Hard exclusive hadron nucleon scattering and color transparency

Heppelmann, S. ; Wu, J.Y. ; Appel, R. ; et al.
Nucl.Phys.A 527 (1991) 581C-583C, 1991.
Inspire Record 327578 DOI 10.17182/hepdata.36761

We present preliminary results on the measurement of a variety of exclusive hadron interactions at center of mass scattering angles of 90°. Data are also presented which show the relative transparency of nuclei to πp and pp elastic scattering in this kinematic range.

3 data tables match query

No description provided.

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Comparison of 20 exclusive reactions at large t

White, C. ; Appel, R. ; Barton, D.S. ; et al.
Phys.Rev.D 49 (1994) 58-78, 1994.
Inspire Record 377535 DOI 10.17182/hepdata.50306

We report a study of 20 exclusive reactions measured at the AGS at 5.9 GeV/c incident momentum, 90° center of mass. This experiment confirms the strong quark flow dependence of two-body hadron-hadron scattering at large angle. At 9.9 GeV/c an upper limit had been set for the ratio of cross sections for (p¯p→p¯p)(pp→pp) at 90° c.m., with the ratio less than 4%. The present experiment was performed at lower energy to gain sensitivity, but was still within the fixed angle scaling region. A ratio R(p¯ppp)≈140 was measured at 5.9 GeV/c, 90° c.m. in comparison to a ratio near 1.7 for small angle scattering. In addition, many other reactions were measured, often for the first time at 90° c.m. in the scaling region, using beams of π±, K±, p, and p¯ on a hydrogen target. There are similar large differences in cross sections for other reactions: R(K−p→π+Σ−K−p→π−Σ+)≈112, for example. The relative magnitudes of the different cross sections are consistent with the dominance of quark interchange in these 90° reactions, and indicate that pure gluon exchange and quark-antiquark annihilation diagrams are much less important. The angular dependence of several elastic cross sections and the energy dependence at a fixed angle of many of the reactions are also presented.

6 data tables match query

Cross sections at 90 degrees in the centre-of-mass.

No description provided.

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Results on Total and Elastic Cross Sections in Proton-Proton Collisions at $\sqrt{s} = 200$ GeV

The STAR collaboration Adam, Jaroslav ; Adamczyk, Leszek ; Adams, Joseph ; et al.
Phys.Lett.B 808 (2020) 135663, 2020.
Inspire Record 1791591 DOI 10.17182/hepdata.94263

We report results on the total and elastic cross sections in proton-proton collisions at $\sqrt{s}=200$ GeV obtained with the Roman Pot setup of the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The elastic differential cross section was measured in the squared four-momentum transfer range $0.045 \leq -t \leq 0.135$ GeV$^2$. The value of the exponential slope parameter $B$ of the elastic differential cross section $d\sigma/dt \sim e^{-Bt}$ in the measured $-t$ range was found to be $B = 14.32 \pm 0.09 (stat.)^{\scriptstyle +0.13}_{\scriptstyle -0.28} (syst.)$ GeV$^{-2}$. The total cross section $\sigma_{tot}$, obtained from extrapolation of the $d\sigma/dt$ to the optical point at $-t = 0$, is $\sigma_{tot} = 54.67 \pm 0.21 (stat.) ^{\scriptstyle +1.28}_{\scriptstyle -1.38} (syst.)$ mb. We also present the values of the elastic cross section $\sigma_{el} = 10.85 \pm 0.03 (stat.) ^{\scriptstyle +0.49}_{\scriptstyle -0.41}(syst.)$ mb, the elastic cross section integrated within the STAR $t$-range $\sigma^{det}_{el} = 4.05 \pm 0.01 (stat.) ^{\scriptstyle+0.18}_{\scriptstyle -0.17}(syst.)$ mb, and the inelastic cross section $\sigma_{inel} = 43.82 \pm 0.21 (stat.) ^{\scriptstyle +1.37}_{\scriptstyle -1.44} (syst.)$ mb. The results are compared with the world data.

2 data tables match query

The B-slope of the exponential fit A*exp(-B*|t|) to the single differential proton-proton elastic cross-section in the t-range 0.045<|t|<0.135 GeV**2 at sqrt(s) = 200 GeV.

The total, elastic and inelastic cross-sections for proton-proton scattering at sqrt(s)=200 GeV, the elastic cross-section measured in the t-range 0.045<|t|<0.135 GeV^2 and the value of the differential cross-section extrapolated to |t| = 0.


