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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Direct Calculation of the Scattering Amplitude Without Partial Wave Analysis

Two new developments in scattering theory are reported. We show, in a practical way, how one can calculate the full scattering amplitude without invoking a partial wave expansion. First, the integral expression for the scattering amplitude f(theta) is simplified by an analytic integration over the azimuthal angle. Second, the full scattering wavefunction which appears in the integral expression for f(theta) is obtained by solving the Schrodinger equation with the finite element method (FEM). As an example, we calculate electron scattering from the Hartree potential. With minimal computational effort, we obtain accurate and stable results for the scattering amplitude.

Shertzer, J.↗
DOE OSTI2025

Investigating the universality of five-point QCD scattering amplitudes at high energy

We investigate 2 → 3 QCD scattering amplitudes in multi-Regge kinematics, i.e. where the final partons are strongly ordered in rapidity. In this regime amplitudes exhibit intriguing factorisation properties which can be understood in terms of effective degrees of freedom called reggeons. Working within the Balitsky/JIMWLK framework, we predict these amplitudes for the first time to next-to-next-to-leading logarithmic order, and compare against the limit of QCD scattering amplitudes in full colour and kinematics. We find that the latter can be described in terms of universal objects, and that the apparent non-universality arising at NNLL comes from well-defined and under-control contributions that we can predict. Thanks to this observation, we extract for the first time the universal vertex that controls the emission of the central-rapidity gluon, both in QCD and $\mathcal{N}$ = 4 super Yang-Mills.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1985

Elastic scattering of alpha particles and the phase of the nucleon-nucleon scattering amplitude

Glauber theory can describe elastic scattering of alpha particles by He-4, He-3, H-2, and H-1 at 7 GeV/c if the phase of the nucleon-nucleon elastic-scattering amplitude varies with momentum transfer. The phase variation leads to diffraction patterns differing markedly from those typical of constant-phase calculations and greatly affects the magnitudes of the intensities. These changes are mainly due to changes in the interference between amplitudes for different orders of multiple scattering and to a decrease in their moduli.

Franco, V.↗
NASA NTRS2003

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE) can be reduced to a 2d partial differential equation (pde), and was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation. The resultant equation can be reduced to a pair of coupled pde's, to which the finite element method can still be applied. The resultant scattering amplitudes, both singlet and triplet, as a function of angle can be calculated for various energies. The results are in excellent agreement with converged partial wave results.

Shertzer, J.↗
DOE OSTI2025

Multipositivity bounds for scattering amplitudes

Lorentz invariance, unitarity, and causality enforce powerful constraints on the theory space of physical scattering amplitudes. However, virtually all efforts in this direction have centered on the very simplest case of four-point scattering. In this work, we derive an infinite web of “multipositivity bounds” that nonlinearly constrain all tree-level higher-point scattering amplitudes under similarly minimal assumptions. Our construction rules out several deformations of the string and implies mixed-multiplicity bounds on the Wilson coefficients of planar effective field theories. Curiously, an infinite class of multipositivity bounds is exactly saturated by the amplitudes of the open string.

effective field theory↗
NASA NTRS2007

Direct Calculation of the Scattering Amplitude Without Partial Wave Decomposition: Inclusion of Correlation Effects - III

In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion of the article Popular summary of Direct calculation of the scattering amplitude without partial wave expansion. III ....." by J. Shertzer and A. Temkin. In this paper we continue the development of In this paper we continue the development of a new approach to the way in which researchers have traditionally used to calculate the scattering cross section of (low-energy) electrons from atoms. The basic mathematical problem is to solve the Schroedinger Equation (SE) corresponding the above physical process. Traditionally it was always the case that the SE was reduced to a sequence of one-dimensional (ordinary) differential equations - called partial waves which were solved and from the solutions "phase shifts" were extracted, from which the scattering cross section was calculated.

Shertzer, Janine↗
NASA NTRS2001

Calculation of the Scattering Amplitude Without Partial Wave Expansion

Two developments in the direct calculation of the angular differential scattering amplitude have been implemented: (a) The integral expansion of the scattering amplitude is simplified by analytically integration over the azimuthal angle. (b) The resulting integral as a function of scattering angle is calculated by using the numerically generated wave function from a finite element method calculation. Results for electron-hydrogen scattering in the static approximation will be shown to be as accurate as a partial wave expansion with as many l's as is necessary for convergence at the incident energy being calculated.

Shertzer, J.↗
NASA NTRS2003

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II: Inclusion of Exchange

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE), which can be reduced to a 2d partial differential equation (pde), was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation, which is reducible to a pair of coupled pde's. The resultant scattering amplitudes, both singlet and triplet, calculated as a function of energy are in excellent agreement with converged partial wave results.

Shertzer, Janine↗
NASA NTRS1993

Strong-field cyclotron scattering. I - Scattering amplitudes and natural line width

The introduction of resonance line width into the QED cyclotron scattering amplitudes is considered. It is shown that the width arises from loop corrections to the electron propagator, which also bring about shifts in the Landau energy levels. A formalism is developed that allows the dressed electron propagator to be derived. It is shown that the states of Herold et al. (1982) and of Sokolov and Ternov (1968), which diagonalize the component of the magnetic moment operator parallel to the external magnetic field, are appropriate for calculation of the scattering amplitudes, whereas the states of Johnson and Lippmann (1949) are not. In addition, it is shown that the Breit-Wigner broadening approximation E tends to E - i(Gamma)/2 is consistent with the perturbation-theoretic order of the calculation, if the former basis states are chosen, but not the latter.

