Measurements of the Total Cross-Section Difference and the Parameter C(LL) in p p Scattering with Longitudinally Polarized Beam and Target

Auer, I.P. ; Beretvas, A. ; Colton, E. ; et al.
Phys.Lett.B 70 (1977) 475-478, 1977.
Inspire Record 5342 DOI 10.17182/hepdata.27516

We have measured the difference between the pp total cross-sections for parallel and anti-parallel longitudinal spin states at beam momenta of 3 and 6 GeV/ c . These results, combined with our previous measurements, at lower momenta, are useful in clarifying a striking structure appearing at around 1.5 GeV/ c . We have also measured for the first time, the spin-spin correlation parameter C LL ( t ) in pp elastic scattering at 6 GeV/ c . We observe evidence for an exchange with A 1 -like quantum-numbers.

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NOTE: HIGHER -T DATA ARE BEING ANALYSED. PUBLISHED GRAPH HAS LARGER ERRORS.

THESE NUMBERS APPEAR TO UPDATE THOSE REPORTED IN I. P. AUER ET AL., PRL 37, 1727 (76). NOTE: DATA MAY HAVE SMALLER ERROR BARS IN THE FINAL ANALYSIS.

NOTE: MORE DATA ARE BEING ANALYSED. SINCE THE POLARIZED TARGET MAGNETIC FIELD WAS TILTED AT 18 DEG AWAY FROM THE BEAM DIRECTION, THE MEASURED CSL CONTAINS AN ADMIXTURE OF CSS. THE CSL VALUES QUOTED HERE HAVE BEEN CORRECTED FOR THIS EFFECT USING THE EXPERIMENTAL VALUES OF CSS.


MEASUREMENT OF DELTA SIGMA-l AND C (L, L) = (L, L : 0, 0) N PROTON PROTON SCATTERING BETWEEN 300-MEV AND 800-MEV

Auer, I.P. ; Ditzler, W.R. ; Hill, D. ; et al.
Phys.Rev.D 29 (1984) 2435-2468, 1984.
Inspire Record 205458 DOI 10.17182/hepdata.23728

Measurements are reported of the difference ΔσL between proton-proton total cross sections for parallel and antiparallel spin states and of the parameter CLL for proton-proton elastic scattering near 90°, for thirteen energies between 300 and 800 MeV. The ΔσL results agree well with previous ANL ZGS and SIN data, but disagree with recent results from TRIUMF. Attempts to understand the cause of the discrepancy have been unsuccessful, but possible sources are discussed. The ΔσL and CLL results have been used with other experimental data to extract quantities which depend only on spin-singlet, coupled spin-triplet, and spin-triplet partial waves. Structure is found in these quantities, which appears to be associated with the resonantlike D21 and F33 partial waves. Additional similar structure is also found, which may be due either to the P03 partial wave or the (P23,F23) partial-wave pair.

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ERRORS ARE STATISTICAL ONLY. THERE IS ADDITION OF 2.0 AND 2.1 PCT SYSTEMATICS.

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Measurement of Proton Proton Elastic Scattering at 6-GeV/c in Polarized Initial and Final Spin States

Borghini, M. ; De Boer, W. ; Fernow, Richard C. ; et al.
Phys.Rev.D 17 (1978) 24-41, 1978.
Inspire Record 134418 DOI 10.17182/hepdata.4518

The differential elastic p−p scattering cross section was measured at 6 GeV/c at the Argonne Zero Gradient Synchrotron in the range P⊥2=0.60−1.0 (GeV/c)2 using a 65% polarized target and a 75% polarized proton beam of intensity 3 × 109 protons/pulse. The polarization of the recoil proton was simultaneously measured with a well calibrated carbon-target polarimeter. All three polarizations were measured perpendicular to the horizontal scattering plane. Our results indicate that P and T invariance are both obeyed to good precision even at our largest P⊥2. Parity invariance implies that the eight single-flip transversity cross sections are zero, so our data gives the magnitudes of the eight remaining pure spin cross sections where all spins are measured. We find that the four double-flip transversity cross sections are nonzero.

