Measurements of the $\pi^{\pm}$, $K^{\pm}$, and proton double differential yields emitted from the surface of the 90-cm-long carbon target (T2K replica) were performed for the incoming 31 GeV/c protons with the NA61/SHINE spectrometer at the CERN SPS using data collected during 2010 run. The double differential $\pi^{\pm}$ yields were measured with increased precision compared to the previously published NA61/SHINE results, while the $K^{\pm}$ and proton yields were obtained for the first time. A strategy for dealing with the dependence of the results on the incoming proton beam profile is proposed. The purpose of these measurements is to reduce significantly the (anti)neutrino flux uncertainty in the T2K long-baseline neutrino experiment by constraining the production of (anti)neutrino ancestors coming from the T2K target.
Double differential yiedls of positively charged pions emitted from the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and in the longitudinal range from 0 to 18cm, as a function of momentum. The normalization is per proton on target.
Double differential yiedls of positively charged pions emitted from the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and in the longitudinal range from 0 to 18cm, as a function of momentum. The normalization is per proton on target.
Double differential yiedls of positively charged pions emitted from the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and in the longitudinal range from 0 to 18cm, as a function of momentum. The normalization is per proton on target.
Measurements of particle emission from a replica of the T2K 90 cm-long carbon target were performed in the NA61/SHINE experiment at CERN SPS, using data collected during a high-statistics run in 2009. An efficient use of the long-target measurements for neutrino flux predictions in T2K requires dedicated reconstruction and analysis techniques. Fully-corrected differential yields of $\pi^\pm$-mesons from the surface of the T2K replica target for incoming 31 GeV/c protons are presented. A possible strategy to implement these results into the T2K neutrino beam predictions is discussed and the propagation of the uncertainties of these results to the final neutrino flux is performed.
Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 0 to 20 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.
Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 20 to 40 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.
Spectra of positively charged pions at the surface of the T2K replica target, in the polar angle range from 40 to 60 mrad and for longitudinal bin $z1$, as a function of momentum. The normalization is per proton on target.
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Measurements of hadron production in p+C interactions at 31 GeV/c are performed using the NA61/ SHINE spectrometer at the CERN SPS. The analysis is based on the full set of data collected in 2009 using a graphite target with a thickness of 4% of a nuclear interaction length. Inelastic and production cross sections as well as spectra of $\pi^\pm$, $K^\pm$, p, $K^0_S$ and $\Lambda$ are measured with high precision. These measurements are essential for improved calculations of the initial neutrino fluxes in the T2K long-baseline neutrino oscillation experiment in Japan. A comparison of the NA61/SHINE measurements with predictions of several hadroproduction models is presented.
The double differential $\pi^+$ production cross section in the laboratory system for p+C interactions at 31 GeV$/c$. The results are presented as a function of momentum, $p$ (in [GeV/$c$]), in different angular intervals, $\theta$ (in [mrad]). The statistical and systematic errors are quoted.
The double differential $\pi^+$ production cross section in the laboratory system for p+C interactions at 31 GeV$/c$. The results are presented as a function of momentum, $p$ (in [GeV/$c$]), in different angular intervals, $\theta$ (in [mrad]). The statistical and systematic errors are quoted.
The double differential $\pi^+$ production cross section in the laboratory system for p+C interactions at 31 GeV$/c$. The results are presented as a function of momentum, $p$ (in [GeV/$c$]), in different angular intervals, $\theta$ (in [mrad]). The statistical and systematic errors are quoted.
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The excitation of theΔ resonance is observed in proton collisions on C, Nb and Pb targets at 0.8 and 1.6 GeV incident energies. The mass E0 and widthΓ of the resonance are determined from the invariant mass spectra of correlated (p, π±)-pairs in the final state of the collision: The mass E0 is smaller than that of the free resonance, however by comparing to intra-nuclear cascade calculations, this reduction is traced back to the effects of Fermi motion, NN scattering and pion reabsorption in nuclear matter.
WITHIN THE DETECTORS ACCEPTANCE RESULTS.
WITHIN THE DETECTORS ACCEPTANCE RESULTS.
WITHIN THE DETECTORS ACCEPTANCE RESULTS.
