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At least 235 records · Page 13

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DOE OSTI2025

Finite-volume quantization condition from the N/D representation

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.

Dawid, Sebastian M. [Univ. of Washington, Seattle,↗

NASA NTRS1984

Radiative transfer theory for active remote sensing of a layer of nonspherical particles

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.

Tsang, L.↗

NASA NTRS1985

Analysis of all-frequency variational behavior of the Kirchhoff approximation for a classic surface-scattering model

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.

Bird, J. F.↗

NASA NTRS1989

Kaon-nucleus scattering

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.

Hong, Byungsik↗

NASA NTRS1989

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.

Hong, Byungsik↗

NASA NTRS1998

Calculation of the Bulk Electromagnetic Properties of Thunderclouds Using a Two-Space Scattering Formalism

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.

Phanord, Dieudonne D.↗

DOE OSTI2025

Higher-derivative corrections in M-theory from precision numerical bootstrap

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.

AdS-CFT correspondence↗

DOE OSTI2021

Electronic scattering off a magnetic hopfion

We study scattering of itinerant electrons off a magnetic hopfion in a three-dimensional metallic magnet described by a magnetization vector S(r). A hopfion is a confined topological soliton of S(r) characterized by an emergent magnetic field Bγ(r)≡ε αβγ S∙(∇ α S×∇ β S)/4≠0 with vanishing average value [B(r)]=0. We evaluate the scattering amplitude in the opposite limits of large and small hopfion radius R using the eikonal and Born approximations, respectively. In both limits, we find that the scattering cross section contains a skew-scattering component giving rise to the Hall effect within a hopfion plane. That conclusion contests the popular notion that the Hall effect in noncollinear magnetic structures necessarily implies [B(r)]≠0. In the limit of small hopfion radius pR<<1, we expand the Born series in powers of momentum p and identify different expansion terms corresponding to the hopfion anisotropy, toroidal moment, and skew scattering.

36 MATERIALS SCIENCE↗

NASA NTRS1993

Quasiparticle Interactions in Neutron Matter for Applications in Neutron Stars

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.

Wambach, J.↗

DOE OSTI2022

A lattice study of ππ scattering at large N c

We present the first lattice study of pion-pion scattering with varying number of colors, N c . We use lattice simulations with four degenerate quark flavors, N f = 4, and N c = 3 – 6. We focus on two scattering channels that do not involve vacuum diagrams. These correspond to two irreducible representations of the SU(4) flavor group: the fully symmetric one, SS, and the fully antisymmetric one, AA. The former is a repulsive channel equivalent to the isospin-2 channel of SU(2). By contrast, the latter is attractive and only exists for N f ≥ 4. A representative state is (|D$^{+}_{s}$π + > – | D + K + >)/√2. Using Lüscher’s formalism, we extract the near-threshold scattering amplitude and we match our results to Chiral Perturbation Theory (ChPT) at large N c . For this, we compute the analytical U(N f ) ChPT prediction for two-pion scattering, and use the lattice results to constrain the N c scaling of the relevant low-energy couplings.

1/N Expansion↗

DOE OSTI2024

Celestial Dual for Maximal Helicity Violating Amplitudes

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

Physics↗

DOE OSTI2024

Incorporating DD π effects and left-hand cuts in lattice QCD studies of the T cc (3875) +

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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Shallow Bound States and Hints for Broad Resonances with Quark Content b ¯ c ¯ u d in B − D ¯ and B * − D ¯ Scattering from Lattice QCD

