hepdata.29782

The analyzing power A N of proton-proton, proton-hydrocarbon, and antiproton-hydrocarbon, scattering in the Coulomb-nuclear interference region has been measured using thhe 185 GeV/ c Fermilab polarized-proton and -antiproton beams. The results are found to be consistent with theoretical predictions within statistical uncertainties.

1 data table match query

No description provided.


Analyzing Powers in $\pi^\pm P$ (Polarized) Elastic Scattering From $T (\pi$) = 98-{MeV} to 263-{MeV}

Sevior, M.E. ; Feltham, A. ; Weber, P. ; et al.
Phys.Rev.C 40 (1989) 2780-2788, 1989.
Inspire Record 288842 DOI 10.17182/hepdata.26219

Angular distributions of the analyzing powers for π+p→ and π−p→ elastic scattering have been measured in a single-scattering experiment employing a polarized proton target. Measurements were obtained for pion energies of 98, 139, 166, 215, and 263 MeV. The addition of these data to the existing πp database significantly reduces the uncertainties in all S and P phase shifts for πp reactions over the delta resonance.

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Measured values of the analyzing power for PI+ P elastic scattering at incident kinetic energy 98 MeV.

Measured values of the analyzing power for PI+ P elastic scattering at incident kinetic energy 139 MeV.

Measured values of the analyzing power for PI+ P elastic scattering at incident kinetic energy 166 MeV.

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Analyzing power measurement of p p elastic scattering in the Coulomb - nuclear interference region with the 200-GeV/c polarized proton beam at Fermilab

The E581/704 collaboration Akchurin, N. ; Langland, J. ; Onel, Y. ; et al.
Phys.Rev.D 48 (1993) 3026-3036, 1993.
Inspire Record 364576 DOI 10.17182/hepdata.22670

The analyzing power AN of proton-proton elastic scattering in the Coulomb-nuclear interference region has been measured using the 200-GeV/c Fermilab polarized proton beam. A theoretically predicted interference between the hadronic non-spin-flip amplitude and the electromagnetic spin-flip amplitude is shown for the first time to be present at high energies in the region of 1.5 × 10−3 to 5.0 × 10−2 (GeV/c)2 four-momentum transfer squared, and our results are analyzed in connection with theoretical calculations. In addition, the role of possible contributions of the hadronic spin-flip amplitude is discussed.

1 data table match query

No description provided.


Charged-Particle Multiplicities in 100-GeV/c anti-p p Interactions

Ansorge, R.E. ; Bust, C.P. ; Carter, J.R. ; et al.
Phys.Lett.B 59 (1975) 299-302, 1975.
Inspire Record 2603 DOI 10.17182/hepdata.27765

Results are presented on the topological cross sections obtained for antiproton-proton interactions from an exposure of the Fermilab 30-inch bubble chamber to a 100 GeV/ c negative beam enriched in p 's. The p p inelastic cross section is found to be σ inel = 34.6 ± 0.4 mb, and the average inelastic charged particle multiplicity to be 〈 n 〉 = 6.74 ± 0.05.

1 data table match query

EXPONENTIAL FIT TO ELASTIC T DISTRIBUTION TO CORRECT FOR AN APPARENT LOSS OF EVENTS AT SMALL -T.


Comparison of $\bar{p} p$ and $p p$ Elastic Scattering With $0.6-{\rm GeV}^ < t < 2.1-{\rm GeV}^2$ at the {CERN} {ISR}

Erhan, S. ; Smith, A.M. ; Meritet, L. ; et al.
Phys.Lett.B 152 (1985) 131-134, 1985.
Inspire Record 206289 DOI 10.17182/hepdata.30431

p p and pp elastic scattering differential cross sections are presented for momentum transfer 0.6< t <2.1 GeV 2 and √ s = 53 GeV. Measurements were made in the same apparatus at the CERN Intersecting Storage Rings. The p p and pp results are in statistical agreement with one another over the entire t range, although the point at t =1.32 GeV 2 is 1.5 σ above the pp data. The p p points appear to have the same shape as the predictions of Donnachie and Landshoff but are significantly lower in magnitude for 0.9< t <1.5 GeV 2 .

1 data table match query

No description provided.


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.

3 data tables match query

DATA REQUESTED FROM AUTHORS.

RESULTS OF FITS.

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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.

4 data tables match query

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Cross-Sections and Charged Multiplicity Distributions for $\pi^- p$ and $K^- p$ Interactions at 147 GeV/c.

Fong, D. ; Heller, M. ; Shapiro, A.M. ; et al.
Nucl.Phys.B 102 (1976) 386-404, 1976.
Inspire Record 112604 DOI 10.17182/hepdata.36057

The results presented in this paper were obtained from a 105 000 frame exposure of the FNAL Hybrid Proportional Wire Chamber-30 inch Bubble Chamber System, in a tagged beam of 147 GeV/ c negative particles. Elastic, total and topological cross sections were obtained for both π − p and K − p interactions. Comparisons with other data, taken with various beam particles over large momentum intervals, show good agreement with KNO scaling, and similarity in the scaling behavior of σ n for the different beam particles.

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THESE CROSS SECTIONS ARE NOT NORMALIZED TO ANY OTHER ABSOLUTE MEASUREMENT. THE ERRORS INCLUDE SOME SYSTEMATIC ERRORS.