The fixed-target MIPP experiment, Fermilab E907, was designed to measure the production of hadrons from the collisions of hadrons of momenta ranging from 5 to 120 GeV/c on a variety of nuclei. These data will generally improve the simulation of particle detectors and predictions of particle beam fluxes at accelerators. The spectrometer momentum resolution is between 3 and 4%, and particle identification is performed for particles ranging between 0.3 and 80 GeV/c using $dE/dx$, time-of-flight and Cherenkov radiation measurements. MIPP collected $1.42 \times10^6$ events of 120 GeV Main Injector protons striking a target used in the NuMI facility at Fermilab. The data have been analyzed and we present here charged pion yields per proton-on-target determined in bins of longitudinal and transverse momentum between 0.5 and 80 GeV/c, with combined statistical and systematic relative uncertainties between 5 and 10%.
The production yields of PI+ and PI- and the ratio of these yields. The first uncertainty given on each value combines statistical uncertainties and systematic uncertainties from backgrounds.
Cross sections of cumulative K exp + and K exp - -meson production in the 200-1000 MeV kinetic energy range at 90 deg, 120 deg, 168 deg (l.c.s.) are measured. The ranges of kinetic energies and emission angles mean that, according to the hypothesis of cum ...
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Invariant cross sections for hadron production (π±,K±,p and\(\bar p\)) by protons off C, Al, Cu, Sn and Pb nuclei have been measured at 70 GeV for theP∧ range from 1 up to 4.65 GeV/c. TheA-dependence of the invariant cross section is not described by the exponentialAα(P∧), which points to the presence of secondary hadron absorption in nuclei.
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Interaction cross sections and charged pion spectra in p+C interactions at 31 GeV/c were measured with the large acceptance NA61/SHINE spectrometer at the CERN SPS. These data are required to improve predictions of the neutrino flux for the T2K long baseline neutrino oscillation experiment in Japan. A set of data collected during the first NA61/SHINE run in 2007 with an isotropic graphite target with a thickness of 4% of a nuclear interaction length was used for the analysis. The measured p+C inelastic and production cross sections are 257.2 +- 1.9 +- 8.9 mb and 229.3 +- 1.9 +- 9.0 mb, respectively. Inclusive production cross sections for negatively and positively charged pions are presented as a function of laboratory momentum in 10 intervals of the laboratory polar angle covering the range from 0 up to 420 mrad. The spectra are compared with predictions of several hadron production models.
The total inelastic cross section and production cross sections. The latter are obtained from the former by subtraction of the quasi-elastic contribution.
The differential PI+ PI- production cross section in the lab. system for the angular range 0 to 20 mrad.
The differential PI+ PI- production cross section in the lab. system for the angular range 20 to 40 mrad.
The HARP collaboration has presented measurements of the double-differential pi+/pi- production cross-section in the range of momentum 100 MeV/c <= p 800 MeV/c and angle 0.35 rad <= theta <= 2.15 rad with proton beams hitting thin nuclear targets. In many applications the extrapolation to long targets is necessary. In this paper the analysis of data taken with long (one interaction length) solid cylindrical targets made of carbon, tantalum and lead is presented. The data were taken with the large acceptance HARP detector in the T9 beam line of the CERN PS. The secondary pions were produced by beams of protons with momenta 5 GeV/c, 8 GeV/c and 12 GeV/c. The tracking and identification of the produced particles were performed using a small-radius cylindrical time projection chamber (TPC) placed inside a solenoidal magnet. Incident protons were identified by an elaborate system of beam detectors. Results are obtained for the double-differential yields per target nucleon d2 sigma / dp dtheta. The measurements are compared with predictions of the MARS and GEANT4 Monte Carlo simulations.
Differential cross section for PI+ production with a C target in the angular range 0.35 to 0.55 radians.. The errors are the square root of the diagonal elements of the covariant matrix.
Differential cross section for PI+ production with a C target in the angular range 0.55 to 0.75 radians.. The errors are the square root of the diagonal elements of the covariant matrix.
Differential cross section for PI+ production with a C target in the angular range 0.75 to 0.95 radians.. The errors are the square root of the diagonal elements of the covariant matrix.