We present the first determination of the energy dependence of the B − D ¯ and B * − D ¯ isospin-0, S -wave scattering amplitudes both below and above the thresholds using lattice QCD, which allows us to investigate rigorously whether mixed bottom-charm b ¯ c ¯ u d tetraquarks exist as bound states or resonances. The scattering phase shifts are obtained using Lüscher’s method from the energy spectra in two different volumes. To ensure that no relevant energy level is missed, we use large, symmetric 7 × 7 and 8 × 8 correlation matrices that include, at both source and sink, B ( * ) − D ¯ scattering operators with the lowest three or four possible back-to-back momenta in addition to local b ¯ c ¯ u d operators. We fit the energy dependence of the extracted scattering phase shifts using effective-range expansions. We observe sharp peaks in the B ( * ) − D ¯ scattering rates close to the thresholds, which are associated with shallow bound states, either genuine or virtual, a few MeV or less below the B ( * ) − D ¯ thresholds. In addition, we find hints for resonances with masses of order 100 MeV above the thresholds and decay widths of order 200 MeV. Published by the American Physical Society 2024

Alexandrou, Constantia↗

NASA NTRS1977

Elastic scattering of deuterons by carbon

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.

Varma, G. K.↗

NASA NTRS1973

Inelastic Light Scattering Processes

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.

Fouche, Daniel G.↗

DOE OSTI2022

Diffuse X-ray scattering from polished silicon: application of the distorted wave Born approximation

Measured diffuse X-ray scattering data for a `smooth' as well as for a `rough' silicon sample were fit to theoretical expressions within the distorted wave Born approximation (DWBA). Data for the power spectral density (PSD) for both samples were also obtained by means of atomic force microscopy and optical interferometry. The Fourier transforms of trial correlation functions were fit to the PSD data and then applied to the DWBA formalism. The net correlation functions needed to fit the PSD data for each sample comprised the sum of two terms with different cutoff lengths and different self-affine fractal exponents. At zero distance these correlation functions added up to yield net values of σ 2 = (2) 2 and (71) 2 Å 2 for the smooth and rough samples, respectively. X-ray scattering data were obtained at beamline 1-BM of the Advanced Photon Source. Data and fits at values of q z = 0.05 and 0.10 Å −1 for the smooth sample are reported. Good fits for the smooth sample were obtained at both q z values simultaneously, that is, identical fitting parameters were applied at both values of q z . The smooth sample also exhibited weak Yoneda wings and a clear distinction between the strong specular scattering and the weak diffuse scattering. Data for the rough sample were qualitatively different and exhibited very weak scattering at the specular condition in contrast to extremely large Yoneda wings. Fits for the rough sample are reported for q z = 0.04, 0.05, and 0.06 Å −1 . Although the large Yoneda wings could be fit quite well in both position and amplitude, scattering near the specular condition could not be equally well fit by applying the same fitting parameters at all values of q z . Albeit imperfect, best-fitting results at the specular condition were obtained by invoking only diffuse scattering, that is, without including a separate theoretical expression for specular scattering.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2002

A method for calculating proton-nucleus elastic cross-sections

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.

NASA Center LaRC↗

DOE OSTI2022

Determination of asymptotic normalization coefficients for the channel 16 O→ α+ 12 C: excited state 16 O(0 + ; 6.05 MeV)

Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In the present paper, we treat the ANC C for the virtual decay 16 O(0 + ; 6.05 MeV)→ α+ 12 C(g.s.), the known values of which are characterized by a large spread (0.29 - 1.65) × 10 3 fm -1/2 . The ANC C is found by analytic continuation in energy of the α 12 C s-wave scattering amplitude, known from the phase-shift analysis of experimental data, to the pole corresponding to the 16O bound state and lying in the unphysical region of negative energies. To determine C, two different methods of analytic continuation are used. In the first method, the scattering data are approximated by the sum of polynomials in energy in the physical region and then extrapolated to the pole. The best way of extrapolation is chosen on the basis of the exactly solvable model. Within the second approach, the ANC C is found by solving the Schrödinger equation for the two-body α 12 C potential, the parameters of which are selected from the requirement of the best description of the phase-shift analysis data at a fixed experimental binding energy of 16 O(0 + ; 6.05 MeV) in the α+ 12 C channel. The values of the ANC C obtained within these two methods lie in the interval (886–1139) fm -1/2 .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