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We propose a novel method to compute in an exact manner the left-hand cut discontinuity of the electron-Atom partial wave scattering amplitude in the complex energy plane within the static stage approximation. Zero energy dispersion relations for electron-Hydrogen scattering are computed numerically for illustration.
The theory of surface gravity waves scattering at vortex flows in the ocean is developed in this paper. A scattering amplitude is found in the Born approximation as a function of Vorticity that appears very convenient for investigation of scattering at simple localized flows.
This project supported a broad set of research in theoretical nuclear physics which has been designed to support current and future experimental DOE facilities. The broad summary of physical observables of interest in this project were the bread-and-butter observables obtained in experimental nuclear and particle physics experiments, namely scattering amplitude including multi-hadronic states. The primary goal of this project was to design a systematically improvable paradigm for accessing such amplitudes directly from the Standard Model of Particle Physics. The main tools that were used and explored in this project were scattering theory, lattice QCD, and future quantum computers. The physics outputs included various novel formalisms, exploratory lattice QCD calculations, and a new proposal for studying any scattering observable using future quantum computers.
We propose a new model-independent method for determining hadronic resonances from lattice QCD. The formalism is derived from the general principles of unitarity and analyticity, as encoded in the N/D representation of a partial-wave two-body amplitude. The associated quantization condition relates the finite-volume spectrum to the infinite-volume numerator $\mathscr{N}$, used to reconstruct the scattering amplitude from dispersive relations. Unlike the original Lüscher condition, this new formalism is valid for energies coinciding with the left-hand cuts from arbitrary one- and multiparticle exchanges.
The radiative transfer theory is applied to calculate the scattering by a layer of randomly positioned and oriented nonspherical particles. The scattering amplitude functions of each individual particle are calculated with Waterman's T matrix method, which utilizes vector spherical wave functions for expansion of incident, scattered, and surface fields. The orientation of the particles is described by a probability density function of the Eulerian angles of rotation. A rotation matrix is used to relate the T matrix of the principal frame to that of the natural frame of the particle. The extinction matrix and phase matrix of the radiative transfer equations are expressed in terms of the T matrix elements. The extinction matrix for nonspherical particles is generally nondiagonal. There are only two attenuation rates in a specified direction of propagation. The radiative transfer equations are solved by an iterative method to first order in albedo. Numerical results are illustrated as functions of incidence angle and frequency with applications to active remote sensing.
In testing a stochastic variational principle at high frequencies by using a Kirchhoffean trial function in an idealized model for surface scattering - a randomly embossed plane - we have found not only the predicted high-frequency improvement but also an unexpected low-frequency improvement in the calculated scattering amplitudes. To investigate systematically the all-frequency variational behavior, we consider here the deterministic one-boss case - Rayleigh's classic model whose exact solution is available for comparison - over all wavelengths, polarizations, and configurations of incidence and scattering. We examine analytically in particular the long-wave limit of the variational-Kirchhoff amplitudes; the results demonstrate improvements in both wavelength and angle depedence for horizontal (TM) polarization and some variational improvements for vertical (TE) polarization. This low-frequency behavior in tandem with the foreseen high-frequency improvement leads to good variational-Kirchhoff results through the intermediate resonance-frequency regime for this model.
The derivations of the Lippmann-Schwinger equation and Watson multiple scattering are given. A simple optical potential is found to be the first term of that series. The number density distribution models of the nucleus, harmonic well, and Woods-Saxon are used without t-matrix taken from the scattering experiments. The parameterized two-body inputs, which are kaon-nucleon total cross sections, elastic slope parameters, and the ratio of the real to the imaginary part of the forward elastic scattering amplitude, are presented. The eikonal approximation was chosen as our solution method to estimate the total and absorptive cross sections for the kaon-nucleus scattering.
