Exchange amplitudes and dispersion relations for electron-atom scattering

The analytic structure of the second Born approximation to the forward elastic exchange amplitude is analyzed for e^?+H scattering, and the importance of the interplay between bound and continuum intermediate state contributions is emphasized.     

Concentratable functionals and asymptotic relations for scattering amplitudes

Very wide classes of concentratable functionals are considered, i.e. classes where the notion of concentrating, which satisfies a certain six axioms, can be introduced, and where it is possible to formulate the microcausality (or the local-commutativity) principle as the requirement of concentration of functionals in the corresponding space-time region. Every such class of functionals is essentially wider than the class of tempered distributions and is defined on some analytic functions only. It is proved that the asymptotic smoothed partially-microcausal amplitude of an arbitrary reaction, under corresponding conditions imposed only in the physical region of changing arguments, satisfies all the asymptotic relations.     

Recursion relations and scattering amplitudes in the light-front formalism

The fragmentation functions and scattering amplitudes are investigated in the framework of light-front perturbation theory. It is demonstrated that, the factorization property of the fragmentation functions implies the recursion relations for the off-shell scattering amplitudes which are light-front analogs of the Berends–Giele relations. These recursion relations on the light-front can be solved exactly by induction and it is shown that the expressions for the off-shell light-front amplitudes are represented as a linear combinations of the on-shell amplitudes. By putting external particles on-shell we recover the scattering amplitudes previously derived in the literature.     

Invariant amplitudes for pion electroproduction

The invariant amplitudes for pion electroproduction on the nucleon are evaluated by dispersion relations at constant t with MAID as input for the imaginary parts of these amplitudes. In the threshold region these amplitudes are confronted with the predictions of several low-energy theorems derived in the soft-pion limit. In general agreement with chiral perturbation theory, the dispersive approach yields large corrections to these theorems because of the finite pion mass.     

Analyticity and dispersion relations in atomic scattering

We study the analyticity properties of forward electron-neutral atom scattering in a second quantized formalism. We derive a Low equation for these processes and deduce from it the location of direct and exchange bound state poles and the presence of both right- and left-hand cuts. We also examine the singularities produced by the exchange Born terms in a potential approximation and identify their physical origin. In a local theory, these Born term singularities are a result of the exchange of ionized atoms accompanied by a photon. Based on the singularity structure that we have obstained, we derive novel dispersion relations for forward electron-atom scattering. These equations contain additional terms not present in the “customary” form of dispersion relations for atomic scattering found in the literature. We comment on, and critically discuss, recent work done in this area. The possibility of anomalous thresholds is examined and they are seen to be irrelevant for these processes.     

High energy pion photoproduction amplitudes from fixed-t dispersion relations and duality

Contributions to the high energy imaginary parts of the charged and neutral pion photoproduction amplitudes from degenerate ? and A₂ exchanges and ω and B exchanges are parametrized similarly to the dual absorptive model. These contributions together with the imaginary parts of the amplitudes found at low energies from partial-wave analyses are then used to evaluate the high energy real parts of the photoproduction amplitudes from fixed-t dispersion relations. A fit is made to data on pion photoproduction at 3.4 and 16 GeV incident photon energies, for momentum transfers up to ?1(GeV/c)². It is shown that much of the data is reproduced both qualitatively and quantitatively by our model. The high energy imaginary parts of the photoproduction amplitudes given by the fit are shown to be in accord with their average low energy behaviour.     

A partial wave dispersion relation analysis of pion-nucleon scattering amplitudes

Partial wave dispersion relations have been evaluated, using various new πN partial wave solutions and our results for the ππN \(\bar N\) amplitudes. The Karlsruhe-Helsinki 80 and CMU-LBL-79 solution forS, P, D, F waves are well compatible with this constraint, which follows from the Mandelstam representation. The VPI 80 solution leads to serious discrepancies in some cases, for instance for the P11 wave.—In both, the KH 80 and CMU-LBL 79, solutions the higher partial waves are not yet satisfactory. They can be improved by adding constraints based on the information on the nearby part of the left hand cuts.—Properties of nucleon resonances are discussed in connection with our results for the “generalized potentials”.     

Reciprocity relations for reflected amplitudes

We derive general reciprocity relations that are applicable to a large class of one-dimensional stratified systems. These results reveal clearly the role of absorption and spatial symmetry in the nonreciprocity of reflection observed in a recent experiment by Armitage et al. [Phys. Rev. B 58, 15, 376 (1998)]. We also present examples of structures for which such nonreciprocal effects can be significant.     