ELASTIC SCATTERING OF pi- AND K- MESONS ON PROTONS AT 43-GeV/c MOMENTUM

The SIGMA-AYaKS & Dubna-Serpukhov-Tbilisi collaborations Antipov, Yu.M. ; Batarin, V.A. ; Bezzubov, V.A. ; et al.
Sov.J.Nucl.Phys. 48 (1988) 85, 1988.
Inspire Record 253399 DOI 10.17182/hepdata.38881

None

3 data tables match query

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FROM EXPONENTIAL FIT OF D(SIG)/D(T) IN RANGE 0. < ABS(T) < 1. GEV.


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.

3 data tables match query

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.


$K^- p$ elastic scattering at 2.24 GeV/c

Dickinson, M. ; Miyashita, S. ; Libby, L.Marshall ; et al.
Phys.Lett.B 24 (1967) 596-598, 1967.
Inspire Record 1389623 DOI 10.17182/hepdata.29569

The differential elastic scattering cross section for 2.24 GeV/ c K − p collisions has been measured in film from the Brookhaven 20″ bubble chamber. The total elastic cross section is found to be 6.2 ± 0.7 mb. The exponential dependence on square of the momentum t in (GeV/ c ) 2 is fitted by ( d σ d Ω elastic = (12.4 ± 1.0 mb/sr) exp (7.81 ± 0.25)t . A A fit to a black disc model requires a radius of 0.95 ± 0.05 fm.

1 data table match query

D(SIG)/D(T) was fitted to CONST*EXP(-SLOPE*T).


Topological and Leading Particle Cross-Sections for 147-GeV/c $\pi^- p$ Interactions.

Fong, D.G. ; Heller, M. ; Shapiro, A.M. ; et al.
Phys.Lett.B 53 (1974) 290-296, 1974.
Inspire Record 93415 DOI 10.17182/hepdata.27916

Results are reported based on a study of π − p interactions at 147 GeV/ c in the FERMILAB 30-inch Proportional Wire Hybrid Bubble Chamber System. We have measured the topological cross sections and separated two-prong elastic and inelastic channels. In addition, we have extracted leading particle cross sections using the increased momentum resolution of the downstream proportional wire chambers. We have compared our results with experiments and predictions of a simple fragmentation hyphothesis.

1 data table match query

No description provided.


$\pi^- p$ 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

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Cross-Sections and Multiplicity Distributions for pi- p Interactions at 11.2-GeV/c

Forino, A. ; Gessaroli, R. ; Quareni-Vignudelli, A. ; et al.
Nuovo Cim.A 31 (1976) 696, 1976.
Inspire Record 3101 DOI 10.17182/hepdata.37695

Results are presented concerning topological cross-sections and multiplicity distribution for a π−p experiment at 11.2 GeV/c. The statistics used are one-half of the total ones (106 bubble chamber pictures). Comparison with data at different energies and theoretical predictions are made, and satisfactory agreement is obtained.

1 data table match query

TABLE ALSO QUOTES PRONG CROSS SECTIONS FOR PRODUCTION OF VEE(S).


$K^- p$ elastic scattering at 3 GeV/c

Focacci, M.N. ; Focardi, S. ; Giacomelli, G. ; et al.
Phys.Lett. 19 (1965) 441-444, 1965.
Inspire Record 851194 DOI 10.17182/hepdata.30175

None

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Only statistical errors are given.


K- p Elastic Scattering at 14.3-GeV/c

Drevillon, B. ; Borenstein, S. ; Chaurand, B. ; et al.
Nucl.Phys.B 97 (1975) 392-402, 1975.
Inspire Record 2869 DOI 10.17182/hepdata.31858

Results are presented of a bubble chamber experiment on K − p elastic scattering at 14.3 GeV/ c , in four-momentum transfer range 0.04 < | t | < 2.74 GeV 2 using an initial set of 40 000 events. The total elastic cross section is (2.96 ± 0.10) mb. The results are compared with K + p elastic scattering data at 13.8 GeV/ c , and the effective Regge trajectory is calculated using K − p data from 5 to 100 GeV/ c .

2 data tables match query

FOR -T < 0.04 GEV**2, CROSS SECTION WAS EXTRAPOLATED TO THE OPTICAL POINT WITH -0.055+-0.040 FOR THE REAL/IMAGINARY RATIO OF THE FORWARD AMPLITUDE.

No description provided.