Graziani, Carlo↗
DOE OSTI2025

QCD Predictions for Physical Multimeson Scattering Amplitudes

We use lattice QCD calculations of the finite-volume spectra of systems of two and three mesons to determine, for the first time, three-particle scattering amplitudes with physical quark masses. Our results are for combinations of 𝜋 + and 𝐾 + , at a lattice spacing 𝑎 = 0.063 fm, and in the isospin-symmetric limit. We also obtain accurate results for maximal-isospin two-meson amplitudes, with those for 𝜋 + ⁢𝐾 + and 2⁢𝐾 + being the first determinations at the physical point. Dense lattice spectra are obtained using the stochastic Laplacian-Heaviside method, and the analysis leading to scattering amplitudes is done using the relativistic finite-volume formalism. Results are compared to chiral perturbation theory and to phenomenological fits to experimental data, finding good agreement.

hadron-hadron interactions↗
NASA NTRS2004

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition: Inclusion of Exchange - 2

The development of a practical method of accurately calculating the full scattering amplitude, without making a partial wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering e-H scattering in the static exchange approximation. The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial wave results.

Shertzer, Janine↗
DOE OSTI2025

Extracting scattering amplitudes for arbitrary two-particle systems with one-particle left-hand cuts via lattice QCD

We derive a general formalism that relates the spectrum of two-particle systems in a finite volume to physical scattering amplitudes, taking into account the presence of any left-hand branch cuts due to single-particle exchanges. The method first relates the finite-volume spectrum to an infinite-volume short-range quantity, denoted ${\mathcal{M}}_0$, and then relates the latter to the physical scattering amplitudes via known integral equations. The derivation of both relations is performed using all-orders perturbation theory and is exact up to neglected exponentially suppressed volume dependence. The relations hold for arbitrary two-particle systems with any number of coupled channels, non-identical and non-degenerate particles, and any intrinsic spin.

algorithms↗
DOE OSTI2025

Two- and three-meson scattering amplitudes with physical quark masses from lattice QCD

We study systems of two and three mesons composed of pions and kaons at maximal isospin using four CLS ensembles with 𝑎 ≈ 0.063 fm, including one with approximately physical quark masses. Using the stochastic Laplacian-Heaviside method, we determine the energy spectrum of these systems including many levels in different momentum frames and irreducible representations. Using the relativistic two- and three-body finite-volume formalism, we constrain the two- and three-meson K matrices, including not only the leading 𝑠 wave, but also 𝑝 and 𝑑 waves. By solving the three-body integral equations, we determine, for the first time, the physical-point scattering amplitudes for 3⁢𝜋 + , 3⁢𝐾 + , 𝜋 + ⁢𝜋 + ⁢𝐾 + , and 𝐾 + ⁢𝐾 + ⁢𝜋 + systems. These are determined for total angular momentum 𝐽 𝑃 = 0 − , 1 + , and 2 − . We also obtain accurate results for 2⁢𝜋 + , 𝜋 + ⁢𝐾 + , and 2⁢𝐾 + phase shifts. We compare our results to chiral perturbation theory and to phenomenological fits.

FOS: Physical sciences↗
NASA NTRS2002

Calculation of Scattering Amplitude Without Partial Analysis: Inclusion of Exchange - II

There was a method for calculating the whole scattering amplitude, f(Omega(sub k)), directly. The idea was to calculate the complete wave function Psi numerically, and use it in an integral expression for f, which can be reduced to a 2 dimensional quadrature. The original application was for e-H scattering without exchange. There the Schrodinger reduces a 2-d partial differential equation (pde), which was solved using the finite element method (FEM). Here we extend the method to the exchange approximation. The S.E. can be reduced to a pair of coupled pde's, which are again solved by the FEM. The formal expression for f(Omega(sub k)) consists two integrals, f+/- = f(sub d) +/- f(sub e); f(sub d) is formally the same integral as the no-exchange f. We have also succeeded in reducing f(sub e) to a 2-d integral. Results will be presented at the meeting.

Temkin, Aaron↗
NASA NTRS1975

Properties of scattering amplitudes at very high energies

The research is reported concerning the (1) total cross sections as the energy becomes infinite, (2) elastic scattering amplitude for nonforward directions, and (3) upper bound of neutrino scattering cross sections.

Mickens, R. E.↗
DOE OSTI2025

Supertranslations from Scattering Amplitudes

On shell methods have found a new application to local observables such as asymptotic radiation fields and gravitational waveforms. While these observables are invariant under small gauge transformations, they are known to depend on a choice of asymptotic gauge; in gravity on asymptotically Minkowski spacetimes, this is a choice of Bondi-Van der Burg-Metzner-Sachs frame. In this Letter, we provide a method for capturing these supertranslations, to all orders in perturbation theory, using the on shell framework of scattering amplitudes.

Classical black holes↗