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THE FIVE INDEPENDENT PURE FOUR-SPIN CROSS SECTIONS AS DERIVED FROM THE EIGHT MEASURED THREE-SPIN CROSS SECTIONS ASSUMING P AND T INVARIANCE. THE ABSOLUTE DIFFERENTIAL CROSS SECTION VALUES ASSUME THAT THE SPIN-AVERAGED D(SIG)/DT IS 2.25, 1.17, 0.365 AND 0.167 MB/GEV**2 FOR EACH VALUE OF PT**2 RESPECTIVELY.

WOLFENSTEIN PARAMETERS. POL(NAME=A) IS (N000) OR (0N00), THE ANALYZING POWER AVERAGED OVER TARGET OR BEAM POLARIZATION. POL(NAME=P) IS (00N0), THE POLARIZATION PARAMETER. TIME-REVERSAL INVARIANCE REQUIRES THAT P = A. POL.POL(NAME=CNN) IS (NN00) USING T-INVARIANCE. POL.POL(NAME=DNN) IS (0N0N). POL.POL(NAME=KNN) IS (N00N). POL.POL(NAME=C3N) IS A COMPONENT OF THE TRIPLE SPIN CORRELATION TENSOR. PARITY INVARIANCE REQUIRES THAT C3N = P.

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MEASUREMENT OF THE SPIN CORRELATION PARAMETER A(00NN) AND OF THE ANALYZING POWER FOR P P ELASTIC SCATTERING IN THE ENERGY RANGE FROM 0.5-GEV TO 0.8-GEV

Bystricky, J. ; Chaumette, P. ; Deregel, J. ; et al.
Nucl.Phys.B 262 (1985) 727-743, 1985.
Inspire Record 227731 DOI 10.17182/hepdata.33710

The spin correlation parameter A oonn and the analyzing powers A oono and A ooon were measured simultaneously, in the energy range 0.5–0.8 GeV and in the angular region 40°–80° CM. The experiment used the polarized proton beam of SATURNE II and the Saclay frozen spin polarized target.

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Spin Dependence of High p-Transverse**2 Elastic p p Scattering

Crabb, D.G. ; Fernow, Richard C. ; Hansen, P.H. ; et al.
Phys.Rev.Lett. 41 (1978) 1257, 1978.
Inspire Record 7117 DOI 10.17182/hepdata.20867

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.

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THE ERRORS INCLUDE STATISTICAL AND SYSTEMATIC ERRORS ADDED IN QUADRATURE. THE PARALLEL/ANTIPARALLEL SPIN CROSS SECTION RATIO IS (1+CNN)/(1-CNN).


DEPOLARIZATION PARAMETER IN P P INCLUSIVE SCATTERING AT 6-GEV/C

Courant, H. ; Kagan, H. ; Makdisi, Y. ; et al.
Phys.Rev.Lett. 44 (1980) 1373-1376, 1980.
Inspire Record 158285 DOI 10.17182/hepdata.20737

The depolarization parameter for pp inclusive scattering at an incident momentum of 6 GeV/c was measured. The D parameter for inclusive scattering indicates the dominance of natural-parity exchange at small t, except in the case of N*(1232) production, where π exchange is more important. D for elastic scattering has also been measured. This parameter shows a small decrease from unity with increasing momentum transfer.

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MEASUREMENT OF POLARIZATION PARAMETERS AND P P SCATTERING ANALYSIS AT 1.0-GeV

Vovchenko, V.G. ; Zhdanov, A.A. ; Kazarinov, Yu.M. ; et al.
LENINGRAD-84-995, 1984.
Inspire Record 208487 DOI 10.17182/hepdata.9315

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Proton proton triple scattering at 1.9 gev

Carithers, W.C. ; Adair, R.K. ; Hawkins, C.B.J. ; et al.
Phys.Rev. 179 (1969) 1304-1314, 1969.
Inspire Record 55504 DOI 10.17182/hepdata.5476

We have measured the Wolfenstein triple-scattering parameters R, D, and A′ at 1.9 GeV for p−p scattering at 90° in the c.m. system. We find that R=0.11±0.16, A′=−0.54±0.16, and D=0.91±0.21, where these parameters are defined in the c.m. system. The possibility of a vector character for the strong inter-actions is discussed. We conclude that neither a single vector-meson exchange nor a single pseudoscalar-meson exchange can account for the data. Spin effects are found to remain an important part of the nucleon-nucleon interaction at four-momentum transfer −t=1.8 (GeV/c)2.