K- p elastic scattering at 10-GeV/c

The Aachen-Berlin-CERN-London-Vienna collaboration Bartsch, J. ; Deutschmann, M. ; Kraus, G. ; et al.
Nucl.Phys.B 29 (1971) 398-404, 1971.
Inspire Record 68635 DOI 10.17182/hepdata.33567

Results are presented on elastic scattering of 10.1 GeV/ c K − mesons on protons, based on a sample of 16 261 kinematically-fitted bubble-chamber events. The differential cross section is given over the | t |- range of 0.06 to 2.5 GeV 2 and is fitted with the expressions a e bt , A e Bt + Ct 2 and ( P e Qt + Re St ) over various intervals of t . The results are compared with those of other experiments at nearby energies. Upper limits of | α | < 0.28 and σ B < 0.4 μ b (both at a 90% confidence level) are given for the ratio of real to imaginary part of the forward-scattering amplitude and the backward-elastic-scattering cross section, respectively.

3 data tables match query

No description provided.

ERROR INCLUDES STATISTICAL ERROR AND ERROR IN TOTAL CROSS SECTION USED FOR NORMALIZATION. EXTRAPOLATION OF D(SIG)/DT TO T=0 PROVIDES ABOUT 0.5 PCT UNCERTAINTY.

NO BACKWARD EVENTS OBSERVED. LARGEST ANGLE EVENT SEEN WAS AT 64 DEG (-T = 2.33 GEV**2).


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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Topological, Total and Elastic Cross-sections for $K^+ p$, $\pi^+ p$ and $p p$ Interactions at 147-{GeV}/$c$

Brick, D. ; Rudnicka, H. ; Shapiro, A.M. ; et al.
Phys.Rev.D 25 (1982) 2794, 1982.
Inspire Record 11840 DOI 10.17182/hepdata.4111

The Fermilab hybrid 30-in. bubble-chamber spectrometer was exposed to a tagged 147-GeV/c positive beam containing π+, K+, and p. A sample of 3003 K+p, 19410 pp, and 20745 π+p interactions is used to derive σn, 〈n〉, f2cc, and 〈nc〉D for each beam particle. These values are compared to values obtained at other, mostly lower, beam momenta. The overall dependence of 〈n〉 on Ea, the available center-of-mass energy, for these three reactions as well as π−p and pp interactions has been determined.

5 data tables match query

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pi+ proton, pi- proton and pp elastic scattering at 8.5, 12.4 and 18.4 GeV/c

Harting, D. ; Blackall, P. ; Elsner, B. ; et al.
Nuovo Cim. 38 (1965) 60, 1965.
Inspire Record 49759 DOI 10.17182/hepdata.1110

Approximately 60 000 events have been collected in a spark chamber experiment at the CERN Proton Synchrotron which studied elastic diffraction scattering of π--p and p-p at incident momenta of 8.5, 12.4 and 18.4 GeV/c and of π+-p at 8.5 and 12.4 GeV/c. Magnetic analysis of the incoming and diffraction scattered particle, together with measurement of all angles, permitted each event to be determined as elastic subject to three constraints, so that the inelastic background was rejected with. high efficiency, even at the larger momentum, transfers. Much of the data have been processed by the CERN Automatic Flying-Spot DigitizerHPD. A detailed description of the experimental technique and of the methods of analysis is given. The results, together with data from lower energies, confirm the remarkable energy-independence of the shape of the pion-proton diffraction scattering peak up to |t| = 1.5 (GeV/c)2, wheret is the square of the four-momentum transfer, over a range of pion energies from 2 to 18 GeV. Proton-proton scattering does however appear to show a shrinking diffraction peak. In general, the data agree with other experiments using both counter and bubble chamber techniques, but some differences do appear. During the experiment, data were taken which set an upper limit of 2·102 μb/(GeV/c)2 on the differential elastic cross-section dσ/dt over a range of |t| from 20.9 to 23.4 (GeV/c)2 at 13.4 GeV/c incident pion momentum.

18 data tables match query

'1'. '2'. '3'. '4'.

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Elastic $\pi^{+}p$ scattering at 1.6 GeV/c

Daudin, A. ; Jabiol, M.A. ; Kochowski, C. ; et al.
Nuovo Cim. 33 (1964) 1300-1308, 1964.
Inspire Record 1187695 DOI 10.17182/hepdata.1107

The c.m. angular distribution of π+p elastic scattering at 1.6 GeV/c shows a strong forward diffraction peak decreasing exponentially with a slopeA + = (6.9±0.5) GeV−2 comparable to thatA − = (7.2±0.5) GeV−2 observed in a previous experiment for π-p elastic scattering at the same incident momentum. The behaviour of the π+ and the π− angular distributions is quite different beyond the diffraction peak. The π+p total elastic cross-section is found to be Σ01 = (16.70±0.45) mb.

