Dispersion relations and low-energy elastic scattering of charged particles from nuclei: (II). Application to N-4He scattering

A “Coulomb-modified” dispersion relation is applied to low-energy p-⁴He forward elastic scattering. To check the validity of the modification, the results are compared with those deduced from n-⁴He elastic scattering. Completely analogous information is obtained for the two processes. The exchange of three bound nucleons is found to contribute strongly to N-⁴He forward scattering. The corresponding ⁴He-³H-p and ⁴He-³He-n coupling constants are evaluated as R_p = 3.8±0.3 and R_n = 3.0±0.3, respectively. These constants are related to the strength of the asymptotic wave function of nucleons in ⁴He and thus to the tail of the nucleon distribution. A comparison of R_p with the empirical proton distribution in ⁴He as deduced from e-⁴He elastic scattering shows excellent agreement. From R_p and R_n the effective ranges of the singlet ³H-p and ³He-n interactions in the ground state of ⁴He are determined to be equal, in accordance with charge symmetry, and to have a value of r_eff = 1.072±0.006 fm.     

Forward dispersion relations and low-energy elastic scattering of charged particles from nuclei

A forward dispersion relation for charged particle scattering from nuclei is deduced. Inclusion of the Coulomb interaction leads to a simple modification of the formalism for uncharged projectiles. The modified forward dispersion relation is applied to p- scattering below 50 MeV.     

Isospin breaking in low-energy charged pion–kaon elastic scattering

We use chiral perturbation theory to evaluate the scattering amplitude for the process at leading and next-to-leading orders in the chiral counting and in the presence of isospin breaking effects. We also discuss the influence of the latter on the combination of the -wave scattering lengths which is relevant for the 2S–2P energy level shift of atoms. Received: 19 November 2001 / Revised version: 21 December 2001 / Published online: 5 April 2002     

Dispersion relations for elastic n-d scattering in the Amado model

The formulation of rigorous, dispersion relations for on-shell three-body amplitudes in a separable model is reported. The results of approximate $\text{N}\text{D}$ calculations of s-wave n-d elastic scattering are compared with exact, numerical solutions of the Faddeev equations.     

Dispersion relations of surface phonons from atomic scattering

We show the existence of a spatial forbidden zone for one-phonon atomic scattering by surfaces. In case of scattering by surface modes, this region is bounded by sharp observable maxima of the scattering intensity, whose angular locations depend only on the dispersion relation of the modes involved. A method for obtaining the dispersion relation of surface modes needing no measurement of scattering energies then follows. The method is applied to the He-NaF system.     

Diffraction scattering of charged particles

It is shown that, contrary to popular belief, diffraction scattering in nuclear and particle physics is not always of Fraunhofer type. By establishing a simple physical connection between scattering in a Coulomb field and Fresnel diffraction we show that diffractive collisions of heavy charged particles are predominantly of Fresnel type. We derive quantitative criteria for Fraunhofer and Fresnel scattering which lead to a classification of all scattering processes by means of a “diffraction diagram.” This enables us to make specific predictions about the gross structure of angular distributions for any experimental conditions.     

Theory of low-energy ππ scattering

A four-parameter family of solutions to the ππ partial-wave dispersion relations is obtained using the inverse amplitude method. Choosing the parameters consistent with phenomenological values and so as to maximize agreement with rigorous sum rules and inequalities leads to a firm prediction of the phase shifts for S and P wave scattering and for the amplitudes below threshold. Neglecting inelasticity, the I = 0S-wave resonates near $\text{s}\text{= 540}\text{MeV}$, the I = 2 S-wave falls to about ?12° near 1 GeV, and the P-wave is ?-dominated. The S-waves have subthreshold zeroes consistent with the Adler condition. Inelastic effects are estimated and found to be small below the rho meson mass.     

Configuration mixing and elastic magnetic electron scattering from nuclei

The role of configuration mixing in the analysis of recent elastic magnetic electron scattering experiments on ⁴⁹Ti, ⁵⁹Co, ⁸⁷Sr and ⁹³Nb is examined. In particular the dependence of the rms radius of the valence nucleon extracted from such analyses on the detailed nuclear configurations used is studied. In addition, the effects of meson-exchange currents together with configuration mixing are discussed. It is found that configuration mixing does play a significant role and that high-precision studies of elastic magnetic electron scattering should proceed beyond the framework of the extreme single-particle model.     

