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Results for “Eikonal approximation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Nucleon and heavy-ion total and absorption cross section for selected nuclei

Approximate solutions of the coupled-channel equations for high-energy composite particle scattering are obtained and are applied to the nuclear scattering problem. Relationships between several approximation procedures are established and discussed. The eikonal formalism is used with a small-angle approximation to calculate the coherent elastic scattered amplitude from which total and absorption cross sections are derived. Detailed comparisons with nucleon-nucleus experiments show agreement within 5 percent except at lower energies where the eikonal approximation is of questionable accuracy. Even at these lower energies, agreement is within 15 percent. Tables of cross sections required for cosmic heavy-ion transport and shielding studies are presented.

Wilson, J. W.↗
DOE OSTI2021

Updated systematics of intermediate-energy single-nucleon removal cross sections

The body of experimental measurements of intermediate-energy reactions that remove a single nucleon from a secondary beam of neutron- or proton-rich nuclei continues to grow. These data have been analyzed consistently using an approximate, eikonal-model treatment of the reaction dynamics combined with appropriate shell-model descriptions of the projectile initial state, the bound final states spectrum of the reaction residue, and single-particle removal strengths computed from their wave-function overlaps. Here, the systematics of the ratio R s of the measured inclusive cross section to all bound final states and the calculated cross section to bound shell-model states—in different regions of the nuclear chart and involving both very weakly bound and strongly bound valence nucleons—is important in relating the empirically deduced orbital occupancies to those from the best available shell-model predictions. Importantly, several new higher-energy measurements, for which the sudden-approximation aspect of the dynamical description is placed on an even stronger footing, now supplement the previously analyzed measurements. These additional data sets are discussed. Their R s values are shown to conform to and reinforce the earlier-observed systematics, with no indication that the approximately linear reduction in R s with increasing nucleon separation energy is a consequence of a breakdown of the sudden approximation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Validation of ray-based cross-beam energy transfer models

Ray-based cross-beam energy transfer (CBET) models have become a common feature of the radiation-hydrodynamic codes used to simulate inertial confinement fusion experiments. Here, these models are necessary for achieving better agreement with experimental measurements, but their detailed implementation can vary widely between the codes and often rely on artificial multipliers. To address this, a series of 2D and 3D test cases has been developed with validated solutions from wave-based calculations. Comparisons of various ray-based CBET models to the wave-based calculations highlight the essential physics that is required for accurate ray-based CBET modeling. Quantitative comparison metrics and/or field data from the wave-based calculations have been made available for use in the validation of other ray-based CBET codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Effective field theory analysis of the Coulomb breakup of the one-neutron halo nucleus $$^{19}$$C

Abstract We analyse the Coulomb breakup of $$^{19}$$ 19 C measured at 67 A MeV at RIKEN. We use the Coulomb-Corrected Eikonal (CCE) approximation to model the reaction and describe the one-neutron halo nucleus $$^{19}$$ 19 C within Halo Effective Field Theory (Halo EFT). At leading order we obtain a fair reproduction of the measured cross section as a function of energy and angle. The description is insensitive to the choice of optical potential, as long as it accurately represents the size of $${}^{18}$$ 18 C. It is also insensitive to the interior of the $${}^{19}$$ 19 C wave function. Comparison between theory and experiment thus enables us to infer asymptotic properties of the ground state of $$^{19}$$ 19 C: these data put constraints on the one-neutron separation energy of this nucleus and, for a given binding energy, can be used to extract an asymptotic normalisation coefficient (ANC). These results are confirmed by CCE calculations employing next-to-leading order Halo EFT descriptions of $${}^{19}$$ 19 C: at this order the results for the Coulomb breakup cross section are completely insensitive to the choice of the regulator. Accordingly, this reaction can be used to constrain the one-neutron separation energy and ANC of $${}^{19}$$ 19 C.

Physics↗
DOE OSTI2023

Photon rings around warped black holes

Abstract The black hole photon ring is a prime target for upcoming space-based VLBI missions seeking to image the fine structure of astrophysical black holes. The classical Lyapunov exponents of the corresponding nearly bound null geodesics control the quasinormal ringing of a perturbed black hole as it settles back down to equilibrium, and they admit a holographic interpretation in terms of quantum Ruelle resonances of the microstate dual to the Kerr black hole. Recent work has identified a number of emergent symmetries related to the intricate self-similar structure of the photon ring. Here, we explore this web of interrelated phenomena in an exactly soluble example that arises as an approximation to the near-extremal Kerr black hole. The self-dual warped AdS 3 geometry has a photon ring as well as S L ( 2 , R ) isometries and an exactly calculable quasinormal mode (QNM) spectrum. We show explicitly that the geometric optics approximation reproduces the eikonal limit of the exact scalar QNM spectrum, as well as the approximate ‘near-ring’ wavefunctions. The S L ( 2 , R ) isometries are directly related to the emergent conformal symmetry of the photon ring in black hole images but are distinct from a recently discussed conformal symmetry of the eikonal QNM spectrum. The equivalence of the classical QNM spectrum—and thus the photon ring—to the quantum Ruelle resonances in the context of a spacetime with a putative holographic dual suggests that the photon ring of a warped black hole is indeed part of the black hole hologram.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Back-to-back dijet production in DIS at arbitrary Bjorken x: TMD gluon distributions to twist-3 accuracy