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Measurements of Polarization and Spin Rotation in Proton Proton Elastic Scattering at 3.83-GeV/c

Deregel, J. ; Bruneton, C. ; Bystricky, J. ; et al.
Nucl.Phys.B 103 (1976) 269-278, 1976.
Inspire Record 113032 DOI 10.17182/hepdata.35989

The polarization P in proton-proton elastic scattering has been measured at 3.83 GeV/ c for 0.35 ⩽ | t | ⩽ 3.0 (GeV/ c ) 2 , i.e. 29° ⩽ θ c.m. ⩽ 93°. The polarization shows a minimum at − ⋍ 1.0 ( GeV /c) 2 followed by a maximum at −⋍1.5 ( GeV /c) 2 . At the same energy the spin rotation parameter R has been measured in the interval 0.18 ⩽ | t | ⩽ 0.57 (GeV/ c ) 2 . Comparison with the results at 6.0 and 15.75 GeV/ c shows a similar t -dependence and the same average value at all three energies.

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POLARIZED TARGET ASYMMETRY EQUALS RECOIL PROTON POLARIZATION BY TIME REVERSAL INVARIANCE.

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A(ll) at Small Momentum Transfers for the First Complete Determination of the Forward $p p$ Scattering Amplitude

Pauletta, G. ; Gazzaly, M. ; Tanaka, N. ; et al.
Phys.Lett.B 211 (1988) 19-23, 1988.
Inspire Record 252973 DOI 10.17182/hepdata.29911

The asymmetry A LL for pp elastic scattering has been measured at 650 and 800 MeV in the region of Coulomb-nuclear interference. The real part of the double-spin-flip amplitude extracted from these data completes our determination of the forward pp scattering amplitudes at these energies. Comparison with the predictions of forward dispersion relations reveals a discrepancy in the spin-dependent channels at 650 MeV.

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Measurement of the Parameters $N$(0nkk), $D$(0s0k) and $K$(0sk0) in $P P$ Elastic Scattering Between 0.84-{GeV} and 2.7-{GeV}

Lac, C.D. ; Ball, J. ; Bystricky, J. ; et al.
Nucl.Phys.B 315 (1989) 269-283, 1989.
Inspire Record 280846 DOI 10.17182/hepdata.33400

The spin-dependent observables N 0 nkk , D 0 s ″0 k and K 0 s ″ k 0 in pp elastic scattering were measured at 11 energies between 0.84 and 2.7 GeV using the SATURNE II polarized proton beam and the Saclay frozen-spin polarized target. The beam and target polarizations were oriented longitudinally. Precession of the recoil-particle spin in the target holding field introduces small contributions from other parameters. The present data agree with the few previously existing measurements. Below 1.3 GeV our data are compared with the predictions of the Saclay-Geneva phase-shift analysis. The new results will considerably affect the phase-shift analysis solutions and will contribute to their extension towards higher energies.

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Measurement of the Parameters $N$(0snk), $K$(0ss0), $K$(0nn0) and $D$(0s0k) in $P P$ Elastic Scattering Between 0.84-{GeV} and 2.7-{GeV}

Lac, C.D. ; Ball, J. ; Bystricky, J. ; et al.
Nucl.Phys.B 321 (1989) 284-298, 1989.
Inspire Record 284691 DOI 10.17182/hepdata.33255

The spin dependent observables N 0s n ″ k , K 0s″s0 and D 0s″0k in pp elastic scattering were measured at 11 energies between 0.84 and 2.7 GeV using the SATURNE II polarized proton beam and the Saclay frozen spin polarized target. The beam polarization was oriented in the vertical plane, the target polarization was oriented along the incident beam direction. Below 1 GeV the present data agree with previously existing measurements. Below 1.3 GeV they are compared with the predictions of the Saclay-Geneva phase shift analysis. The results will improve the phase shift analysis solutions and will contribute to their extensions towards higher energies. Together with our previous results the data allow a direct reconstruction of the pp elastic matrix over the energy region from 0.84 too 2.7 GeV.