Construction of a unitary analytic scattering amplitude (I). Scalar particles

By imposing cos θ analyticity, we extend earlier investigations into the problem of constructing a unitary scattering amplitude from experimental measurements. The new approach is superior to earlier work, inasmuch as (a) the partial waves fall off exponentially, (b) we can handle cross sections with zeros, (c) we have a convergent Newton-Kantorovich interaction even when the fixed-point theorems do not apply, (d) we can study bifurcation points, (e) in the inelastic region, we find that analyticity does not remove the continuum ambiguity, (f) for quasi-elastic reactions (e.g. photoproduction) we resolve the Watson ambiguity for the phase shifts. We work at fixed energy, and throughout this first paper we neglect spin and isospin.     

Large-angle scattering of heavy ions: (I). General structure of elastic cross section

Closed-form expressions are derived for the differential cross section of elastic heavy-ion scattering at large angles. The derivation is based on the general form of the elastic partial-wave S-matrix in real l-space. By a generalization of analytic techniques developed in earlier work, it is shown that the large-angle scattering cross section has a universal structure involving combinations of Bessel functions and the Fourier transforms of the rapidly varying parts of the S-matrix, irrespective of their dynamical origin. Anomalous large-angle scattering is attributed to deviations of the S-matrix from its “normal strong-absorption profile”, and general conditions for backward-angle enhancement are given. Our model-independent formulation provides the framework for an “inductive” method of analyzing experimental angular distributions and excitation functions aimed at identifying, as uniquely as possible, the dynamical mechanisms that operate in large-angle heavy-ion scattering. Extensions of the formalism to inelastic scattering and transfer reactions, and applications of the analytic method, will be described in subsequent papers.     

Microscopic description of low-energy neutron scattering by nuclei

The Bloch and Gillet shell-model formalism extended to continuum states is applied to lowenergy neutron scattering by nuclei. It is shown that complete antisymmetrization leads in the r-representation to corrective terms which yield important corrections to the scattering lengths. Calculations are performed within a model restricted configuration space for the target nuclei ¹²C, ¹³C, ¹⁶O, ¹⁷O and ⁴⁰Ca. We predict values for the spin-dependent scattering amplitude for ¹³C and ¹⁷O. The antisymmetrization problem in the case of a large configuration mixing is studied for the ¹⁹F target nucleus. The resonant effects of the compound nucleus are then very important and the results become very sensitive to the configuration space and the interaction parameters.     

Nucleon-nucleon dynamics at medium energies: (I). Unitary model for elastic and inelastic scattering

A framework is presented for a unified theory of elastic nucleon-nucleon scattering and single-pion production at medium energies. The model is relativistic, unitary, and takes into account all spin complications. In the simplest version of the theory the driving mechanism is one-pion exchange but the model can be extended to include short-range forces. The resulting set of coupled linear integral equations have the structure of three-body equations and can be solved exactly. The method of solution is discussed.     

Dispersive treatment of low-energy pion-nucleus forward elastic scattering

The amplitudes for pion-nucleus forward elastic scattering are studied by means of dispersion relations, with emphasis on the low-energy and unphysical regions. The importance of the threshold behaviour of inelastic pion scattering is pointed out, and effective coupling constants, a news-wave parameter and the real part of thep-wave scattering length are determined.     

Determination of adsorbate orientation from symmetry rules in low-energy elastic electron scattering

In this Letter we describe a particular elastic-scattering experiment which is simple to perform and which establishes a connection between the scattering pattern and the orientation of a molecule adsorbed on a solid surface. This approach is illustrated by examining the cases of CO and C₂H₄.     

Theory of the scattering of pions from nuclei

A nonrelativistic quantum field theoretic formulation of pion-nucleus scattering is presented. A nonrelativistic boson-complex-target Low equation is developed, in which the coupling between the incident boson and target constituent particles is completely general. This development is then particularized to the case where the bosons are pions and the target is a nucleus of A nucleons. Special detailed attention is paid to the case where the pion-nucleon coupling is linear. The pion-nucleus Low equation is decomposed into a finite series of A terms, referred to as a spectator expansion, of which the first term involves one active particle and (A-1) spectators and the higher terms involve an increasingly larger number of active target particles. Within the framework of the nonrelativistic pion-nucleus Low equation, a formal definition of the pion-nucleus optical potential is also given.     

Parity non-conservation in low energy scattering of nucleons by light nuclei: (I). Theoretical framework

The low energy scattering of nucleons by ²H, ³He and ⁴He are analyzed for parity non-conserving effects. The asymmetry in the total cross section of longitudinally polarized projectiles is formulated in terms of the optical theorem and a distorted wave Born approximation. For two nucleons at low energies it is only necessary to consider l = 0 to l = 1 matrix elements of the weak nucleon-nucleon potential. The asymmetries in the scattering from nuclear targets are related to the parameters of an effective weak nucleon-nucleon potential, so that they may be used to help differentiate between various proposed theoretical potentials.