We derive the gluon transverse-momentum-dependent (TMD) operator structure of back-to-back\\\\r\\\\nquark–antiquark dijet production in deep inelastic scattering at arbitrary Bjorken-x to twist-3 ac\\\\r\\\\ncuracy. Working at leading order in the strong coupling and in the kinematic regime where the\\\\r\\\\ntransverse momentum imbalance of the jets is much smaller than their individual transverse mo\\\\r\\\\nmenta, we perform a systematic gradient expansion of the quark propagator in a background gluon\\\\r\\\\nfield. This expansion organizes multiple interactions with the target in terms of longitudinal Wilson\\\\r\\\\nlines and gauge-invariant field-strength insertions, yielding a TMD description valid beyond the\\\\r\\\\nstrict high-energy eikonal (x → 0) approximation. We obtain explicit cross sections for longitudi\\\\r\\\\nnally and transversely polarized virtual photons, identifying all contributing gluon TMD operators\\\\r\\\\nup to twist-3, including structures involving F+−, Fij, and three-gluon correlators. The full lon\\\\r\\\\ngitudinal phase eixP+z− associated with Bjorken-x is retained throughout. In the small-x limit,\\\\r\\\\nour results reproduce the known sub-eikonal expressions obtained in the Color Glass Condensate\\\\r\\\\nframework, establishing a direct connection between the general-x TMD expansion and high-energy\\\\r\\\\nfactorization. We further reduce the operator basis using equations of motion, minimizing the num\\\\r\\\\nber of independent nonperturbative matrix elements entering the cross section. This work provides\\\\r\\\\na systematic foundation for extending TMD analyses of dijet production beyond leading twist, es\\\\r\\\\ntablishing a unified operator framework valid at arbitrary Bjorken-x that smoothly interpolates\\\\r\\\\nbetween moderate- and small-x descriptions of gluon TMDs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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↗
DOE OSTI2023

Black and gray box learning of amplitude equations: Application to phase field systems

Here, we present a data-driven approach to learning surrogate models for amplitude equations and illustrate its application to interfacial dynamics of phase field systems. In particular, we demonstrate learning effective partial differential equations describing the evolution of phase field interfaces from full phase field data. We illustrate this on a model phase field system, where analytical approximate equations for the dynamics of the phase field interface (a higher-order eikonal equation and its approximation, the Kardar-Parisi-Zhang equation) are known. For this system, we discuss data-driven approaches for the identification of equations that accurately describe the front interface dynamics. When the analytical approximate models mentioned above become inaccurate, as we move beyond the region of validity of the underlying assumptions, the data-driven equations outperform them. In these regimes, going beyond black box identification, we explore different approaches to learning data-driven corrections to the analytically approximate models, leading to effective gray box partial differential equations.

42 ENGINEERING↗
DOE OSTI2025

Classical eikonal from Magnus expansion

In a classical scattering problem, the classical eikonal is defined as the generator of the canonical transformation that maps in-states to out-states. It can be regarded as the classical limit of the log of the quantum S-matrix. In a classical analog of the Born approximation in quantum mechanics, the classical eikonal admits an expansion in oriented tree graphs, where oriented edges denote retarded/advanced worldline propagators. The Magnus expansion, which takes the log of a time-ordered exponential integral, offers an efficient method to compute the coefficients of the tree graphs to all orders. We exploit a Hopf algebra structure behind the Magnus expansion to develop a fast algorithm which can compute the tree coefficients up to the 12th order (over half a million trees) in less than an hour. In a relativistic setting, our methods can be applied to the post-Minkowskian (PM) expansion for gravitational binaries in the worldline formalism. We demonstrate the methods by computing the 3PM eikonal and find agreement with previous results based on amplitude methods. Importantly, the Magnus expansion yields a finite eikonal, while the naïve eikonal based on the time-symmetric propagator is infrared-divergent from 3PM on.

Black Holes↗
DOE OSTI2021

Quasinormal modes and shadow of a Schwarzschild black hole with GUP

Highlights: • The physics of quantum corrected Schwarzschild Black Hole via GUP is investigated. • Quasinormal Modes (QNM) are obtained via WKB and numeric methods. • The relationship between shadow and QNM in the eikonal limit is established. • The quadratic and linear GUP parameters affect the results in a clear way. We consider quantum corrections for the Schwarzschild black hole metric by using the generalized uncertainty principle (GUP) to investigate quasinormal modes, shadow and their relationship in the eikonal limit. We calculate the quasinormal frequencies of the quantum-corrected Schwarzschild black hole by using the sixth-order Wentzel–Kramers–Brillouin (WKB) approximation, and also perform a numerical analysis that confirms the results obtained from this approach. We also find that the shadow radius is nonzero even at very small mass limit for finite GUP parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1983