Two kinds of number density distributions of the nucleus, harmonic well and Woods-Saxon models, are used with the t-matrix that is taken from the scattering experiments to find a simple optical potential. The parameterized two body inputs, which are kaon-nucleon total cross sections, elastic slope parameters, and the ratio of the real to imaginary part of the forward elastic scattering amplitude, are shown. The eikonal approximation was chosen as the solution method to estimate the total and absorptive cross sections for the kaon-nucleus scattering.
A two-space scatterer formalism and equivalent medium approach of Twersky are used to obtain formulae for the bulk electromagnetic parameters of a thundercloud medium that is illuminated by lightning optical emissions. A modified WKB approximation is applied to derive the two-space scattering amplitude. Optical constants of dry air, moist atmosphere, and water,.are inserted into the formulae to generate numerical values via iteration. The two-space scatterer formalism results are close to those obtained from free- or sin-le-space formalisms for the dilute case. The numerical values of the bulk parameters are required to successfully transform the scattering problem to that of an equivalent obstacle excited by an incident wave traveling in K - space but radiating in k(sub 1) -space.
We study higher-derivative corrections to the graviton scattering amplitude in M-theory, via the stress tensor correlator of 3d$\mathcal{N}$= 8 U(N) k × U(N) –k ABJM theory (dual to graviton scattering in M-theory on AdS 4 × S 7 /ℤ k ). We use the conformal bootstrap combined with an integral constraint derived from supersymmetric localization in order to constrain semishort OPE coefficients appearing in the stress tensor correlator. We obtain islands that are significantly more precise than those in previous studies that did not use the integral constraint. Using these islands, we can estimate the powers and coefficients in a large central charge expansion. This allows us to accurately read off the N 3 LO contribution, from the protected D 6 R 4 correction, and also estimate the N 4 LO contribution, from the unprotected D 8 R 4 correction.
A microscopic model for the quaisiparticle interaction in neutron matter is presented. Both particle-particle (pp) and particle-hole (ph) correlation are are included. The pp correlations are treated in semi-empirical way, while ph correlations are incorporated by solving coupled two-body equations for the particle hole interaction and the scattering amplitude on the Fermi sphere. The resulting integral equations self-consistently sum the ph reducible diagrams. Antisymmetry is kept at all stages and hence the forward-scattering sum rules are obeyed. Results for Landau parameters and transport coefficients in a density regime representing the crust of a neutron star are presented. We also estimate the S-1 gap parameter for neutron superfluidity and comment briefly on neutron-star implications.
It is shown that a 2D conformal field theory consisting of a central charge c Liouville theory, a chiral level one, rank N Kac-Moody algebra, and a weight − 3 / 2 free fermion holographically generate 4D maximal helicity violating tree-level scattering amplitudes. The correlators of this 2D conformal field theory give directly the 4D leaf amplitudes associated to a single hyperbolic slice of flat space. The 4D celestial amplitudes arise in a large- N and semiclassical large- c limit, according to the holographic dictionary, as a translationally invariant combination of leaf amplitudes. A step in the demonstration is showing that the semiclassical limit of Liouville correlators are given by contact 3D anti–de Sitter Witten diagrams. Published by the American Physical Society 2024
We generalize the relativistic field-theoretic three-particle finite-volume scattering formalism to describe generic DDπ systems in the charm C = 2 sector. This includes the isospin-0 channel, in which the recently discovered doubly-charmed tetraquark T cc (3875) + is expected to manifest as a pole in the DDπ → DDπ scattering amplitude. The formalism presented here can also be applied to lattice QCD settings in which the D * is bound and, in particular, remains valid below the left-hand cut in DD * scattering, thus resolving an issue in previous analyses of lattice-determined finite-volume energies.
