The scattering amplitude for four dual fermions

The amplitude for the scattering of four dual fermions is written down and evaluated in terms of three complicated functions. One of these is then expressed in terms of the other two. The s-channel spectrum is that of the Neveu-Schwarz model, but it is not possible at present to describe the t-channel spectrum. The spinor structure of the amplitude is also discussed.     

On the inverse-scattering solutions for the off-shell πN amplitude

The inverse-scattering problem for separable interactions in the presence of inelasticity has no unique solution. Additional assumptions are needed to make the problem soluble. The formalisms of Nakano and of Coronis and Landau are compared and the form factors are evaluated numerically.     

Approximation of off-shell scattering operators for non-lorentzian line shape calculations

A previously derived approximation for the matrix elements of the Fano relaxation operator m(ω), which gives rise to non-Lorentzian line wings, is examined. This approximation is expressed in terms of an off-the-energy shell scattering operator. Calculation of this operator by a second-order Born expansion is unsuitable because this procedure limits the radiation frequency dependence to the same order. The main part of this paper is devoted to expressing the off-shell scattering operator in the time-ordered formalism. In this form, a scattering operator approximation suggested by Dillonet al.⁽⁶⁾ can be applied which is not restrictive to the frequency dependence.     

The QCD scattering amplitude from area behaved Wilson loops

We explicitly construct the dominant saddle-point trajectory in the sum-over-path representation of meson scattering amplitudes in large N QCD for area-behaved Wilson loops and show that it dominates in the Regge regime. The graphic representation of the leading trajectory is very similar to the diagrams widely used to illustrate meson scattering.     

The pion-nucleon forward scattering amplitude

The pion-nucleon forward scattering amplitude has been calculated from new data of the total cross sections, using several assumptions on the energy dependence above 20 GeV. The results are presented as complex diagrams of the forward amplitude, which are of interest for the discussion of the nucleonic resonances and the non-resonant background scattering. In addition the predictions for the elastic forward cross sections are given as well as the contributions of the real parts to this quantity. A comparison with the new Saclay data of the charge exchange forward cross section leads to the estimate αρ≈0.6, if a Regge behaviour is assumed above 20 GeV. There are indications in favour of a new\(T = \tfrac{1}{2}\) resonance at the total c.m. energyW≈2.8 GeV.     

Generator coordinate amplitude for scattering

In the generator coordinate method for scattering the proper boundary condition is accomplished by requiring the GC amplitude to satisfy an integral equation of the first kind. Attempts to solve this problem are first reviewed and then an improved approximation is proposed which is applicable to a wider class of scattering problems in addition to the Coulomb scattering.A better approximation is obtained in the asymptotic region, where the generator coordinate, i.e., the distance between two shell-model wells of the fragments, is larger than the touching distance of the colliding nuclei, by deriving partial differential equations of first order for the terms of an asymptotic series in $\text{1}\text{E}$, where E is the scattering energy.Extracting the information on the GC amplitude for small values of the generator parameter from the integral equation of the first kind is an ill-posed problem. It is shown that the method of statistical regularization offers a powerful and controllable procedure to uncover the GC amplitude. The unknown GC amplitude is treated as a random function with an a priori distribution of probability which is based on the assumption that the amplitude is bounded and that the errors in the input are random with zero expectation value. A useful procedure is found for fixing parameters of the a priori distribution. The solution for small values of the GC parameter is expressed in the form of a Dini series.The method is applied to the calculation of the GC amplitude for scattering of two α-particles at 15 MeV c.m. energy. The measure of the accuracy is the difference between the input wave function of relative motion and the result of folding of the GC amplitude with the kernel of the integral equation. The prescribed accuracy is reached with this method on a much larger interval than with any previously proposed method.     

The off-shell electromagnetic T-matrix: momentum-dependent scattering from spherical inclusions with both dielectric and magnetic contrasts

The momentum- and frequency-dependent T-matrix operator for the scattering of electromagnetic waves by a dielectric/conducting and para- or diamagnetic sphere is derived as a Mie-type series, and presented in a compact form emphasizing various symmetry properties, notably the unitarity identity. This result extends to magnetic properties one previously obtained for purely dielectric contrasts by other authors. Several situations useful to spatially-dispersive effective-medium approximations to one-body order are examined. Partial summation of the Mie series is achieved in the case of elastic scattering.     

Variable amplitude equations for one-dimensional scattering

Nonlinear first-order equations, similar to Calogero's equations, are derived for the forward and backward one-dimensional scattering amplitudes. In particular, the even potential case yields two uncoupled equations for the even and odd parity phase shifts. The present approach provides a fast and accurate means for the numerical solution of one-dimensional scattering problems. It also has many analytic merits, some of which are discussed. The connection between one-dimensional and three-dimensional high-energy scattering is reviewed. It is demonstrated that in the one-dimensional case, a slightly modified WKB wavefunction provides an excellent approximation to the exact wavefunction in the shortwave limit. In this limit, additivity of phase shifts for nonoverlapping static potentials is satisfied.     