Measurements of double-differential charged pion production cross-sections in interactions of 12 GeV/c protons on O_2 and N_2 thin targets are presented in the kinematic range 0.5 GeV/c < p_{\pi} < 8 GeV/c and 50 mrad < \theta_{\pi} < 250 mrad (in the laboratory frame) and are compared with p--C results. For p--N_2 (p--O_2) interactions the analysis is performed using 38576 (7522) reconstructed secondary pions. The analysis uses the beam instrumentation and the forward spectrometer of the HARP experiment at CERN PS. The measured cross-sections have a direct impact on the precise calculation of atmospheric neutrino fluxes and on the improved reliability of extensive air shower simulations by reducing the uncertainties of hadronic interaction models in the low energy range. In particular, the present results allow the common hypothesis that p--C data can be used to predict the p--N_2 and p--O_2 pion production cross-sections to be tested.
Double differential cross section for pion production in P-N2 interactions for the pion scattered polar angle range 50 to 100 mrad.
Double differential cross section for pion production in P-N2 interactions for the pion scattered polar angle range 100 to 150 mrad.
Double differential cross section for pion production in P-N2 interactions for the pion scattered polar angle range 150 to 200 mrad.
The results of the measurements of the double-differential production cross-sections of pions in p-C and $\pi^\pm$-C interactions using the forward spectrometer of the HARP experiment are presented. The incident particles are 12 GeV/c protons and charged pions directed onto a carbon target with a thickness of 5% of a nuclear interaction length. For p-C interactions the analysis is performed using 100035 reconstructed secondary tracks, while the corresponding numbers of tracks for $\pi^-$-C and $\pi^+$-C analyses are 106534 and 10122 respectively. Cross-section results are presented in the kinematic range 0.5 GeV/c $\leq p_{\pi} <$ 8 GeV/c and 30 mrad $\leq \theta_{\pi} <$ 240 mrad in the laboratory frame. The measured cross-sections have a direct impact on the precise calculation of atmospheric neutrino fluxes and on the improved reliability of extensive air shower simulations by reducing the uncertainties of hadronic interaction models in the low energy range.
Double-differential cross section for 12 GeV proton-carbon interactions with the scattered polar angle 30 to 60 mrad.
Double-differential cross section for 12 GeV proton-carbon interactions with the scattered polar angle 60 to 90 mrad.
Double-differential cross section for 12 GeV proton-carbon interactions with the scattered polar angle 90 to 120 mrad.
Measurements of the double-differential charged pion production cross-section in the range of momentum 100 MeV/c < p < 800 MeV/c and angle 0.35 < \theta < 2.15 rad in proton-beryllium, proton-carbon, proton-aluminium, proton-copper, proton-tin, proton-tantalum and proton-lead collisions are presented. The data were taken with the large acceptance HARP detector in the T9 beam line of the CERN PS. The pions were produced by proton beams in a momentum range from 3 GeV/c to 12.9 GeV/c hitting a target with a thickness of 5% of a nuclear interaction length.
Double-differential cross section for inclusive PI+ production in the LAB system with the BE target for a PI+ polar angle from 0.35 to 0.55 radians.
Double-differential cross section for inclusive PI+ production in the LAB system with the BE target for a PI+ polar angle from 0.55 to 0.75 radians.
Double-differential cross section for inclusive PI+ production in the LAB system with the BE target for a PI+ polar angle from 0.75 to 0.95 radians.
A measurement of the double-differential $\pi^{\pm}$ production cross-section in proton--carbon, proton--copper and proton--tin collisions in the range of pion momentum $100 \MeVc \leq p < 800 \MeVc$ and angle $0.35 \rad \le \theta <2.15 \rad$ is presented. The data were taken with the HARP detector in the T9 beam line of the CERN PS. The pions were produced by proton beams in a momentum range from 3 \GeVc to 12 \GeVc hitting a target with a thickness of 5% of a nuclear interaction length. The tracking and identification of the produced particles was done using a small-radius cylindrical time projection chamber (TPC) placed in a solenoidal magnet. An elaborate system of detectors in the beam line ensured the identification of the incident particles. Results are shown for the double-differential cross-sections at four incident proton beam momenta (3 \GeVc, 5 \GeVc, 8 \GeVc and 12 \GeVc).
Double-differential cross section for PI+ production from C in the LAB system for PI+ polar angle from 0.35 to 0.55 radians.
