Antiproton-nucleus scattering with self-consistent model for medium corrections

The antiproton-nucleon t-matrix with propagation in the nuclear medium is calculated selfconsistently and applied to the construction of optical potentials for the elastic scattering of antiprotons from nuclei. We find that this treatment gives results that are sensitive to medium corrections even though the strong absorption acts to mask these corrections partially. The agreement with scattering experiments at 46.8 MeV on ¹²C is very good. We compare potentials containing medium corrections to those based on free $\text{p}\text{N}$ amplitudes for ¹²C and ⁴⁰Ca. The local approximation to the optical potential is found attractive at low energies, becoming shallower with increasing bombardment energy in the range considered here (up to about E_L = 120 MeV).     

Parity violating effects in the coherent scattering of neutrons by 209Bi

We study the rotation of the spin in the coherent scattering of polarized thermal neutrons by ²⁰⁹Bi. Contributions due to direct weak scattering by the nucleus, parity admixtures into the nuclear wave functions and scattering by the electrons are calculated. We use a parity violating potential derived in the framework of the Salam-Weinberg model and several other semi-empirical potentials. The results show that the direct scattering on nuclei is the dominant contribution and some potentials predict results up to an order of magnitude larger than expected on dimensional grounds. The sign of the effect depends on the isospin properties of the potential and can distinguish between potentials with large isotensor or large isovector contributions.     

Nuclear-rainbow scattering and nucleus-nucleus potentials at short distances

The elastic scattering of strongly bound nuclei at energies of 10 to 70 MeV per nucleon shows the phenomenon of “rainbow scattering.” A nuclear rainbow appears because of deflection to negative angles. This process involves a strong overlap of nuclear densities, with values of up to twice the saturation density of nuclear matter. The ¹⁶O+¹⁶O system is studied with a high precision over a wide energy range from 7 to 70 MeV per nucleon in several laboratories. Primary Airy maxima and higher order Airy structures are observed. At all energies, excellent fits are obtained with deep potentials as deduced from the double-folding model involving a nucleon-nucleon interaction weakly dependent on the density. It is shown that Pauli blocking expected at low energies is strongly reduced if the local momenta are calculated self-consistently. Systematics confirms a refractive origin of large-angle scattering, at low energies inclusive. Thus, nuclear-rainbow scattering yields unique information about the properties of cold nuclear matter at higher densities.     

Study of the structure of light,unstable nuclei and the mechanism of elastic proton scattering

The review presents calculations of elastic p ⁶He-, p ⁸Li-, p ⁹Li- and p ⁹C scattering in the framework of the Glauber theory of multiple diffraction scattering at intermediate energies of 70 and 700 MeV/nucleon. The most significant result of the calculations is that we have utilized realistic three-body wave functions obtained within modern nuclear models. The relation is found between differential cross sections and intercluster potentials, where the nuclear wave functions are calculated. Conclusions are made concerning the types of potentials which describe most realistically the available experimental data. The method for calculation of three-body wave functions in α-n-n-, α-t-n-, ⁷Be-p-p-, α-t-2n-, and ⁷Li-n-n models is described with discussion of inter-cluster potentials and the quantum-number configurations taken into consideration. It is revealed how the wave functions and the nuclear electromagnetic characteristics calculated using these wave functions depend on the choice of intercluster potentials. The derivation of matrix elements (amplitudes) of pA scattering in the framework of the Glauber approach with three-body wave functions is presented by an example of ⁶He nucleus. Discussing the results of calculation of differential cross sections and the analyzing power (A _y ), we established how the calculated characteristics depend on a wave-function structure and dynamics of the process determined by a Glauber operator of multiple scattering. The calculated differential cross sections and analyzing powers are compared with available experimental data and calculations by other authors performed for different formalisms, which allows us to make justified conclusions.     

DWIA calculation of the 16O(α, 2α) reaction

The cross sections for the ¹⁶O(α, 2α) reaction have been calculated in the distorted wave impulse approximation. The influence of the optical potentials in the incident and final channels on the energy sharing distribution and the spectroscopic factors has been investigated. Optical potentials with small imaginary content are shown to fit both elastic scattering and the experimental data well and give a spectroscopic factor of 1.1; the contribution from the nuclear interior broadens the energy sharing distributions, in agreement with observations.     

Low-energy theorems for nuclear compton and raman scattering and 0+ → 0+ two-photon decays in nuclei

Low-energy theorems for elastic photon scattering (nuclear Compton scattering) from a nucleus of arbitrary spin are derived in the nonrelativistic approximation through terms quadratic in the photon frequency. The same derivation is made for the special case of 0⁺ → 0⁺ nuclear excitation by inelastic photon scattering (nuclear Raman scattering). Use is made of the general principle of gauge invariance, which bypasses the need to specify the form of the current operator explicitly. A general discussion of the contribution of mesonic exchanges is made and their effect is isolated. The center-of-mass correction to the nuclear diamagnetic susceptibility is calculated. The 0⁺ → 0⁺ two-photon decay amplitude is obtained from the nuclear Raman amplitude and the transition rate is calculated.     