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Measurement of $N P$ Analyzing Power A(00n0) Using the Deuteron Polarized Beam of Saturne-{II}

Ball, J. ; Lehar, F. ; De Lesquen, A. ; et al.
Nucl.Phys.B 286 (1987) 635-642, 1987.
Inspire Record 248563 DOI 10.17182/hepdata.33621

Both the np and the pp analyzing powers were measured simultaneously using the SATURNE II polarized deuteron beam at 0.550, 0.725, 0.900 and 1.15 GeV/nucleon. The results for the pp analyzing power coincide with the free pp elastic scattering data. We thus can assume that also the np analyzing power is equal to the one for scattering of free polarized neutrons. The np data cover the angular region 90° ≤ θ CM ≤ 125°. Our results for the np analyzing power clarify a discrepancy between earlier data at 0.5 GeV and allow conclusions about the energy dependence of the minimum of polarization at θ CM ⋍ 100° in the region from 0.5 to 0.9 GeV.

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MEASUREMENT OF THE SPIN CORRELATION PARAMETER A(00NN) FOR P P ELASTIC SCATTERING IN THE ENERGY RANGE FROM 0.83-GEV TO 1.1-GEV

Bystricky, J. ; Chaumette, P. ; Deregel, J. ; et al.
Nucl.Phys.B 262 (1985) 715-726, 1985.
Inspire Record 227730 DOI 10.17182/hepdata.33718

The spin correlation parameter A oonn (pp) and the analyzing power A oono (pp) have been measured in the angular region 45°< θ CM <90° at 0.834, 0.874, 0.934, 0.995 and 1.095 GeV beam kinetic energy using the SATURNE II polarized proton beam incident on the polarized proton target.

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Measurement of the spin correlation parameter A00kk for pp elastic scattering in the energy range 0.72–1.1 GeV

Bystricky, J. ; Chaumette, P. ; Deregel, J. ; et al.
Nucl.Phys.B 258 (1985) 90623 483-504, 1985.
Inspire Record 221352 DOI 10.17182/hepdata.33761

The spin correlation parameter A00kk (pp) has been measured in the angular region 45°<θCM<90° at 0.719, 0.834, 0.874, 0.934, 0.995 and 1.095 GeV using the SATURNE II polarized proton beam incident on a polarized target. The parameters A00nn(pp and A00sk(pp) were measured at 0.874 in the same angular region.

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C(LL) = (L, L: 0, 0) MEASUREMENTS AND A STRUCTURE DUE TO A P PARTIAL WAVE IN THE P P SYSTEM

Burleson, G.r. ; Cottingame, W.b. ; Greene, S.j. ; et al.
Nucl.Phys.B 213 (1983) 365-370, 1983.
Inspire Record 191085 DOI 10.17182/hepdata.34015

Measurements of C LL of pp elastic scattering near θ c.m. = 90° at thirteen energies between 300 and 800 MeV are reported. These, together with previous values of C NN , are used to extract values of two quantities, ƒ s and ƒ t , which contain only spin-singlet and only coupled spin-triplet partial waves, respectively. The ƒ s curve, which is not dependent on C LL , exhibits the behavior expected for the previously conjectured 1 D 2 resonance. The ƒ t curve also exhibits a resonance-like behavior, which could be due either to the 3 P 0 or the 3 P 2 partial wave.

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THE ENERGY DEPENDENCE OF THE 90-degrees P P ELASTIC SCATTERING DEPOLARIZATION PARAMETER AND AMPLITUDES BETWEEN 0.9-GEV/C AND 1.5-GEV/C

Hollas, C.L. ; Cremans, D.J. ; Ransome, R.D. ; et al.
Phys.Lett.B 143 (1984) 343-346, 1984.
Inspire Record 208375 DOI 10.17182/hepdata.30531

The depolarization parameter D NN for pp elastic scattering at θ cm = 90 ° has been measured at twelve momenta between 0.9 and 1.5 GeV/ c . The moduli of the three transversity amplitudes T 1 , T 3 , and T 4 have been extracted from these data and from previous measurements of the differential cross section and spin correlation parameter A NN (90 °). Smooth energy dependence is found for all three amplitude moduli.

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Axis error includes +- 3/3 contribution (DUE TO UNCERTAINTIES IN THE TARGET ANALYSING POWER).


