Calculation of the non forward scattering amplitude for long range potentials

The regularization factor technique is considered as a summation method for divergent, oscillating and slowly convergent partial wave expansions of the non-forward scattering amplitude for long range central potentials. Its convergence properties are studied and its efficiency is compared with that of the Punctual Padé approximant method in the cases of the Kratzer and Lennard-Jones potentials.     

Determination of the scattering amplitude

The problem to determine the elastic scattering amplitude from the differential cross-section by the unitarity equation is reexamined. We prove that the solution is unique and can be determined by a convergent iteration if the parameter =sin of Newton and Martin is bounded by <₂0.86. The method is based on a fixed point theorem for holomorphic mappings in a complex Banach space.     

Constraints on the derivatives of the π π scattering amplitude from positivity

Conditions derived from positivity are given both above and below threshold for the derivatives of the scattering amplitude.On leave of absence from the University of Kent at Canterbury.     

Determination of the scattering amplitude from the differential cross-section and unitarity

When the differential cross-section for spin-zero elastic scattering is given, the elastic unitarity condition constitutes a nonlinear integral equation for the phase of the scattering amplitude. Existence and uniquences theorems for solutions of the equation were obtained by Newton and Martin. Some improvements of the Newton-Martin results on uniqueness and iterative construction of solutions are obtained. Certain details of rigour in the applications of Schauder's theorem by Newton and by Martin are supplied. The case of inelastic spin-zero scattering is treated by adding a term to the unitarity condition to account for absorption. It is shown that in the inelastic region one may have infinitely many different scattering amplitudes with a given differential cross-section. This result is potentially important in phase-shift analysis, since it means that there is a continuum ambiguity in the determination of phases and elasticities from scattering data.Work supported in part by the National Science Foundation and a NATO Research Grant.     

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.     

Hamilton-Jacobi expansion of the scattering amplitude

The calculation of the scattering amplitude is reduced to the problem of solving a set of classical Hamilton-Jacobi equations. This allows one to incorporate classical intuition into approximations at a fundamental level. The result is actually an iterative expansion for the scattering amplitude which is expected to be convergent in the high-energy limit. The first term in the expansion is shown to be the Glauber approximation, which is an approximation used extensively in nuclear as well as atomic and particle physics.     

Performance of discrete dipole approximation for prediction of amplitude and phase of electromagnetic scattering by particles

Electromagnetic scattering provides useful signatures for nonintrusive particle characterization. Scattered wave which carries characteristic information about particles is identified completely by its intensity, polarization state and phase. Recent developments in measurement techniques have enabled measurement of phase of the scattered wave which is a source of additional information about particles. In the present study, accuracy of discrete dipole approximation (DDA) in predicting amplitude and phase of scattered wave is investigated via publicly available DDSCAT code by Draine and Flatau, which is a well-established tool for DDA and has found wide range of applications in the literature due to its flexibility. DDSCAT routine is modified to enable accurate computation of phase of complex amplitude scattering matrix (ASM) elements as well as their magnitude. DDA method was implemented by using lattice dispersion relation for dipole polarizabilities, generalized prime factor algorithm for fast-Fourier transformation and pre-conditioned bi-conjugate gradient method with stabilization for the solution of the complex linear system of equations. Accuracy of ASM elements predicted by DDA is assessed on single sphere problems with various size parameters and refractive indices by validation against Mie theory solutions. Excellent agreement between predictions and exact solutions proves the reliability of the modified DDSCAT code for prediction of amplitude and phase of scattered electromagnetic wave. Applicability conditions and requirements of the present DDA application to ensure accurate prediction of complete set of scattering parameters are mapped for single spheres, on an extensive domain of size parameters and refractive indices. A correlation is presented to estimate the magnitude and phase errors associated with given size parameter, refractive index and cubic lattice subdivision. Assessment of computational time requirements for different optical constants shows that implementation of DDA with the present specifications is unfeasible for size parameters larger than 4 when Re(m)>2 and Im(m)<0.1 at the same time, due to slow convergence rate.     

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.     

Structure of the antiproton-proton elastic scattering amplitude

It is found that the simple expression [(πcq)/sinh(πcq)][J ₁(Rq)/(Rq)] for the elastic scattering amplitude makes it possible to well describe differential cross sections over a broad range of energies from 100 MeV to \(\sqrt s \) = 1800 GeV. This parametrization can be used to calculate antiproton-nucleus and antinucleus-nucleus amplitudes and cross sections, which are necessary in accelerator experiments and in cosmic ray physics. The generalization of the wavelet expansion to the case of functions defined on a semi-infinite interval is also proposed.     

Approximate construction of the scattering amplitude from Mandelstam representation and elastic unitarity

An approximate expression for the scattering amplitude is derived from the Mandelstam representation and the elastic unitarity. To demonstrate our procedure in the relativistic case we considerπ-N scattering, omitting spin and isospin for simplicity. Non-relativistic potential scattering is discussed in detail.     

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 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.     

The scattering amplitude for four off-shell tachyons from functional integrals

We use functional integral techniques to calculate the scattering amplitude for four open off-shell tachyons in Witten's string field theory and show that the residues of the first three poles agree with those obtained using oscillator methods.     

Calculation of generalp-adic Feynman amplitude

The generaln-point masslessp-adic Feynman amplitude with arbitrary parameters of analytic regularization for each line is calculated. This result is presented in the form of a sum over hierarchies of a given graph. The structure of ultraviolet and infrared divergences ofp-adic Feynman amplitudes is characterized and the startriangle uniqueness identity in thep-adic case is derived.Supported by Alexander von Humboldt-Stiftung     

Exponentially small scattering amplitude in high energy potential scattering

The high energy scattering amplitude of spherical symmetric potentials, which are expandable in ascending even powers of r and are nonsingular in coordinate space, is calculated. The Gaussian potential, which serves as a prototype of these potentials, is dealt with extensively. The first Born approximation is completely inadequate to estimate the amplitude off the forward direction. We show that the amplitude decreases faster than any power law as function of the momentum transfer q, and thus in that respect is similar in behavior to that of elastic scattering of elementary particles. Essentially, the whole range of the scattering angle is covered. Some speculations concerning shrinkage and antishrinkage effects are briefly mentioned.