An approximate three-body theory of deuteron stripping

A treatment of deuteron stripping is developed in which the three-body effects associated with deuteron break-up in the nuclear field are included explicitly. The essence of the method is the choice of a convenient discrete set of n-p eigenfunctions as a representation of the three-body continuum effects. This approach leads to a distorted wave stripping matrix element similar to that of the DWBA, except that the elastic deuteron wave is replaced by a three-body wave function given as the solution of a set of coupled two-body Schrödinger equations. The adiabatic theory of Johnson and Soper appears as the solution in a suitable first approximation. This new formalism should prove useful in the evaluation of corrections to three-body models of the deuteron-nucleus system, in particular those models in which the nucleon-target interaction is represented by a complex local optical potential.     

Spin-orbit effects in the optical model analysis of deuteron and proton elastic scattering

Spin-orbit effects on the differential cross-sections for the deuteron and proton elastic scattering are considered. Relations between the parameters of the optical potentials of the deuteron and its constituent nucleons are discussed. The variation of the deuteron and proton potential depths with energy is also considered.     

The optical model for the elastic deuteron scattering

An optical model for the elastic scattering of deuterons by nuclei is derived from first principles. The influence of the Pauli principle is investigated in nuclear matter and found to be small. Surface effects due to the finite size of the deuteron are studied in terms of a perturbation expansion. The first order term agrees well with the 100 MeVfit of the real potential depth to the experimental data, the second order term is shown to be two orders of magnitude smaller.     

Low-energy elastic scattemng of pions by the deuteron

The problem of the elastic scattering of pions by a deuteron is considered using the separable representation of the two-body t-matrix. The Faddeev equations are reduced to a set of one-dimensional integral equations by separating the angular variables. The dependence of the π-d scattering length on the form of two-body interaction and on the values of the π-N scattering lengths is studied in the case of a one-term nonlocal potential with separable variables. The π-d scattering length proves to be practically independent of the two-body interaction form, and is essentially dependent on the values of the π-N scattering lengths.     

Proton-deuteron elastic scattering at medium energy and relativistic models of multiple scattering

We have constructed a simple model of proton-deutron elastic scattering which can incorporate either a two-dimensional Pauli matrix or four-dimensional Dirac matrix parametrization of the nucleon-nucleon scattering amplitude. The model includes the S-and D-wave components of the deuteron wave function but neglects interactions with the spins of the target nucleons and is intended to provide an estimate of the magnitude of the differences between relativistic and non-relativistic treatments. We find these differences to be quite large and attribute them primarily to the intermediate negative energy states which are present only in the relativistic calculation.     

Pauli Correlation Effect for the Elastic Scattering of Protons by Different Nuclei at 800 MeV

The angular distributions of the elastic scattering of protons at an energy of 800 MeV by ¹⁶O and ²⁰Ne nuclei are described in terms of the optical model scattering theory. Single folding model is applied to calculate the optical potential taking the effective nucleon-nucleon interaction to be in two forms. One form includes the zero-range pseudo-potential term and the other includes a two-body Pauli correlation function. Analytical expressions for the real part of the optical potential are obtained for both forms. The imaginary part of the optical potential is taken to be of the Woods-Saxon's shape. It is found that introducing the Pauli correlation function improves the agreement with the experimental data for the elastic scattering differential cross-sections of protons with the target nuclei ¹⁶O and ²⁰Ne.     

Pauli exchange effects in the elastic scattering of O + O

The real optical potential for ¹⁶O+¹⁶O system is calculated within a generalized version of the double-folding model with the Pauli knock-on exchange effects between the projectile nucleons and the target nucleons taken into account from first principle. The elastic scattering data at E_lab=350 MeV supplemented by the new measurement at larger angles seem to be the first case in heavy-ion scattering where one can test the reliability of different theoretical heavy-ion optical potentials. Predictions are made for the elastic scattering of ¹⁶O+¹⁶O at laboratory energies of 240–480 MeV to illustrare the energy dependence of the rainbow structure which has been clearly observed in experiment at 350 MeV.     

On the validity of dwba for deuteron stripping: (I). The Mitra three-body model

Previous work showing that there exists an exact formulation of the DWBA for stripping in the S-wave, separable potential, three-body model of Mitra is discussed and extended. The one-body equation obeyed by the c.m. wave function used in the reformulated DWBA is derived and compared with the equation obeyed by the wave function used in the standard formulation of DWBA, viz., the deuteron elastic scattering wave function. Results obtained by other workers on application of three-body methods to direct reactions are discussed in light of the fact that an exact DWBA exists for the separable potential model.     

The origin of the spin-dependence of low energy deuteron scattering

The spin-dependence of the interaction between a deuteron and a heavy target nucleus at low bombarding energies, resulting from coupling between the deuteron elastic and (d, p) transfer reaction channels, is studied quantitatively. By use of approximate two-step distorted wave Born approximation calculations, deuteron D-state effects are easily included. In the case of a ²⁰⁸Pb target, transfer channel coupling and not the folding model spin-dependent interactions, are shown to be primarily responsible for the experimentally observed spin-dependence of the deuteron elastic scattering at sub-Coulomb barrier energies.     