Microscopic analysis of antiproton-nucleus elastic scattering

Elastic antiproton-nucleus scattering is analysed with a microscopic optical model potential obtained by convoluting an effective interaction with target densities. Local, energy- and density-dependent complex effective interactions are constructed from reaction matrices generated with the Dover-Richard and Paris potentials. Effects of nuclear medium correction on the final results are examined. Comparison is made between the calculated results and the experimental data from LEAR which include the first polarization data as well as differential cross sections.     

正、负电子被原子散射的光学势方法──e~±－Na散射总截面的计算

将原子核散射理论中的光学势方法应用于正、负电子被原子散射的计算，提出了不含任意参数的光学势以及由此确定散射矩阵元的方法，计算了低能（≤５０ｅＶ）正、负电子被Ｎａ散射的总截面并与实验结果进行了比较。     

Nuclear matter approach to the heavy-ion optical potential

An energy-dependent local potential for heavy-ion (HI) scattering is derived from Reid's softcore interaction using the Brueckner theory. The Bethe-Goldstone equation in momentum space is first solved with the outgoing boundary condition for two colliding systems of nuclear matter with the relative momentum K_r per nucleon. The Fermi distribution is assumed to consist of two spheres without double counting of their intersection separated by the relative momentum K_r. The angle-averaged Pauli projection function is given in the form of a one-dimensional integral. Secondly the optical potential for HI scattering is evaluated using the energy-density formalism. The energy density is calculated for two limiting cases: (i) the sudden approximation in which the spatial distribution of the two HI is described by an antisymmetrized cluster wave function, and (ii) the adiabatic limit represented by an antisymmetrized two-centre wave function. The complex HI potential is defined in terms of the energy density from nuclear matter so that both volume elements in the finite and the infinite systems have the same nucleon and kinetic energy density. This method is applied to the ¹⁶O + ¹⁶O, ⁴⁰Ca + ¹⁶O, and ⁴⁰Ca + ⁴⁰Ca potentials. The calculated results are compared with phenomenological potentials. Though in principle our approach can generate an imaginary part for the HI potential, the magnitude is too small. Reasons and possible improvements of this point are discussed.     

Comparative analysis of the characteristics of the elastic scattering of protons by lithium isotopes 6, 7, 8, 9Li, performed using Glauber’s multiple diffraction scattering theory

Differential cross sections and vector analyzing powers are calculated for the elastic scattering of protons by lithium isotopes ⁶Li, ⁷Li, ⁸Li, and ⁹Li at energies of 60 and 200 MeV. The calculations are performed using Glauber??s multiple diffraction scattering theory in the two-particle (for ⁷Li) and three-particle (for ^6,8,9Li) models with realistic intercluster interaction potentials. An analysis of the relationship between the differential elastic scattering cross section and various wave functions, calculated using different interaction potentials, is presented for the ^{8, 9}Li isotopes.     

Nucleon elastic scattering from 40Ca between 11 and 48 MeV

Differential cross sections for the elastic scattering of neutrons from ⁴⁰Ca have been measured in the 19–26 MeV region. The neutron elastic scattering data, previous neutron measurements and additional proton elastic scattering data are analyzed using three different approaches to the optical model potential: Woods-Saxon parameterization, model independent analysis and microscopic calculations. The difference between the phenomenological neutron and proton real potentials is studied in terms of Coulomb effects, nuclear polarization and charge symmetry breaking in the nuclear mean field.     

Nuclear effects in deep inelastic scattering of charged-current neutrino off nuclear target

The nuclear effects in the neutrino–nucleus charged-current inelastic scattering process is studied by analyzing the CCFR and NuTeV data. The structure functions F₂(x,Q²) and xF₃(x,Q²) as well as differential cross sections are calculated by using CTEQ parton distribution functions and the EKRS and HKN nuclear parton distribution functions, and these are compared with the CCFR and NuTeV data. It is found that the corrections of the nuclear effect to the differential cross section for the charged-current antineutrino scattering on the nucleus are negligible, the EMC effect exists in the neutrino structure function F₂(x,Q²) in the large x region, the shadowing and anti-shadowing effect occur in the distribution functions of valence quarks in the small and medium x region, respectively. It is also found that shadowing effects on F₂(x,Q²) in the small x region in the neutrino–nucleus and the charged-lepton–nucleus deep inelastic scattering processes are different. It is clear that the neutrino–nucleus deep inelastic scattering data should further be employed in restricting the nuclear parton distributions. PACS 13.15.+g; 24.85.+p; 25.30.-c     