Double-differential cross section for PI+ production from C in the LAB system for PI+ polar angle from 0.55 to 0.75 radians.
Double-differential cross section for PI+ production from C in the LAB system for PI+ polar angle from 0.75 to 0.95 radians.
The mean multiplicities of π− mesons and protons originating from pC, dC, αC, and CC interactions at a momentum of p=4.2 GeV/c per projectile nucleon and the distributions of these particles in kinematical variables are presented. These experimental distributions are compared with the corresponding predictions obtained on the basis of the FRITIOF model. It is shown that the FRITIOF version used in the present analysis describes satisfactorily our experimental data.
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The analyzing powers of π+ and π− were measured using an incident 22−GeV/c transversely polarized proton beam at the Brookhaven Alternating Gradient Synchrotron. A magnetic spectrometer measured π± inclusive asymmetries on a hydrogen and a carbon target. An elastic polarimeter with a CH2 target measured pp elastic-scattering asymmetries to determine the beam polarization using published data for the pp elastic analyzing power. Using the beam polarization determined from the elastic polarimeter and asymmetries from the inclusive spectrometer, analyzing powers AN for π± were determined in the xF and pT ranges (0.45–0.8) and (0.3–1.2 GeV/c), respectively. The analyzing power results are similar in both sign and character to other measurements at 200 and 11.7 GeV/c, confirming the expectation that high-energy pion inclusive analyzing powers remain large and relatively energy independent. This suggests that pion inclusive polarimetry may be a suitable method for measuring future beam polarizations at BNL RHIC or DESY HERA. Analyzing powers of π+ and π− produced on hydrogen and carbon targets are the same. Various models to explain inclusive analyzing powers are also discussed.
Analyzing power measurements for PI+ and PI- production on the carbon target at incident momentum 21.6 GeV. See text of article for definitions of method 'A' and 'B'.
Analyzing power measurements for inclusive PI- production from the hydrogen target.
Analyzing power measurements for inclusive PI+ production from the hydrogen target.
An enormous enhancement of antiproton production in deuteron- and α-induced reactions has been observed in the subthreshold energy region between 2 and 5 GeV/nucleon. Antiprotons produced at 5.1° with a momentum range of between 1.0 and 2.5 GeV/ c were measured by a beam-line spectrometer and identified by the time-of-flight method. The production cross sections in the deuteron- and α-induced reactions at an incident energy of 3.5 GeV/nucleon were 2 and 3 orders of magnitude larger than those in proton-induced reaction at the same energy. The enhancement in light-ion reactions could not be explained by the internal motion in the projectile and target nuclei. The target-mass dependence (C, Al, Cu and Pb) of the cross sections has also been studied. Further, the cross sections of π and K productions were measured.
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Detailed measurements of the production of charged π mesons in proton-proton collisions are reported. The observed results are compared with the "isobar" and "one-pion exchange" models and for single production are in agreement if only the "resonant" part of the π−p cross section is used and if the angular distribution cos16θ is introduced for the production of the N1* isobar. The effects of higher resonances are also considered.
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1.0 cm WT target.
1.0 cm C target.
1.0 cm CU target.
We have measured the differential cross section d2σdΩdTπ and the polarization parameter P for the production of π+ and π− in various target nuclei (H1, H2, Be, C, O, Al, Ni, Cu, Mo, and Pb) by protons with a kinetic energy of 585 MeV, for production angles θπ=22.5°, 45°, 60°, 90°, and 135°, and for pion kinetic energies Tπ of 24, 35, 46, 88, 151, 192, and 254 MeV (all quantities in the laboratory system). Our data disagree strongly with recent data for 580-MeV protons. On the other hand, for pion energies up to 150 MeV, our cross sections differ little from those measured for a proton energy of 730 MeV. For nuclei with A>20, the total production cross sections σ(π+) and σ(π−) show the Z13 and N23 proportionality expected from theoretical arguments. There is evidence in our data of a shift of the π+ energy distributions compared to the π− distributions due to the effects of the Coulomb field of the nuclear protons on the emitted pions. NUCLEAR REACTIONS H1, H2, Be, C, O, Al, Ni, Cu, Mo, Pb p, π±, Tp=585 MeV; measured σ(Tπ, θπ) and asymmetry parameter P(Tπ, θπ).