3 data tables match query

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Two-prong fitted channels at 11.7 gev/c

Evans, D. ; Neat, K. ; Caso, C. ; et al.
Nuovo Cim.A 16 (1973) 299-314, 1973.
Inspire Record 87004 DOI 10.17182/hepdata.37784

A sample of 43000 two-prong events obtained at a momomentum of 11.7 GeV/c is used to determine the cross-sections of the fitted channels, and to study the reaction π+p→π+pπ0. We investigate in particular the quasi-two-body channels π0Δ++ and ρ+p.

1 data table match query

No description provided.


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.


Inelastic Two Prong Events in 147-GeV/c $\pi^- p$ Collisions.

Fong, D. ; Heller, M. ; Shapiro, A. ; et al.
Nucl.Phys.B 104 (1976) 32-51, 1976.
Inspire Record 112609 DOI 10.17182/hepdata.36026

None

1 data table match query

No description provided.


$\{pi}-p$ interactions at 1.59 GeV/c

Alitti, J. ; Baton, J.P. ; Berthelot, A. ; et al.
Nuovo Cim. 29 (1963) 515, 1963.
Inspire Record 851185 DOI 10.17182/hepdata.980

Report on the investigation of interactions in π−p collisions at a pion momentum of 1.59 GeV/c, by means of the 50 cm Saclay liquid hydrogen bubble chamber, operating in a magnetic field of 17.5 kG. The results obtained concern essentially the elastic scattering and the inelastic scattering accompanied by the production of either a single pion in π−p→ pπ−π0 and nπ−π+ interactions, or by more than one pion in four-prong events. The observed angular distribution for the elastic scattering in the diffraction region, can be approximated by an exponential law. From the extrapolated value, thus obtained for the forward scattering, one gets σel= (9.65±0.30) mb. Effective mass spectra of π−π0 and π−π+ dipions are given in case of one-pion production. Each of them exhibits the corresponding ρ− or ρ0 resonances in the region of ∼ 29μ2 (μ = mass of the charged pion). The ρ peaks are particularly conspicuous for low momentum transfer (Δ2) events. The ρ0 distribution presents a secondary peak at ∼31μ2 due probably to the ω0 → π−π+ process. The branching ratio (ω0→ π+π−)/(ω0→ π+π− 0) is estimated to be ∼ 7%. The results are fairly well interpreted in the frame of the peripheral interaction according to the one-pion exchange (OPE) model, Up to values of Δ2/μ2∼10. In particular, the ratio ρ−/ρ0 is of the order of 0.5, as predicted by this model. Furthermore, the distribution of the Treiman-Yang angle is compatible with an isotropic one inside the ρ. peak. The distribution of\(\sigma _{\pi ^ + \pi ^ - } \), as calculated by the use of the Chew-Low formula assumed to be valid in the physical region of Δ2, gives a maximum which is appreciably lower than the value of\(12\pi \tilde \lambda ^2 = 120 mb\) expected for a resonant elastic ππ scattering in a J=1 state at the peak of the ρ. However, a correcting factor to the Chew-Low formula, introduced by Selleri, gives a fairly good agreement with the expected value. Another distribution, namely the Δ2 distribution, at least for Δ2 < 10 μ2, agrees quite well with the peripheral character of the interaction involving the ρ resonance. π− angular distributions in the rest frame of the ρ exhibit a different behaviour for the ρ− and for the ρ0. Whereas the first one is symmetrical, as was already reported in a previous paper, the latter shows a clear forward π− asymmetry. The main features of the four-prong results are: 1) the occurrence of the 3/2 3/2 (ρπ+) isobar in π−p → pπ+π−π− events and 2) the possible production of the ω0→ π+π−π0 resonance in π−p→ pπ−π+π−π0 events. No ρ’s were observed in four-prong events.

