Momentum-space optical model for K+-nucleus scattering

The momentum-space optical model of K⁺-nucleus scattering is analyzed and comparison with other conventional models is shown. The model is based on the multiple scattering formalism in which the optimal factorization approximation is used. Off-energy-shell extension of the elementary K⁺-nucleon amplitude is neglected which reduces non localities in the optical potential. Predictions of the model are sensitive to the definition of the K⁺-nucleon energy (energy shifts) but they are independent (1–2%) of a particular form of the covariant K⁺-nucleus scattering equation (relativistic Lippmann-Schwinger, Gross, Erkelenz-Holinde). The Coulomb distortion in the total cross section is important for²⁸Si and⁴⁰Ca at low momenta (≈10%). Off-energy-shell effects in the optical potential are discussed too. Results for the total and reaction cross sections are systematically below the data. The reaction cross sections are in a larger disagreement with the data than the total cross sections. This work was supported by grants ASCR A1048703 (P. Bydžovsky) and GACR 202/96/1566 (M. Sotona).     

Momentum-space calculations for three-nucleon scattering including a three-nucleon force

The formalism to include a three-nucleon force into three-nucleon continuum calculations is presented. First numerical results, obtained in momentum space, are shown. The two- and three-nucleon forces have been restricted to act only in the¹ S ₀ and³ S ₁-³ D ₁ partial-wave states. As two-nucleon interaction the Bonn-B potential and as three-nucleon interaction the Tucson-Melbourne two-pion exchange model has been used.     

Experiments on four-nucleon reactions

The status of experimental evidence on four-nucleon reactions in the range from very low to medium energies (50 MeV) is reviewed. The recent progress of microscopic theories as well as computer capabilities, the renewed interest in astrophysical and the new fusion-energy aspects of the four-nucleon reactions, the emphasis on improved measurements of polarization observables especially at very low energies and on new types of studies such as break-up reactions with polarized projectiles prompt such a survey. The aim is to stimulate interest in the four-nucleon system. It is expected that the four-nucleon system will undergo a development similar to the three-nucleon system as a special testing ground for nuclear forces.     

Momentum-space Monte Carlo

Using the quenched, reduced form of large-N field theories, we show that it is possible to directly measure momentum-space Green functions, via Monte Carlo, without going through the intermediate step of measurement in position space plus Fourier transformation. This promises to be useful tool for investigating the infrared structure of planar field theories. As an application (and test) of the method, we compute mass-gaps in the quenched U(N) × U(N) lattice chiral model, in D = 1 and 2 dimensions.     

Nonrelativistic description of nucleon-nucleus scattering

Within the three-dimensional semiclassical approximation, an analytic expression is obtained for the amplitude of proton-nucleus scattering at intermediate energies of incident protons. The method for deriving this amplitude is based on the use of the high-energy approximation with distorted waves. In view of the short-range character of proton-nucleon interaction, the process of proton-nucleus scattering is represented as a series of single scattering events occurring on each individual nucleon. With the aid of the proposed mathematical formalism, a recursion relation is derived that makes it possible to express the nuclear form factor obtained within the distorted-wave method in terms of the sum of an infinite Born series. Parameters that characterize the distributions of protons and neutrons in the spherical nuclei ⁴⁰Ca, ⁴⁸Ca, ⁹⁰Zr, and ²⁰⁸Pb and which include the width of the surface layer of nucleons and the root-meansquare radii of the proton-, neutron-, and nucleon-density distributions are determined from an analysis of the measured cross sections for the elastic scattering of 1-GeV protons, a modified Fermi function being employed for the nucleon-density distribution.     

Eikonal description of quantal scattering

Elastic and inelastic quantal scattering is described by a theory in which the contribution of a range of impact parameters to the scattering amplitude is determined by a phase integral (“eikonal”) which is integrated along a real curved “quantal” trajectory. This amplitude reduces to the Glauber expression in the high-energy, forward-angle limit, and to the usual semiclassical amplitude in the classical limit. The formulation can be applied to the study of heavy-ion scattering. The quantal trajectories are investigated analytically for the case of Coulomb scattering. A numerical analysis of elastic ¹⁶O¹⁶O scattering is carried out. The results show appreciable improvement as compared with the Glauber approximation.     