Measurement of the Parameters $N$(0skn), $D$(0n0n) and $K$(0sk0) in $P P$ Elastic Scattering Between 0.84-{GeV} and 2.1-{GeV}

Lac, C.D. ; Ball, J. ; Bystricky, J. ; et al.
Nucl.Phys.B 321 (1989) 269-283, 1989.
Inspire Record 284690 DOI 10.17182/hepdata.33254

The spin-dependent observables N 0 s ″ kn , D 0 n 0 n and K 0 s ″ k 0 in pp elastic scattering were measured at nine energies between 0.84 and 2.1 GeV using the SATURNE II polarized proton beam and the Saclay frozen spin polarized target. The beam polarization was oriented longitudinally and the target polarization was oriented vertically. Precession of the recoil particle spin in the target holding field introduces a small contribution from other parameters. The present results for K 0 s ″ k 0 and D 0 n 0 n agree with our previous measurements of the same observables carried out in different beam and target spin configurations as well as with previously existing measurements. The observable N 0 s ″ kn had not been measured previously above 0.58 GeV. Below 1.3 GeV our data are compared with the predictions of the Saclay-Geneva phase shift analysis. The new results will considerably affect the phase shift analysis solutions and will contribute to their extension towards higher energies.

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Measurement of the Parameters $D$(0n0n) and $K$(0nn0) in $P P$ Elastic Scattering Between 0.84-{GeV} and 2.7-{GeV}

Lac, C.D. ; Ball, J. ; Bystricky, J. ; et al.
Nucl.Phys.B 315 (1989) 284-294, 1989.
Inspire Record 280847 DOI 10.17182/hepdata.33259

The spin-dependent observables D 0 n 0 n and K 0 nn 0 in pp elastic scattering were measured at 11 energies between 0.84 and 2.7 GeV using the SATURNE II polarized proton beam and the Saclay frozen-spin polarized target. The beam and target polarizations were oriented along the normal to the scattering plane. Below 1 GeV the present data agree with previously existing measurements. Below 1.3 GeV they are compared with the predictions of the Saclay-Geneva phase-shift analysis. The results will improve the phase-shift analysis solutions and will contribute to their extension towards higher energies.

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Measurement of the Spin Correlation Parameters A(00kk) and A(00sk) in $P P$ Elastic Scattering From 0.88-{GeV} to 2.4-{GeV}

Fontaine, J.M. ; Perrot, F. ; Bystricky, J. ; et al.
Nucl.Phys.B 321 (1989) 299-310, 1989.
Inspire Record 284692 DOI 10.17182/hepdata.33222

The spin correlation parameters A 00 kk and A 00 sk were measured at 0.874, 0.934, 1.095, 1.295, 1.596, 1.796, 2.096, and 2.396 GeV, using the SATURNE II polarized proton beam and tha Saclay frozen spin polarized target. The present results for beam-target spin correlations obtained during measurements of three-spin index observables confirm, in particular, relatively large positive values of A 00 sk at certain energies and angles, as was shown in previously published data from a dedicated experiment.

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Measurement of Analyzing Power and Spin Correlations in $N P$ Elastic Scattering at 0.744-{GeV} and 0.794-{GeV} Using a Deuteron Polarized Beam

De Lesquen, A. ; Lehar, F. ; Van Rossum, L. ; et al.
Nucl.Phys.B 304 (1988) 673-686, 1988.
Inspire Record 268253 DOI 10.17182/hepdata.33258

The np and the pp analyzing powers A oono d and spin correlations A oonn d and A oosk d were measured simultaneously using the SATURNE II polarized deuteron beam at 0.744 and 0.794 GeV/nucleon. The results for the pp observables coincide with the free pp elastic scattering data. We thus can assume that also the np analyzing power A oono d and spin correlations A oonn d and A oosk d are equal to those for scattering of free polarized neutrons. The np data cover the angular region 95°⩽ θ CM ⩽122°. Our results for A oono d (np) confirm the phase-shift analysis predictions but spin correlations A oonn d (np) and A oosk d (np) have never been measured in this energy region and will considerably affect the PSA solution. Present results allow conclusions about the angular dependence near the minimum of A oono (np) and A oonn (np) in the vicinity of 0.8 GeV.

