Noneikonal approach to the scattering of hadrons from nuclei. II. Proton and pion scattering from D, 3He and 4He (kL ≳ 1 GeV/c)

A previously formulated noneikonal theory for hadron-nucleus scattering valid for all angles is applied to p and π scattering on the lightest targets (k_L ? 1 GeV/c). When the required input is known, calculated differential cross sections agree well with experiments out to medium angles, far beyond the region of previous analyses. In the case of pA scattering at k_L = 1.2 GeV/c at which momentum some parameters in the elementary amplitudes F_xN are badly known, limits on their values have been obtained by demanding simultaneous agreement between theory and data for several targets. Generally speaking the agreement evidences the existence of some major corrections to the eikonal amplitude, namely, propagator off-shell and nucleon recoil effects. Inclusion of the latter primarily affects the single scattering amplitude, which may dominate the large-q² cross section if F_xN (like F_pp) itself rises with q². The calculation of pD and p⁴He cross sections requires knowledge of body form factors S_A often unknown for large q². Consistency requirements for angular distributions at several k_L lead to a conjectured large-q² behavior of S_A(q). In the case of the D the conjecture has been largely confirmed by a recent measurement of the electric form factor. The agreement leaves little room for $\text{NN}{}^1$ components in the D as heretofore derived from pD scattering. We speculate that in general, reasonable estimates for nuclear form factors out to very large q² may be obtained from hadron-nucleus scattering data with existing facilities. Since higher q² values can be reached in hadron-nucleus than in eA scattering, the former may well provide the first tests for predicted scaling of nuclear form factors.     

The tensor analyzing power in backward pd elastic scattering and its relation to pp → πd at intermediate energies

The tensor analyzing power for pd backward elastic scattering is calculated in the energy range 150 ≤ T_{p ≤ 800 MeV}. Two main contributions are considered: the one-nucleon-exchange and the so-called triangle graph, including pp → πd as a subprocess. The pd backward elastic cross section and tensor analyzing power are fairly well reproduced by the model.     

DWIA analysis of quasifree proton-proton scattering in nuclei at intermediate energies

The distorted wave impulse approximation to the (p, 2p) reaction cross section is briefly reviewed, having foremost in mind its practical implementation as a computer program, suitable for extracting information on nuclear structure. The treatment of the distorted waves, and the approximation of the overlap integral between the ground state of the target nucleus and the final state of the residual nucleus, are discussed in more detail. As far as possible we have chosen methods which enable us to minimize the number of free reaction-theoretical parameters by deducing them from independent experimental data. As an illustration of how one can use a program constructed according to these principles, we analyze 460 MeV and 600 MeV data on the reaction ⁴⁰Ca(p, 2p)³⁹K with rather detailed discussion of various theoretical and experimental questions that must be taken into consideration before any conclusions can be drawn.     

Multiparticle emission in the interactions of hadrons with complex nuclei at incident momenta from 2 to 4 GeV/c

The charged secondary particles emitted in inelastic reactions of 4 GeV/cπ⁺ and π^? with the nuclei Be, Cu and Ta are thoroughly studied in their multiplicities, particle correlations and the distributions of kinematical variables, with the 1 m hydrogen bubble chamber into which the three nuclear target plates were installed. The numbers of charged secondaries emitted in the π^?(2.3 GeV/c), π⁺(2 GeV/c) and p(4 GeV/c) reactions are also investigated. From these data, characteristic features of the multiplication process of secondaries in nuclear matter are clarified. The experimental results are compared with the calculation of an intra-nuclear cascade model which takes into account the process of pion absorption by two-nucleon clusters in the nucleus. It is found that the experimental results on the properties of charged secondaries are consistently explained by the model. The model can also give an account of the experimental finding that fairly high momentum protons are emitted from the heavier nuclei into the backward hemisphere in the lab system.     

Shell-model approach to the nucleon elastic scattering by nuclei

On the basis of the shell-model approach to nuclear reactions the averaged scattering matrix is parametrized. The method is applied to the calculation of s-neutron strength functions. It is shown that in contrast to the optical model predictions the isotopic dependence of the strength function in its minimum (A ≈ 100?140) is mainly determined by the 3s-state spectroscopic factor.     

Group theory approach to scattering III. Realistic models

We discuss how to construct a class of solvable S-matrices in arbitrary space dimensions starting from a dynamic group G and using the technique of Euclidean connection. We construct explicitly the S-matrices corresponding to the dynamic groups SO(2, 1), SO(2, 2), and SO(2, 3). The latter provides a realistic model for studying heavy-ion collisions.     