Deuteron-carbon elastic scattering is studied within the framework of the Glauber approximation. The full Glauber multiple scattering series is evaluated with simplified nuclear wave functions. An approximation in which deuteron-nucleus scattering is expressed in terms of nucleon-nucleus scattering amplitudes is shown to be accurate for small momentum transfers. The effects of the Coulomb field and the deuteron D state are investigated. The impressive fit to the 650 MeV d-(C-12) elastic scattering data, obtained in a recent calculation, is shown to be due to additional approximations made in that analysis.
Five different inelastic light scattering processes will be denoted by, ordinary Raman scattering (ORS), resonance Raman scattering (RRS), off-resonance fluorescence (ORF), resonance fluorescence (RF), and broad fluorescence (BF). A distinction between fluorescence (including ORF and RF) and Raman scattering (including ORS and RRS) will be made in terms of the number of intermediate molecular states which contribute significantly to the scattered amplitude, and not in terms of excited state lifetimes or virtual versus real processes. The theory of these processes will be reviewed, including the effects of pressure, laser wavelength, and laser spectral distribution on the scattered intensity. The application of these processes to the remote sensing of atmospheric pollutants will be discussed briefly. It will be pointed out that the poor sensitivity of the ORS technique cannot be increased by going toward resonance without also compromising the advantages it has over the RF technique. Experimental results on inelastic light scattering from I(sub 2) vapor will be presented. As a single longitudinal mode 5145 A argon-ion laser line was tuned away from an I(sub 2) absorption line, the scattering was observed to change from RF to ORF. The basis, of the distinction is the different pressure dependence of the scattered intensity. Nearly three orders of magnitude enhancement of the scattered intensity was measured in going from ORF to RF. Forty-seven overtones were observed and their relative intensities measured. The ORF cross section of I(sub 2) compared to the ORS cross section of N2 was found to be 3 x 10(exp 6), with I(sub 2) at its room temperature vapor pressure.
Recently [Nucl. Instr. and Meth. B 145 (1998) 277; Extraction of in-medium nucleon-nucleon amplitude from experiment, NASA-TP, 1998], we developed a method of extracting nucleon-nucleon (N-N) cross-sections in the medium directly from experiment. The in-medium N-N cross-sections form the basic ingredients of several heavy-ion scattering approaches including the coupled-channel approach developed at the NASA Langley Research Center. We investigated [Proton-nucleus total cross-sections in coupled-channel approach, NASA/TP, 2000; Nucl. Instr. and Meth. B 173-174 (2001) 391] the ratio of real to imaginary part of the two body scattering amplitude in the medium. These ratios are used in combination with the in-medium N-N cross-sections to calculate proton-nucleus elastic cross-sections. The agreement is excellent with the available experimental data. These cross-sections are needed for the radiation risk assessment of space missions. c2002 Elsevier Science B.V. All rights reserved.
For an incident plane wave, the field inside a thin scatterer (disk and needle) is estimated by the generalized Rayleigh-Gans (GRG) approximation. This leads to a scattering amplitude tensor equal to that obtained via the Rayleigh approximation (dipole term) with a modifying function. For a finite-length cylinder the inner field is estimated by the corresponding field for the same cylinder of infinite lenght. The effects of different approaches in estimating the field inside the scatterer on the backscattering cross section are illustrated numerically for a circular disk, a needle, and a finite-length cylinder as a function of the wave number and the incidence angle. Finally, the modeling predictions are compared with measurements.
The paper presents a detailed development of the coupled-states approximation for the general case of two colliding diatomic molecules. The high-energy limit of the exact Lippman-Schwinger equation is applied, and the analysis follows the Shimoni and Kouri (1977) treatment of atom-diatom collisions where the coupled rotor angular momentum and projection replace the single diatom angular momentum and projection. Parallels to the expression for the differential scattering amplitude, the opacity function, and the nondiagonality of the T matrix are reported. Symmetrized expressions and symmetrized coupled equations are derived. The present correctly labeled coupled-states theory is tested by comparing its calculated results with other computed results for three cases: H2-H2 collisions, ortho-para H2-H2 scattering, and H2-HCl.