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Measurement of the Spin Correlation Parameter A(00sk) in $P P$ Elastic Scattering From 0.88-{GeV} to 2.7-{GeV}

Perrot, F. ; Fontaine, J.M. ; Lehar, F. ; et al.
Nucl.Phys.B 296 (1988) 527-534, 1988.
Inspire Record 266151 DOI 10.17182/hepdata.33396

The spin correlation parameter A oosk was measured using the SATURNE II polarized proton beam and the Saclay frozen spin polarized target. The measurements at 0.88 and 1.1 GeV were carried out in the angular region θ CM from 28° to ⋍ 50°. At 0.88 GeV they complete our previous measurements from 45° to 90°. Above 1.1 GeV the measurements presented here cover both regions, extending from gq CM = 28° (at lower energies) or θ CM = 18° (at higher energies) to θ CM > 90°. The shape of the angular distribution A oosk (pp) = ƒ(θ CM ) changes considerably between 1.8 and 2.4 GeV.

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Measurement of the Spin Correlation A(00kk) in $P P$ Elastic Scattering From 0.88-{GeV} to 2.7-{GeV}

Lehar, F. ; De Lesquen, A. ; Van Rossum, L. ; et al.
Nucl.Phys.B 296 (1988) 535-545, 1988.
Inspire Record 266152 DOI 10.17182/hepdata.33462

The spin correlation parameter A ookk in pp elastic scattering was measured using the SATURNE II polarized proton beam and the Saclay frozen spin polarized target. The measurements at 0.88 and 1.1 GeV were carried out in the angular region θ CM from 28° to ⋍ 50° and complete our previous measurements from 45° to 90°. Above 1.1 GeV the measurements presented here cover both regions, extending from θ CM = 28° (at the lower energies) or θ CM = 18° (at the higher energies) to θ CM > 90°. The shape of the angular distribution A ookk (pp) = f ( θ CM ) changes considerably between in our energy region.

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MEASUREMENT OF THE SPIN CORRELATION PARAMETERS A(OOSK) AND A(OOKK) IN P P ELASTIC SCATTERING AT 0.84-GEV AND 1-GEV

Lac, C.D. ; Ball, J. ; Bystricky, J. ; et al.
Nucl.Phys.B 297 (1988) 653-660, 1988.
Inspire Record 264165 DOI 10.17182/hepdata.33528

The spin correlation parameters A oosk and A ookk were measured at 0.834 and 0.995 GeV using the SATURNE II polarized proton beam and the Saclay frozen spin polarized target. The measurements were carried out in the angular region φ CM from 50° to ≃ 90°. The shape of the angular distribution A oosk (pp) = f ( θ CM ) changes rapidly from 0.8 to 1.0 GeV. The A ookk data points specify our previous measurements.

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Measurement of the Spin Correlation Parameter A(00nn ($P P$ in a Large Angular Region Between 0.88-{GeV} and 2.7-{GeV}

Lehar, F. ; De Lesquen, A. ; Meyer, J.P. ; et al.
Nucl.Phys.B 294 (1987) 1013-1021, 1987.
Inspire Record 255230 DOI 10.17182/hepdata.33526

The spin correlation parameter A oonn for pp elastic scattering was measured at 0.88, 1.1, 1.3, 1.6, 1.8, 2.1, 2.4 and 2.7 GeV using the SATURNE II polarized proton beam and the Saclay frozen spin polarized target. At the first two energies, the new measurements at θ CM < 50° complete our previous data from 45° to 90°. Between 1.3 and 2.7 GeV the measurements were performed in two overlapping angular regions covering together the CM angles from 28° (at the lower energies) or 18° (at the highest energy) to > 90°. At all energies above 1.3 GeV the angular distribution shows a dip at fixed four-momentum transfer − t ∼ 0.90 (GeV/ c ) 2 . The value of A oonn ( θ CM = 90°) decreases from A oonn (90°) ≅ 0.57 at 0.88 GeV to A oonn (90°) ≅ 0.35 at 2.7 GeV. However, the large value found at 1.8 GeV indicates that the energy dependence is not monotonic.

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Errors are statistical plus random-like instrumental uncertainties.

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