In-medium isovector piN amplitude from low-energy pion scattering

Differential cross sections for elastic scattering of 21.5 MeV positive and negative pions by Si, Ca, Ni, and Zr have been measured as part of a study of the pion-nucleus potential across the threshold. The "anomalous" repulsion in the s-wave term was observed, as is the case with pionic atoms. The extra repulsion can be accounted for by a chiral-motivated model where the pion decay constant is modified in the medium. Unlike in pionic atoms, the anomaly cannot be removed by merely introducing an empirical on-shell energy dependence.     

Calculation of the scattering amplitude from discrete eigenvalues

We show that the scattering amplitude for a target with spherical symmetry can be directly calculated from the discrete eigenvalues of the corresponding stationary wave equation solved under an absorbing boundary condition, and thus uncover a direct connection between the scattering amplitude and the wave number spectrum. As an illustration, we apply this approach to the scattering of an electromagnetic wave by an array of dielectric slabs and find the transmission coefficient of the array to be completely determined by the spacing between adjacent eigenvalues.     

The scattering amplitude for a newly found exactly solvable potential

The scattering amplitude for a recently discovered exactly solvable shape invariant potential, which is isospectral to the generalized Pöschl–Teller potential, is calculated explicitly by considering the asymptotic behavior of the X₁$X_1$ Jacobi exceptional polynomials associated with this system.     

A Veneziano amplitude for four spinning pions

A Veneziano formula for four spinning particles, previously obtained by factorization of many point functions, is modified in order to kill the spin 0 particles on the leading trajectories. The formula obtained may now refer to particles on the pion trajectory, and we verify that it has Adler zeros when any one of the particles is spinless and soft.     

Semiclassical functional integrals for self-dual gauge fields

The semiclassical approximation to the functional integral for four-dimensional Euclidean gauge theories is discussed in detail for general stationary points of the action. It is shown how to take the limit from a compact space to flat space, and the zero modes corresponding to global gauge transformations are carefully discussed. The results are specialised to general self-dual multi-instanton gauge fields given by the general construction of Atiyah et al. It is shown how the normalization matrix of the zero modes can be determined and the complete expression for the functional measure is given for the two instanton case. This is shown to factorise for well-separated instantons. Some technical matters are discussed in an appendix and a resume of results for multi-instanton functional determinants is included.     

Simplified expressions of the T-matrix integrals for electromagnetic scattering

The extended boundary condition method, also called the null-field method, provides a semianalytic solution to the problem of electromagnetic scattering by a particle by constructing a transition matrix (T-matrix) that links the scattered field to the incident field. This approach requires the computation of specific integrals over the particle surface, which are typically evaluated numerically. We introduce here a new set of simplified expressions for these integrals in the commonly studied case of axisymmetric particles. Simplifications are obtained using the differentiation properties of the radial functions (spherical Bessel) and angular functions (associated Legendre functions) and integrations by parts. The resulting simplified expressions not only lead to faster computations, but also reduce the risks of loss of precision and provide a simpler framework for further analytical work.     

New finite-energy lower boundaries for the scattering amplitude

Within the framework of axiomatic quantum field theory, conditional finite-energy lower boundaries are obtained for the moduli of the scattering amplitudes. The conditionality of the new boundaries consists in that they are provable under particular additional conditions which, although they do not follow axiomatically, are directly verifiable from experiment.Translated from Izvestiya Vysshikh Uchebnykh, Fizika, No. 8, pp. 16–19, August, 1984.     

The Lorentz force and energy-momentum for off-shell electromagnetism

The kinematics of pre-Maxwell electrodynamics is examined and interpretations of these fields is found through an examination of the associated Lorentz force and the structure of the energy-momentum tensor.     

The analytic continuation of the high-energy quark-quark scattering amplitude

It is known that the high-energy quark-quark scattering amplitude can be described by the expectation value of two lightlike Wilson lines, running along the classical trajectories of the two colliding particles. Generalizing the results of a previous paper, we give here the general proof that the expectation value of two infinite Wilson lines, forming a certain hyperbolic angle in Minkowski space-time, and the expectation value of two infinite Euclidean Wilson lines, forming a certain angle in Euclidean four-space, are connected by an analytic continuation in the angular variables. This result could be used to evaluate the high-energy scattering amplitude directly on the lattice. Received: 18 April 1997 / Revised version: 27 August 1997