Excitation of states of medium-mass nuclei in the region of giant resonances in inelastic deuteron scattering

Results are presented that were obtained by measuring a continuum in the inelastic scattering of 37-MeV deuterons on ¹²C, ⁴⁸Ti, and ^58,64Ni nuclei in the angular range 16° ≤ θ ≤ 61°. Broad excitation maxima are found for deuteron scattering angles in the range θ ≤ 21°. The region of a broad maximum includes giant resonances of target nuclei, whose levels are excited quite readily at E _d = 37 MeV. Summation of the inelastic-scattering cross sections over all final states of the excited| nucleus and the use of completeness of the wave functions for these states make it possible to express the total cross section for inelastic (incoherent) deuteron scattering only in terms of the wave functions for the ground state of the target nucleus. The corresponding quasielastic-scattering amplitude is taken in the diffraction approximation. Nucleon correlations in the target nucleus are disregarded. Upon disregarding a small contribution of multiple quasielastic scattering at small scattering angles, the cross section for incoherent deuteron scattering is represented approximately as the product of known factors—the square of the absolute value of the amplitude for diffractive quasielastic scattering and the effective number of target nucleons scattering deuterons. The results of these calculations agree qualitatively with experimental data.     

Polarization effects in elastic electron deuteron scattering

The vector and tensor polarization of the deuteron after scattering and the dependence of the cross section on the polarization before scattering are given for elastic electron deuteron scattering treating the deuteron as a spin 1 elementary particle characterized by three electromagnetic formfactors and describing the interaction by the first Born approximation. By using polarization measurements a separation of the charge and quadrupole formfactors may be accomplished, and thus the assumptions may be tested, which are necessary for the extraction of the isoscalar nucleon formfactors from the deuteron formfactors.     

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.     

Deformed tensor interactions in deuteron elastic and inelastic scattering

The various forms of tensor potentials present in deuteron elastic and inelastic scattering on a deformed target nucleus are derived using a folding model for the deuteron-nucleus interaction. Approximate expressions for the radial dependence of the deformed tensor interactions parametrized with the derivatives of Woods-Saxon potentials are obtained and discussed for the case of a rotational nucleus.     

The folding deuteron optical model potentials

In this paper we construct a kind of deuteron optical potential with the folding model. For the nucleon optical potential, we choose two kinds of forms: the phenomenological global nucleon optical potential and the microscopic nucleon optical potential based on the nuclear-matter approach. We use our folding and global deuteron optical potential to calculate the reaction cross-sections, elastic scattering angular distributions, and the values for 64 target nuclei.     

Relativistic effects and spin observables in deuteron electrodisintegration

The influence of relativistic effects in deuteron electrodisintegration, in particular their manifestation in spin observables, is discussed. We have used a simple phenomenological approach by adding the lowest-order relativistic corrections to the nonrelativistic one-body current and including the kinematic wave-function boost. Furthermore, final-state interaction, meson-exchange currents and isobar configurations are included in order to study kinematic regions off the quasi-free case. Sizeable relativistic effects in many observables are found even at low energies.Supported by the Deutsche Forschungsgemeinschaft (SFB 201)     

Three-body model of deuteron breakup and stripping

For a three-body model Hamiltonian, the scattering eigenfunction that corresponds to an incident deuteron is expanded in terms of eigenfunctions of the neutron-proton relative Hamiltonian, as suggested by Johnson and Soper. In this expansion, breakup is represented by an integral over the continuum of neutron-proton scattering states. Only states of zero relative angular momentum are included; the validity and advantages of this approximation are discussed. The continuum is divided into five discrete channels, whose coupling to each other and to the deuteron channel is treated by solving coupled differential equations with appropriate boundary conditions. It is found necessary to use a simple WKB method to take account of the long-range coupling among breakup channels; this method introduces potential matrices W and S that describe local and derivative coupling of the channels. The reaction of breakup on the elastic channel is neglected.The properties of W and S and the breakup wavefunction are examined for the case of 22.9 MeV deuterons incident on a target of mass number A ≈ 40. The Coulomb interaction is ignored, and a local Gaussian shape is used for both the real and imaginary parts of the nucleon-nucleus optical potential.It is found that a rather broad spectrum of n-p continuum states is excited, especially for low center-of-mass angular momentum. This result weakens the justification for the Johnson-Soper adiabatic theory, which emphasizes breakup into states of low relative energy.The breakup part of the wavefunction at zero n-p separation is comparable with the elastic part, but is important only over a surprisingly short range in the center-of-mass coordinate, with the result that breakup cross sections are quite small. Nevertheless, breakup produces major modifications of (d, p) cross sections. These modifications can to some extent be simulated by the Johnson-Soper method. The breakup wavefunctions show several interesting effects in their dependence on angular momentum and radius.