An application of dispersion relations to Kaon-nucleon scattering

In this paper we have made predictions for the invariant KN and $\text{K}$N scattering amplitudes in the kinematical region q_lab < 15 GeV/c and 0 >; t > -0.7 (GeV/c)².We have performed a direct fit to medium and high-energy data using a parametrization where the imaginary part of the amplitudes for energies above the phase-shift region is identical with the imaginary part of a Regge-pole amplitude, and the real part of the amplitudes has been obtained from a dispersion relation.The s-channel helicity amplitudes are compared with their counterparts in pion-nucleon scattering and other reactions. Exact exchange degeneracy can not be verified.Also the real part of the amplitudes are compared with the real part of phase-shift solutions. There is a qualitative agreement between these two real parts even though they differ in detail.     

Coupling constants for several light nuclei from a dispersion analysis of nucleon and deuteron scattering amplitudes

A forward dispersion relation cannot be applied to charged particle scattering amplitudes unless the influence of the Coulomb interaction is explicitly considered. Earlier studies have shown how Coulomb effects can be taken into account when direct (s-channel or bound-state) poles are investigated. In this paper we extend the Coulomb modification to include I = 0 exchange (u-channel) processes as well. We then apply a forward dispersion relation to empirical d + α, p + d and n + d elastic scattering amplitudes which contain both direct and exchange poles with and without Coulomb effects. We obtain detailed and model-independent information on the following vertices: ⁶Li-α-d (S- and D-state) ⁴He-d-d, ³He-d-p, ³H-d-n and d-p-n. From the coupling constants we calculate the asymptotic normalization (spectroscopic factors) C²₁ of the corresponding cluster wave functions, which become: $\text{C}{}^2{}_0\text{(}{}^6\text{Li}\text{, α}\text{d}\text{) = 4.62 ± 0.23}$, $\text{C}{}^2{}_2\text{(}{}^6\text{Li}\text{, α}\text{d}\text{) = (1 ± 6) × 10}{}^{\mathrm{?4}}$, C²₀(α, dd) < 2, $\text{C}{}^2{}_0\text{(}{}^3\text{He, dp}\text{) = 3.5 ± 0.4}$, $\text{C}{}^2{}_0\text{(}{}^3\text{H, dn}\text{) = 2.6 ± 0.3}\text{and}\text{C}{}^2{}_0\text{(}\text{d, np}\text{) = 1.66 ± 0.1}$.     

Renormalization group and relations between scattering amplitudes in a theory with different mass scales

In the Yukawa model with two different mass scales, the renormalization group equation is used to obtain relations between scattering amplitudes at low energies. By considering fermion-fermion scattering as an example, a basic one-loop renormalization group relation is derived which gives the possibility to reduce the problem to the scattering of light particles in the “external field” substituting a heavy virtual state. Applications of the results to problems of searches for new physics beyond the Standard Model are discussed.     

Glauber exchange amplitudes for electron-helium scattering

An exact closed form expression is obtained for the Glauber-Bonham-Ochkur exchange amplitudes for the electron helium scattering. The results thus obtained are compared with the results from Ochkur approximation and are used further for obtaining closed form expressions for the differential and total exchange cross-sections for the elastic scattering of electrons from the ground state of helium atom.     

Universal amplitudes for critical surface scattering

Scattering of x-rays or neutrons at grazing angles is studied for semi-infinite systems which exhibit a second order phase-transition in the bulk. We present the results of a calculation to order ² (ind=4- dimensions) of the amplitudes of leading and next-to-leading terms in the angular dependence and in the temperatur dependence (forT>T _c) of the scattering cross-section. The results are discussed for the three-dimensional Ising case.This work was supported by Bundesministerium für Forschung und Technologie     

Application of modulus-phase dispersion relations to πN backward scattering

We derive modulus-phase dispersion relations for the πN backward scattering amplitudes. The convenience of these dispersion relations in treating πN backward scattering is pointed out. A numerical evaluation of the π^?p backward scattering phase is also given.     

Analytic proton-nucleus scattering amplitudes

Analytic expressions for the elastic nucleon-nucleus amplitudes F(q) and G(q) are derived. They are based on analytic approximations of the nuclear profile functions in the Glauber formulation. Our amplitudes are sums of terms with a familiar structure, black-sphere Bessel functions multiplied by form factors accounting for the diffuseness of the nuclear surface. Their accuracy is tested with the Woods-Saxon density and found to be excellent for momentum transfers q? 5fm^?1.