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Antiproton production cross-sections have been measured for p+C, C+C, C+Cu and C+Pb collisions at 3.65 GeV/nucleon.\(\bar p\) laboratory momentum and angle are 0.8 GeV/c and 24°. The target mass dependence parameter is found to be 0.43±0.1. A strong increase in antiproton yield is observed from p+C, d+C to C+C collisions. Projectile mass parameter is 1.2±0.2 for d+C to C+C. The construction and calibration of APAKI, an annihilation detector for\(\bar p\) identification, are also described.
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MOMENTUM SPECTRA IN THE WINDOW P=0.1-6.0 HAVE BEEN FITTED BY THE FORMULA: (1/N)*D(N)/D(P)=CONST(Q=1)*EXP(-SLOPE(Q=1)*P)+CONST(Q=2)*EXP (-SLOPE(Q=2)*P).
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Light ion collisions with carbon target at 4.2 GeV/c/N are studied. Pion multiplicity distributions, momentum and angular spectra are analysed. These data are described in terms of models assuming independent interactions of nucleons from the projectile nucleus with the target.
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The differential cross sections of π − and π + meson production at a laboratory angle of 159° in collisions of 15–65 GeV protons with Be, C, Al, Ti, Mo and W targets are measured. The data are presented in the tables for Lorentz-invariant cross sections over the momentum range of pions from 0.25 to 0.95 GeV/ c . The slopes (“temperatures”) of a cumulative part of the pion spectra (the pion kinetic energy is >0.35 GeV) increase by 15–20% with changing A from 9 up to 184. Some discrepancy in the E -dependence of the temperature of the cumulative pion spectra is observed in the high-energy region studied, namely the temperature at 15–65 GeV, taking its slow rise over this range into account, contradicts that at 400 GeV.
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The π − yield in the momentum range 500–740 MeV/ c produced by 800 MeV protons incident on targets of Be and C has been measured at laboratory production angles between 0° and 20°. The yield of 725 MeV/ c π − from Be and C at 0° is a factor of 6 greater than at 20°, for 600 MeV/ c π − the factor is 3. The yield from beryllium is typically 30% higher than from carbon.
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Highly inelastic processes in hadron-nucleus reactions at several GeV have been studied by measuring multi-particle emission in the target-rapidity region. Events with no leading particle(s) but with high multiplicities were observed up to 4 GeV. Proton spectra from such events were well reproduced with a single-moving-source model, which implied possible formation of a local source. The number of nucleons involved in the source was estimated to be (3–5)A 1 3 from the source velocity and the multiplicity of emitted protons. In those processes the incident energy flux seemed to be deposited totally or mostly (>62;75%) in the target nucleus to form the local source. The cross sections for the process were about 30% of the geometrical cross sections, with little dependence on incident energies up to 4 GeV and no dependence on projectiles (pions or protons). The E 0 parameter in the invariant-cross-section formula E d 3 σ /d p 3 = A exp (− E / E 0 ) for protons from the source increases with incident energy from 1 to 4 GeV/ c , but seems to saturate above 10 GeV at a value E 0 = 60–70 MeV. Three components in the emitted nucleon spectra were observed which would correspond to three stages of the reaction process: primary, pre-equilibrium and equilibrium.
BEAM ERROR D(P)/P = 0.300 PCT. X ERROR D(EKIN)/EKIN = 8.00 PCT.
BEAM ERROR D(P)/P = 0.300 PCT. X ERROR D(EKIN)/EKIN = 8.00 PCT.
BEAM ERROR D(P)/P = 0.300 PCT. X ERROR D(EKIN)/EKIN = 8.00 PCT.
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FRAGT IS CHARGE BARYON WITH PATH < 4 CM.
FRAGT IS CHARGE BARYON WITH PATH < 4 CM.
FRAGT IS CHARGE BARYON WITH PATH < 4 CM.
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Measurements of the invariant cross sections for the reaction p(400 GeV)+(Li6, Be,C,Al,Cu,Ta)→(π±, K±)+X at laboratory angles from 70° to 160° are reported. Upper limits for p¯ production are given. Comparisons of the data are made using several scaling variables. NUCLEAR REACTIONS Inclusive cross section; 400 GeV incident protons; Li6, Be, C, Al, Cu, Ta targets; production of π, K, and p¯; lab angles 70° to 160°.