Time-dependent variational description of αα scattering

The time-dependent variational principle is applied to the simple but quite realistic situation of αα scattering. The effects of antisymmetrization are included and we show that they lead to a change in the structure of the phase space of relative motion. The main new feature is the appearance of forbidden regions in the phase space which have, in the quantum treatment, a close connection with states excluded by the Pauli principle. The elastic phase shifts are evaluated semiclassically in the distorted phase space and compared to a quantum calculation by the resonating group method.     

Isobar-hole description of pion-nucleus inelastic scattering

The Δ−h formalism is applied to a systematic study of π-nucleus inelastic scattering. In the formal part of this work, the following basic excitation mechanisms are identified in π-nucleus inelastic scattering: coupling to the transition density, coupling to convection and magnetization currents and coupling to the spin-flux tensor. The properties of these modes of coupling are discussed, in particular implications of certain symmetries of the corresponding transition amplitudes. As an application, calculations are presented for various excitations in π−¹²C scattering in the resonance region. In the comparison with the data the interplay is emphasized between the nuclear structure aspects, on the one hand, and the reaction mechanisms contained in the Δ−h formalism, on the other hand.     

Quantal description of inelastic heavy-ion scattering

A model Schrödinger equation for scattering with energy loss is discussed. The equation is linear and is closely related to the coupled-channels approach to elastic and inelastic scattering. A possible parametrization of the model for applications to heavy-ion scattering is considered.     

N-body integral equations and four-nucleon calculations

N-body extension of the Faddeev three-body theory is formulated in a novel approach. Comparison with other formulations is performed and first numerical results for the⁴He nucleus are briefly discussed.     

On the Regge-pole description of nucleus-nucleus scattering

The properties of the Regge poles of theS-matrix for scattering of strongly-absorbed nuclear particles are considered. Simple formulae are obtained for describing the Regge trajectories in terms of the nuclear radius, the quasi stationary levels in the combined nuclear-Coulomb-potential and the widths of these levels. The predictions of these formulae are compared with the Regge trajectories obtained previously, for a Woods-Saxon potential, and with those required to fit¹⁶O-¹²C backward scattering.     

Momentum-space calculation of electron-CO elastic collision

We report a momentum-space study on low-energy electron-CO collisions.Elastic differential cross sections(DCS) are obtained using a static-exchange-optical(SEO) model for the incident energies of 2,3,5,and 10 eV.Polarization effect of higher reaction channels,including the ionization continuum,on the elastic collision is represented by an ab initio equivalent-local optical potential.The cross sections are compared with experimental measurements and other theoretical results.     

Closed-form quantal description of inelastic heavy ion scattering

The amplitude for inelastic heavy ion scattering, given by the distorted-wave theory for excitation of low-lying collective states, is evaluated in closed form. Use is made of the Austern-Blair relation and of other approximations appropriate for strongly absorptive interaction to express the inelastic partial-wave amplitude entirely in terms of the elastic S-matrix elements in the initial and final channels. The resulting formulae display explicitly the various contributions to the transition amplitude, whose superposition gives rise to the variety of interference patterns observable in the angular distributions and excitation functions of inelastic heavy ion scattering. It is shown that, as for elastic scattering, the dominant mechanism in inelastic heavy ion collisions near and above the Coulomb barrier is diffractive scattering of Fresnel type.     

Impact parameter description of multiparticle and elastic scattering

Impact parameter variables are defined for a multiparticle production process. The equation of unitarity for elastic scattering is written at high energy in terms of these variables. The overall impact parameter can be expressed in terms of the impact parameters of all the produced particles. The unitarity equation becomes an “optical theorem” at each impact parameter — diffractive scattering is given by beam depletion. These features allow this technique to give a much clearer interpretation of unitarity in any model than has therefore been possible. This technique can be used to study existing models, and to suggest new ones.