Quasimolecular nuclear optical potentials

A theory is presented to calculate potentials for the elastic nuclear heavy-ion scattering in a phenomenological way. The density properties of finite nuclei are derived with a schematic ansatz for the interaction energy between nuclear matter. The same interaction energy is applied to the calculation of the real part of the heavy-ion potential, which is of the quasimolecular type. The imaginary part is connected with the outflow time of nuclear matter out of compressed regions of overlapping nuclei. The resulting cross section for the elastic O¹⁶-O¹⁶ scattering reproduces the experiment up to 30 MeV quite well. An effective compression modulus of the S³² compound system can be deduced from the scattering experiment. It results to be about 200 MeV.     

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.     

Multi-step processes in high-energy elastic and inelastic nuclear scattering

Multi-step processes in elastic and inelastic nuclear scattering at intermediate and high energies are investigated using a formulation whereby a finite number of channels are explicitly treated while all the other channels are approximately accounted for through a “second-order potential matrix”. Within the framework of the eikonal approximation the problem reduces to a finite system of first-order coupled integro-differential equations with non-local potentials which depend on the two-body density matrix of the target nucleus. The relationship of the above formulation to the DWIA, the close-coupling method, and the Glauber multiple scattering model is examined. This approach is applied to the elastic and inelastic (2⁺, 4.43 MeV) scattering of 1 GeV nucleons by ¹²C. The corrections to the DWIA are sizeable, and the inelastic scattering appears to be very sensitive to the multi-step contributions and the nuclear structure.     

Folding model analysis of pion elastic and inelastic scattering from 6Li and 12C

π ^±-Nucleus scattering cross sections are calculated applying the Watanabe superposition model with a phenomenological Woods-Saxon potential. The phenomenological potential parameters are searched for π ^± scattering from ⁶Li and ¹²C to reproduce not only differential elastic cross sections but also inelastic and total and reaction cross sections at pion kinetic energies from 50 to 672 MeV. The optical potentials of ⁶Li and ¹²C are calculated in terms of the alpha particle and deuteron optical potentials. Inelastic scattering has been analyzed using the distorted waves from elastic-scattering data. The values of deformation lengths thus obtained compare very well with the ones reported earlier.     

η in the nuclear medium within a chiral unitary approach

The s-wave η self-energy in the nuclear medium is calculated in a chiral unitary approach. A coupled channel Bethe–Salpeter equation is solved to obtain the effective ηN interaction in the medium. The base model reproduces well the free space πN elastic and inelastic scattering at the ηN threshold or N^*(1535) region. The Pauli blocking on the nucleons, binding potentials for the baryons and self-energies of the mesons are incorporated, including the η self-energy in a self-consistent way. Our calculation predicts about −54−i29 MeV for the optical potential at normal nuclear matter for an η at threshold but also shows a strong energy dependence of the potential.     

Charged pion photoproduction from light nuclei

The photoproduction of 0–150-MeV charged pions from light nuclei is studied from a distorted wave impulse approximation (DWIA) approach. The final nuclear states are restricted to a finite set of isospin analogs of excited states of the target nucleus. The final state interactions of the pion with the residual nucleus are incorporated via optical potentials. The elementary photoproduction operator used is that of Blomqvist and Laget which is derived in a general reference frame. To gain insight into the predictive power of this DWIA approach, total and differential cross sections for π^± production from ⁶Li, ⁷Li, ¹⁰B, ¹²C, and ¹⁴N are calculated and compared with available data. It is found that, with a few exceptions, reasonable agreement is obtained between theory and experiment as long as the nuclear wave functions are constrained to fit other electromagnetic and weak processes and the optical potentials are constrained to fit pion-nucleus elastic scattering data. We conclude that, at this stage, using the Blomqvist-Laget operator in a DWIA calculation adequately describes the dynamics of charged pion photoproduction from complex nuclei. We illustrate how this reaction can be used to obtain information on the short range nature of the pion wave function and on nuclear wave functions. Shortcomings of and improvements on this calculation are also suggested.     

Isospin-dependent relativistic microscopic optical potential in the Dirac Brueckner-Hartree-Fock method

There is growing evidence to suggest that the binding energy of nucleon in nuclear matter comes from a cancellation between large Lorentz scalar and vector potentials[1,2]. The relativistic approach has been of a great success in describing not only the ground state properties of stable nuclei, but also those of exotic nuclei. In the relativistic frame, the spin-orbit coupling can be deduced automatically, which is usually given by hand in the non-relativistic approach. The relativistic method…