On high-energy elastic scattering of protons by nuclei

The two coupled channel formalism for high energy elastic scattering [1] is extended to include spin and isospin effects. For a spin and isospin zero nucleus these manifest themselves by additional spin-orbit terms in the potentials. Explicit formulas for these potentials are obtained in terms of the fully spin and isospin dependent nucleon-nucleon scattering amplitude, the ground state nuclear form factor and the state dependent correlation functions. The coupling potential except for a small term arising from double spin and isospin flip process involving nuclear excitation depends only upon the pair correlations.Numerical calculations are performed for the elastic scattering of 1 GeV protons incident on ⁴He. Various phenomenological dynamical two-body correlations as well as correlations generated from the Reid soft-core and Tabakin potentials in an approximate Brueckner-Hartree-Fock calculation are considered. The angular distribution beyond its first diffraction minimum as well as the polarization in the same angular range are shown to be sensitive to these correlations. However, the present accuracy of the experimental data and the lack of knowledge of the nucleon-nucleon scattering amplitude prevent any definitive conclusion about their nature.     

Nuclear effects in the diffraction scattering of protons by nuclei at high energies

Processes of the diffraction scattering of protons on nuclei in the context of developing the HARDPING (Hard Probe Interaction Generator) Monte Carlo event generator are considered with allowance for nuclear effects in the initial and final states. Effects such as the length of formation, energy losses, and the multiple rescattering of incident and produced hadrons are studied.     

Elastic scattering of 1-GeV protons by nuclei

The calculated elastic scattering of 1.04-GeV protons by ²⁰⁸Pb, ⁵⁸Ni, and ⁴⁰Ca is compared with experiment. The effects of the spin-orbit potential, Pauli and short-range correlations, variations in the ratio of the real to the imaginary part of the nucleon-nucleon scattering amplitude at 0° are found to have similar effects. Further experiments are required before these effects can be disentangled. Changes of the neutron density compared to the proton density can be distinguished. The proton polarization by elastic scattering by ²⁰⁸Pb and ⁴⁰Ca is calculated omitting the effects of correlations.     

Elastic scattering of high-energy protons from nuclei

The elastic scattering of high-energy protons from zero-spin nuclei is considered within the framework of Glauber theory. The sensitivity of the cross sections to the nuclear structure and to the proton-nucleon amplitude is studied. Results of calculations demonstrating the investigated effects are presented for the case of 1 GeV proton scattering from ⁴He, ¹⁶O and ⁵⁸Ni.     

Vacuum polarization effects in elastic scattering of protons by nuclei

Sensitivity of spin observables in elastic proton scattering by nuclei to the vacuum polarization correction δϱ_VAC is explored. The Dirac optical potential is calculated from a complete set of Lorentz invariant amplitudes, Dirac-Hartree densities and the existing estimate of δϱ_VAC based on quantum hadrodynamics.     

Elastic scattering of 800-MeV protons by 20Ne nuclei

The differential cross section and polarization observables are calculated for the elastic scattering of 800-MeV protons by ²⁰Ne nuclei. The assumption that the ²⁰Ne nucleus has an alpha-cluster structure is shown to lead to results that agree with the measured values of observables of the above scattering process.     

Target excitations and the optical potential for protons scattering from nuclei

We calculate the contributions to the optical potential for 30 MeV protons due to inelastic excitations of the target nucleus. The scattering due to this non-local potential is calculated exactly and some of the results subjected to conventional optical model analysis. When only one excited state is included, a resonant dependence on the excitation energy is observed. Even with ten excited states, the position of a single one can strongly influence the scattering. It is possible to account for about $\text{3}\text{4}$ of the observed absorption in ⁴⁰Ca and ²⁰⁸Pb, but only by postulating unobserved states which exhaust the remainder of the experimental sum rules at somewhat unreasonably low energies. It was not possible to find simple local potentials which gave the same scattering because of the strong L-dependence of the absorption. The constructed potentials concentrate the absorption at too small radii. It is suggested that rearrangement (pick-up) processes contribute a substantial amount of absorption at larger radii, while compound formation will give rise to a volume term in the imaginary potential.     

High energy proton scattering by medium and heavy nuclei

The recent data on both elastic and inelastic scattering of 1 GeV protons by ⁴⁰Ca and ²⁰⁸Pb are analyzed by means of the first term of the multiple scattering series for the optical potential and the DWIA. Theory and experiment agree quite well. Coulomb effects are taken into account. Neutron and proton ground state densities given by Hartree-Fock calculations employing a density-dependent Hamiltonian and which provide a good fit to elastic electron scattering are used. The Tassie form factors, normalized by comparison with inelastic electron scattering, are employed in the DWIA.     

Proton-proton and deuteron-deuteron correlations in interactions of relativistic helium nuclei with protons

The reactions⁴Hep pp+X,³Hep pp+X and⁴Hep ddp have been investigated and the correlation function has been measured for protons and deuterons with small relative momenta. Strong positive correlation has been observed for protons related mainly to the final state interactions in¹S₀ state. The root mean square radius of the proton source calculated from the correlation function has been found to be equal to (1.7±0.3) fm and (2.1±0.3) fm for⁴He and³He respectively. It agrees with the known radii of these nuclei.We would like to thank Dr R. Lednicky for discussion, helpful suggestions and for making available the computer program that calculates the theoreticalpp correlation function. The authors also thank Dr D.H. Boal for providing the results of the two-deuteron correlation function calculations.     

Multiplicity correlations of medium energy protons in hadron-nucleus collisions

Data on forward-backward multiplicity correlations of medium energy protons from hadron-nucleus collisions are presented and discussed.     