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PRELIMINARY DATA.
PRELIMINARY DATA.
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Axis error includes +- 0.0/0.0 contribution (?////DUE TO UNACCURASY IN OUTGOING PARTICLES MOMENTUM).
Axis error includes +- 0.0/0.0 contribution (?////DUE TO UNACCURASY IN OUTGOING PARTICLES MOMENTUM).
Axis error includes +- 0.0/0.0 contribution (?////DUE TO UNACCURASY IN OUTGOING PARTICLES MOMENTUM).
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An experiment was done in the external proton beam of the Berkeley 184-in. cyclotron to measure the production cross sections for pions from various target nuclei, from hydrogen to lead. The cross-section data are presented and the reaction mechanisms discussed. The hydrogen production appears to fit the one-pion-exchange model.
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Inclusive cross sections for production of π+, π−, p, d, H3, He3, and He4 have been measured at laboratory angles from 10° to 145° in nuclear collisions of Ne + Naf, Ne + Cu, and Ne + Pb at 400 MeV/nucleon, C + C, C + Pb, Ne + NaF, Ne + Cu, Ne + Pb, Ar + KCl, and Ar + Pb at 800 MeV/nucleon, and Ne + NaF and Ne + Pb at 2.1 GeV/nucleon. The production of light fragments in proton induced collisions at beam energies of 800 MeV and 2.1 GeV has also been measured in order to allow us to compare these processes. For equal-mass nuclear collisions the total integrated yields of nuclear charges are well explained by a simple participant-spectator model. For 800 MeV/nucleon beams the energy spectra of protons at c.m. 90° are characterized by a "shoulder-arm" type of spectrum shape with an exponential falloff at high energies, whereas those of pions are of a simple exponential type. The inverse of the exponential slope, E0, for protons is systematically larger than that for pions. This value of E0 is larger for heavier-mass projectiles and targets. It also increases monotonically with the beam energy. The angular anisotropy of protons is larger than that of pions. The yield ratio of π− to total nuclear charge goes up with the beam energy, whereas the yields of composite fragments decrease. The ratio of low-energy π− to π+, as well as that of H3 to He3, is larger than the neutron to proton ratio of the system. The spectrum shape of the composite fragments with mass number A is explained very well by the Ath power of the observed proton spectra. The sizes of the interaction region are evaluated from the observed coalescence coefficients. The radius obtained is typically 3-4 fm. The yield ratio of composite fragments to protons strongly depends on the projectile and target masses and the beam energy, but not on the emission angle of the fragments. These results are compared with currently available theoretical models. NUCLEAR REACTIONS Ne + NaF, Ne + Cu, Ne + Pb, EA=400 MeV/nucleon; C + C, C + Pb, Ne + NaF, Ne + Cu, Ne + Pb, Ar + KCl, Ar + Pb, EA=800 MeV/nucleon; Ne + NaF, Ne + Pb, EA=2100 MeV/nucleon; p + C, p+ NaF, p + KCl, p + Cu, p + Pb, E=800 MeV; p + C, p + NaF, p + KCl, p + Cu, p + Pb, E=2100 MeV; measured σ(p,θ) for π+, π−, p, d, H3, He3, and He4.
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Without abstract
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We report on double-differential inclusive cross-sections of the production of secondary protons, charged pions, and deuterons, in the interactions with a 5% nuclear interaction length thick stationary carbon target, of proton and pion beams with momentum from \pm 3 GeV/c to \pm 15 GeV/c. Results are given for secondary particles with production angles between 20 and 125 degrees. Cross-sections on carbon nuclei are compared with cross-sections on beryllium, copper, tantalum and lead nuclei.
The measured deuteron to proton ratios for each of the 8 GeV Proton, PI+ and PI- beams for the angular range 20 to 30 degrees.
The measured deuteron to proton ratios for each of the 8 GeV Proton, PI+ and PI- beams for the angular range 30 to 45 degrees.
The measured deuteron to proton ratios for each of the 8 GeV Proton, PI+ and PI- beams for the angular range 45 to 60 degrees.
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