THE FORWARD CROSS SECTION AGREES WELL WITH THE OPTICAL POINT FROM TOTAL CROSS SECTION MEASUREMENTS.

THESE CROSS SECTIONS ARE NOT NORMALIZED TO ANY OTHER ABSOLUTE MEASUREMENT.


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).

No description provided.

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


Cross-Sections and Charged Particle Multiplicities in pi+ p and p p Collisions at 60-GeV/c

Bromberg, C. ; Ferbel, T. ; Jensen, T. ; et al.
Phys.Rev.D 15 (1977) 64, 1977.
Inspire Record 108488 DOI 10.17182/hepdata.24538

We have measured charged-particle multiplicities and elastic and inelastic cross sections for π+p and pp interactions at 60 GeV/c. The data are from a 30 000-picture exposure of the 30-inch bubble chamber to a tagged but unseparated positive-particle beam at Fermilab. The low-order moments of the inelastic multiplicity distributions for all charged particles are 〈n〉 = 5.60±0.09, f2 = 0.96±0.31, and 〈n〉D = 2.19±0.06 for pp reactions and 〈n〉6.23±0.10, f2 = 1.63±0.37, and 〈n〉D = 2.22±0.06 for π+p collisions.

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NORMALIZED TO A TOTAL CROSS SECTION OF 38.3 MB. CORRECTED FOR SMALL -T LOSSES AND FOR PI0 MESONS.

NORMALIZED TO A TOTAL CROSS SECTION OF 23.2 MB. CORRECTED FOR SMALL -T LOSSES AND FOR PI0 MESONS.

FORWARD CROSS SECTIONS ARE CONSISTENT WITH OPTICAL POINT FOR PURELY IMAGINARY ELASTIC AMPLITUDES.


Cross-sections and Multiplicity Distributions for $K^+ p$ Interactions at 70-{GeV}/$c$

Barth, M. ; De Clercq, C. ; De Wolf, E. ; et al.
Z.Phys.C 2 (1979) 285, 1979.
Inspire Record 141693 DOI 10.17182/hepdata.2107

Cross sections and charged multiplicity distributions forK+p interactions at 70 GeV/c are presented and compared withK+p data at other energies. Comparisons are also made with available π+p,pp, andK−p data.

1 data table match query

No description provided.


Differential Cross-sections for $\pi^+ P$ and $\pi^- P$ Elastic Scattering From 378-{MeV}/c to 687-{MeV}/c

Sadler, M.E. ; Briscoe, W.J. ; Fitzgerald, D.H. ; et al.
Phys.Rev.D 35 (1987) 2718-2735, 1987.
Inspire Record 250023 DOI 10.17182/hepdata.23362

Differential cross sections have been measured for π+p and π−p elastic scattering at 378, 408, 427, 471, 509, 547, 586, 625, 657, and 687 MeV/c in the angular range -0.8<cosθc.m.<0.8. The scattered pion and recoil proton were detected in coincidence using scintillation-counter hodoscopes. A liquid-hydrogen target was used except for measurements at forward angles, in which a CH2 target was used. Statistical uncertainties in the data are typically less than 1%. Systematic uncertainties in acceptance and detection efficiency are estimated to be 1%. Absolute normalization uncertainties are 2–3 % for most of the data. The measurements are compared with previous data and with the results of recent partial-wave analyses. The data are fit with Legendre expansions from which total elastic cross sections are obtained.

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Normalisation uncertainty = 3.1 pct.

Normalisation uncertainty = 4.1 pct.

Normalisation uncertainty = 2.1 pct.

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Differential cross-sections of elastic p p scattering in the energy range 8-70 gev

Beznogikh, G.G. ; Bujak, A. ; Kirillova, L.F. ; et al.
Nucl.Phys.B 54 (1973) 78-96, 1973.
Inspire Record 84176 DOI 10.17182/hepdata.8006

In this paper we present tables of absolute differential cross sections of elastic pp scattering together with the values of the slope parameter B and the real-part parameter α, where B= d d t In dσ d t α= Re A(0) Im A(0) and A (0) is the amplitude of elastic pp scattering at t = 0. The cross-section data have been obtained at the Serpukhov accelerator from 8 to 70 GeV in the | t |-range 0.0007 − 0.12 (GeV/ c ) 2 .

30 data tables match query

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Diffraction Dissociation of Photons on Hydrogen

Chapin, T.J. ; Cool, R.L. ; Goulianos, Konstantin A. ; et al.
Phys.Rev.D 31 (1985) 17-30, 1985.
Inspire Record 216071 DOI 10.17182/hepdata.4332

We report results from a measurement of the inclusive diffraction dissociation of photons on hydrogen, γp→Xp, in the range 75<pγ<148 GeV/c, 0.02<‖t‖<0.1 (GeV/c)2, and MX2/s<0.1. Our data show an exponential t dependence and a dominant 1/MX2 behavior for MX2>4 GeV2. We test the finite-mass sum rule and, by comparing γp with π−p data obtained in the same apparatus, we test factorization.

4 data tables match query

EXTRACTED ELASTIC CROSS SECTIONS.

RESULTS OF EXPONENTIAL FITS TO ELASTIC CROSS SECTIONS.

EXPONENTIAL FITS TO THE INELASTIC CROSS SECTIONS.

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