New approach to solving the problem of composite-particle scattering on nuclei

An essentially new approach to solving the problem of elastic and inelastic scattering of a composite particle on stable nuclei is described. Within this approach, all channels of virtual breakup and stripping in the intermediate states are included in a nonlocal complex-valued interaction operator with the aid of the projection-operator technique.The three-particle continuum spectrum of the Hamiltonian for intermediate states in Q space is calculated within the orthogonalizing-pseudopotential method by introducing a pseudo-Hamiltonian, which is diagonalized in a full space in terms of a relevant oscillator basis. As was shown by a number of authors, the use of special quadratures makes it possible to reduce integration over the continuous spectrum of intermediate states to summation over a discretized continuum. On the basis of the formalism developed in this study, a closed Schrödinger equation with a nonlocal complex potential for partial waves is derived for describing elastic scattering of a composite particle by a target, and an explicit approximate formula for the amplitude of three-particle breakup is obtained on the same basis. This method has a number of obvious advantages over currently well-known approaches of the type of the discretized-continuum coupled-channel method, where solving the problem in question reduces to solving a cumbersome set of coupled equations.     

Analysis of intermediate energy nucleon-deuteron elastic scattering

We present a theoretical analysis of a broad range of aspects of intermediate energy nucleon-deuteron scattering. This analysis is based on a multiple scattering approach using knowledge of the deuteron's structure and nucleon-nucleon interactions. Conversely, comparison of this theory with experiment can yield information about low and intermediate energy strong interactions. The relationship of this multiple scattering type of approach to the complementary Faddeev equation approach is discussed. Our program consists of calculating the single scattering and one nucleon exchange contributions in a realistic way then parametrizing the remaining contributions as an S-wave. We argue that the largest error in this analysis is the P-wave part of the double scattering and we give estimates of its size. The single scattering integral is evaluated numerically. Coulomb effects are neglected. We derive the relativistic expressions for single scattering and nucleon exchange and discuss the approximations made, including the off-mass-shell extrapolation of the nucleon-nucleon scattering amplitude. Fits are made to experimental measurements of differential cross sections, nucleon polarizations, and total elastic cross sections. Unitarity is maintained. We tabulate the partial waves for $\text{J ?}\text{5}\text{2}$, L ? 2. They are consistent with recent Faddeev calculations. We argue that with the additional calculation of double scattering the deuteron D-state percentage can be determined to the same relative uncertainty as the differential cross section. Even without the calculation of double scattering, our results indicate a D-state percentage around 8%. In an effort to provide benchmarks for future work, we have tried to be conscientious in describing our techniques and in tabulating numerical results. Comparisons are also made with earlier analyses.     

Fragmentation of light nuclei by intermediate energy photons

New data on the fragmentation of carbon nuclei by photons with energies from 800 to 1500 MeV, obtained in the collaboration GRAAL, are presented. These data include the yields of heavier fragments than nucleons. Comparison of new results with literature data, obtained with real and virtual photons in reactions with electrons and relativistic ions (Coulomb dissociation) is done using a general approach in frame of the Weizsäcker–Williams model. Possible reasons for the observed differences between them are discussed.     

Yield ratios and directed flows of light fragments from reactions induced by neutron-rich nuclei at intermediate energy

The yield ratios of neutron/proton and ~3H/~3He and the directed flow per nucleon for these projectile-like fragments at large impact parameters are studied for ~(50)Ca + ~(40)Ca and ~(50)Cr + ~(40)Ca for comparison at 50 MeV/u using the isospin-dependent quantum molecular dynamics(IQMD) model.It is found that the yield ratios and the directed flows per nucleon are different for reactions induced by the neutron-rich nucleus ~(50)Ca and the stable isobaric nucleus ~(50)Cr,and depend on the hardness of the EOS.The ratios of neutron/proton and ~3H/~3He and the difference of directed flow per nucleon of neutron-proton are suggested to be possible observables to investigate the isospin effects.     

Analysis of elastic proton-nucleus scattering on the basis of the Glauber-Sitenko approach with allowance for intermediate excitations of nuclei

On the basis of the Glauber-Sitenko approach, the cross sections and spin observables for proton-nucleus scattering at intermediate energies are calculated with allowance for intermediate excitations of target nuclei. The calculations are performed by using the Hartree-Fock and model-independent nuclear densities and nucleon-nucleon amplitudes determined from partial-wave analyses. It is shown that the inclusion of intermediate excitations of nuclei strongly affects the behavior of observables in the region of moderately small scattering angles.     

Relativistic mean field approach to the scattering of antinucleons and nucleons by nuclei

A realistic mean field approach based on the Walecka theory for nuclear matter is used to derive the optical potential for nucleon and antinucleon-nucleus systems. The total and reaction cross sections are calculated in the WKB approximation for different nuclei ranging from carbon to lead and for incident energies between 0.1 and 2 GeV.