3 data tables match query

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Pi- p elastic scattering at 2.29 gev/c

Hagopian, S. ; Hagopian, V. ; Bogart, E. ; et al.
Phys.Rev.D 5 (1972) 2684-2688, 1972.
Inspire Record 74158 DOI 10.17182/hepdata.3597

The reaction π−+p→π−+p has been studied in the 15-in. bubble chamber at the Princeton-Pennsylvania Accelerator. The elastic scattering cross section was determined to be 8.5 ± 0.2 mb. The forward peak fits to an exponential in t with a slope of 8.1 ± 0.2 (GeV/c)−2. The forward differential cross section dσdΩ(0)=17.9±0.7 mb/sr. A fit of the center-of-mass angular distribution to Legendre polynomials needed terms up to the 12th order, corresponding to the highest nonzero partial wave of L=6.

4 data tables match query

No description provided.

FORWARD D(SIG)/DOMEGA IS 17.9 +- 0.7 MB/SR. SLOPE IS 8.1 +- 0.2 GEV**-2 (-T = 0.1 TO 0.4 GEV**2).

OTHER 2.27 GEV/C DATA ALSO QUOTED.

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Determination of the proton proton elastic cross-section at 30-GeV center-of-mass energy

Holder, M. ; Radermacher, E. ; Staude, A. ; et al.
Phys.Lett.B 35 (1971) 361-364, 1971.
Inspire Record 69227 DOI 10.17182/hepdata.28484

The absolute luminosity of the CERN Intersecting Storage Rings has been determined by the Van der Meer method. Combining the measurement with small angle proton-proton elastic events, we find σ elastic = (6.8±0.6)mb.

1 data table match query

No description provided.


Single-Pion Production in pp Collisions at 0.95-GeV/c (I)

The COSY-TOF collaboration El-Samad, S.Abd ; Bilger, R. ; Brinkmann, K. -Th. ; et al.
Eur.Phys.J.A 30 (2006) 443-453, 2006.
Inspire Record 725793 DOI 10.17182/hepdata.43429

The single-pion production reactions $pp\to d\pi^+$, $pp\to np\pi^+$ and $pp\to pp\pi^0$ were measured at a beam momentum of 0.95 GeV/c ($T_p \approx$ 400 MeV) using the short version of the COSY-TOF spectrometer. The implementation of a central calorimeter provided particle identification, energy determination and neutron detection in addition to time-of-flight and angle measurements. Thus all pion production channels were recorded with 1-4 overconstraints. The total and differential cross sections obtained are compared to previous data and theoretical calculations. Main emphasis is put on the discussion of the $pp\pi^0$ channel, where we obtain angular distributions different from previous experimental results, however, partly in good agreement with recent phenomenological and theoretical predictions. In particular we observe very large anisotropies for the $\pi^0$ angular distributions in the kinematical region of small relative proton momenta revealing there a dominance of proton spinflip transitions associated with $\pi^0$ $s$- and $d$-partial waves and emphasizing the important role of $\pi^0$ d-waves.

1 data table match query

Measured angular distribution for elastic P P scattering in the CM system normalised to the data in the SAID database (Arndt et al. PR C62,034005(2000). This measurement is made to determine the luminosity.


Evidence for dominance of pomeron like exchange in p + p ---> n + n + pi at 19 gev/c

Boggild, H. ; Hansen, K. ; Johnstad, H. ; et al.
Phys.Lett.B 30 (1969) 369-372, 1969.
Inspire Record 56657 DOI 10.17182/hepdata.28910

The reactions pp → NN π are studied at 19 GeV/ c and analysed in terms of the amplitudes with the low mass N π system in isospin states 1 2 and 3 2 respectively. The I − 1 2 cross section is compared with the corresponding one in π p→ ππ N at 8 GeV/ c .

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Study of $p p$ Interactions in the Momentum Range 0.9-{GeV}/$c$ to 2.0-{GeV}/$c$

Shimizu, F. ; Koiso, H. ; Kubota, Y. ; et al.
Nucl.Phys.A 389 (1982) 445-456, 1982.
Inspire Record 12089 DOI 10.17182/hepdata.37051

pp interactions at 11 momenta in the range 0.9 to 2.0 GeV/ c have been studied. The elastic angular distributions, covering the c.m. angular range 22°–90°, agree in general with Hoshizaki's phase-shift analysis which shows the looping 1 D in and 3 F 3 amplitudes in the Argand diagram. About 80% of pn π + events come from the n Δ ++ state at all momenta above 1.2 GeV/ c . The behavior of the density matrix elements of the Δ ++ show no momentum or angular dependence. A large fraction of pp π 0 events also come from the p Δ + state at all momenta above 1.2 GeV/ c . The behavior of the Δ + density matrix elements is similar to that for the case of Δ ++ .

1 data table match query

No description provided.