Elastic and the 2+ inelastic scattering of high energy protons on12C and the alpha-particle model

The alpha-particle model has been applied to calculate the elastic and the 2⁺ inelastic angular distribution of 1 GeV protons on¹²C within the framework of Glauber multiple scattering theory. The results are compared with the recent experimental data and with some previous calculations. The model gives a fairly good account of the inelastic data and its predictions for the elastic scattering are essentially the same as those of the shell model.     

Polarization measurements in high energy elastic scattering of pions,kaons, protons and antiprotons on protons and comparison with regge phenomenology

The polarization parameterP has been measured for elastic scattering on polarized protons, of ^–, K^– and ¯p at 40 GeV/c and of ⁺, K⁺ and p at 45 GeV/c. Four-momentum transfer ranges from –0·08 to –1·8 (GeV/c)² for ^–p, and from –0·08 to about –1sd0(GeV/c)² for p, ⁺, K^± and ¯p.The angular distribution of the polarization in ^–p exhibits the well known non sense double zero att=–0·6 (GeV/c)². The K^–p and ¯pp results are compatible with exchange degeneracy for ¦t¦_r <0·5 (GeV/c)². The energy dependence of the polarizationP(t) in ^–p and in K⁺p above 10 GeV/c incident momentum is compatible with interference between Pomeron and Regge poles. On the contrary, the polarization in pp elastic scattering decreases faster than ordinary Regge model predictions. This result can be explained by interference between non flip and flip amplitudes of the Pomeron, leading to negative values for the polarization.Presented by A.de Lesquen at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.     

Microscopic analysis of the elastic scattering of 11Li neutron-rich nuclei on protons

Amicroscopic optical potential is used to calculate cross sections for elastic ¹¹Li +p scattering at the energies of 62, 68.4, and 75 MeV per nucleon, and the results are compared with available experimental data. The potential used does not involve free parameters, but the depths of its real and imaginary parts are renormalized. The known trend in the energy dependence of the volume integrals of the optical potential is taken into account in analyzing experimental data. The role of spin-orbit interaction is studied, and the total reaction cross sections that are proposed to be measured in future experiments are calculated.     

The multiple scattering model analysis of high energy multiparticle production on emulsion nuclei

Data on multiparticle production on emulsion nuclei in the range 50–400 GeV/c have been analyzed in the framework of multiple scattering model developed by Capella and Krzywicki. It is shown that under some reasonable assumptions multiple scattering type models qualitatively reproduce multiplicity distributions of relativistic charged particles, one-particle spectra and two-particle inclusive correlations. When considering one-particle distributions a particular attention was given to the regions of small and large pseudorapidities. In the first region we found an apparent evidence for low-energy cascading, contribution and main features of which have been discussed. It is also discussed how strongly the behaviour of one-particle spectra at large rapidities would depend on the internal structure of a projectile particle.     

The influence of short-range correlations on nucleon emission in electron scattering by nuclei

The nucleon emission induced by high-energy electrons is analysed in three experimental situations: electron-proton coincedence and single detection of electron or proton. The coincidence and proton detection experiments are recommended as sensible tools for studying the nuclear correlations.     

On the role of longitudinal momenta in high energy hadron-hadron scattering

We demonstrate a new method to calculate inelastic scattering cross-sections, which in contrary to the Regge-based methods takes into account the energy momentum conservation law. It is shown that the main contribution to integral expressing inelastic scattering cross-sections does not come from the multi-Regge domain. In particular, accounting for the longitudinal momenta contribution to virtualities is sufficient and results in the new mechanism of cross-section growth. The reasons for taking into account the sufficiently high number of interference contributions are shown and the approximate method for this purpose is developed. By fitting single free parameter of the model achieved a qualitative agreement of the total and inelastic cross sections with experimental data.     

Polarization in the quasielastic scattering of 1-GeV/c protons on light nuclei

Polarization measurements in the A(p, 2p)B reactions on ⁶Li, ⁷Li, and ²⁸Si nuclei at a proton-beam energy of 1 GeV were performed in a kinematically complete experiment. By using a two-arm magnetic spectrometer, two secondary protons were recorded in coincidence at asymmetric scattering angles of θ₁=15°?26° and θ₂=58.6° for residual-nucleus momenta in the range K _B=0–150 MeV/c. Either arm of the spectrometer was equipped with polarimeters based on proportional chambers. The data coming from this experiment are analyzed within the distorted-wave impulse approximation. It is shown that the polarization of recoil protons formed at angle θ₂ in the interaction featuring a proton from the P shell of the ⁷Li nucleus can be described under the assumption of an effective intranuclear-proton polarization by using the single-particle shell-model wave function of the nucleus. Our data on the polarizations of the two protons from the reaction (p, 2p) on a ²⁸Si nucleus also suggest the effective polarization of the protons in the D shell of the ²⁸Si nucleus. It is found that, for high recoil-nucleus momenta of K _B≥90 MeV/c, the effective polarization of the protons in the P shell of the ⁶Li nucleus—this polarization was discovered in studying the polarization of recoil protons in the reaction ⁶Li(p, 2p)⁵He—cannot be described within the shell model assuming LS coupling. As might have been expected, the polarization of recoil protons knocked out from the S shells of the ⁶Li and ⁷Li nuclei comply well with the predictions obtained in the impulse approximation with allowance for the depolarization effect alone.     

On the investigation of nucleon-nucleon correlations by means of high-energy scattering

The possible effects of short-range dynamical nucleon-nucleon correlations on high-energy hadron scattering on ⁴He are examined. The Glauber theory of multiple scattering is used as the basis for the computations. The conclusion is that very small effects are to be expected for elastic and sum total inelastic scattering of commonly available projectiles.