Eikonal phase shift analyses of carbon-carbon scattering

A high-energy double-folding optical potential approximation to the exact nucleus-nucleus multiple-scattering series is used in determining eikonal phase shifts for carbon-carbon scattering at 204.2, 242.7, and 288.6 MeV. The double-folding potentials are derived by folding the energy-dependent free nucleon-nucleon interaction with densities for the projectile and target; these latter are obtained by unfolding the finite nucleon charge density from harmonic-well carbon charge distributions. The charge parameters for these distributions are taken from the results of electron scattering experiments. Predictions are made for total, reaction, and elastic differential cross sections using standard partial wave analysis for the scattering of identical particles and are then compared with recent experimental results. Excellent agreement is obtained despite the absence of arbitrarily adjusted parameters in the theory.

Townsend, L. W.↗
NASA NTRS1983

Abrasion cross sections for Ne-20 projectiles at 2.1 GeV/nucleon

Utilizing eikonal scattering theory, an optical model potential approximation to the exact nucleus-nucleus multiple scattering series is used in an abrasion-ablation collision formalism to predict abrasion cross sections for relativistic Ne-20 projectile nuclei. Excellent agreement with recent experimental abrasion results is obtained. The sensitivity of the abrasion predictions to Pauli exclusion principle correlation effects and to the assumed shape of the nuclear single-particle density distribution is also demonstrated.

Townsend, L. W.↗
NASA NTRS1981

Optical-model abrasion cross sections for high-energy heavy ions

Within the context of eikonal scattering theory, a generalized optical model potential approximation to the nucleus-nucleus multiple scattering series is used in an abrasion-ablation collision model to predict abrasion cross sections for relativistic projectile heavy ions. Unlike the optical limit of Glauber theory, which cannot be used for very light nuclei, the abrasion formalism is valid for any projectile target combination at any incident kinetic energy for which eikonal scattering theory can be utilized. Results are compared with experimental results and predictions from Glauber theory.

Townsend, L. W.↗
NASA NTRS1982

On the geometric nature of high energy nucleus-nucleus reaction cross sections

Within the context of a high energy double-folding optical potential approximation to the exact nucleus-nucleus multiple-scattering series, eikonal scattering theory is used to investigate the validity of geometric reaction cross sections in relativistic heavy ion collisions. The potential used includes a finite range interaction and nuclear single-particle densities extracted from nuclear charge distributions by unfolding the finite proton charge distribution. Pauli correlation effects are also included in an approximate way. The sensitivity of the predictions to the assumed interaction, Pauli correlation approximation, and nuclear density distributions is investigated. These results are in agreement with early predictions concerning the geometric nature of relativistic heavy ion collisions and in disagreement with a recent analysis, utilizing the zero range approximation, which suggested otherwise. Reasons for the lack of agreement between the analyses are also presented. Finally, approximate applicability limits for geometric reaction cross sections are determined.

Townsend, L. W.↗
DOE OSTI2021

Electron emission from fluorene (C 13 H 10 ) upon 3.5 MeV/u Si 8+ ion impact: double differential distributions

In this work, we have studied the electron emission from one of the polycyclic aromatic hydrocarbon (PAH) molecules namely, fluorene (C13H10), upon 3.5 MeV/u Si8+ ion impact. The experimentally measured absolute double differential cross sections (DDCS) are compared with the continuum distorted wave-eikonal initial state (CDW-EIS) model and the first Born approximation including correct boundary conditions (CB1). The measurements are carried out in the ejected e⁻-energy range of 1 eV–400 eV and in the angular range of 20°–160°. We have obtained the single differential and the total cross sections (TCSs) of e⁻-emission as well. The CB1 calculation largely underestimates the data. The CDW-EIS model, which is applied for the PAH molecule for the first time, provides an overall better agreement with the double differential, single differential and TCS data. The DDCS data for fluorene has also been compared with that for CH4 molecule, at a few angles. The forward–backward angular asymmetry shows a relatively flatter distribution compared to the theoretical predictions. The contribution due to the giant plasmon resonance could not be clearly observed except a mild indication in the asymmetry parameter. The angular distribution of the carbon KLL Auger electron cross section shows certain variations. The study of the KLL hyper-satellite component indicates the double K-ionization cross section is about 8.6% of the single K-ionization one.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1983

Nucleon and deuteron scattering cross sections from 25 MV/Nucleon to 22.5 GeV/Nucleon

Within the context of a double-folding optical potential approximation to the exact nucleus-nucleus multiple-scattering series, eikonal scattering theory is used to generate tables of nucleon and deuteron total and absorption cross sections at kinetic energies between 25 MeV/nucleon and 22.5 GeV/nucleon for use in cosmic-ray transport and shielding studies. Comparisons of predictions for nucleon-nucleus and deuteron-nucleus absorption and total cross sections with experimental data are also made.

Townsend, L. W.↗
DOE OSTI2020

Helicity-dependent extension of the McLerran–Venugopalan model

We construct a generalization of the McLerran-Venugopalan (MV) model including helicity effects for a longitudinally polarized target (a proton or a large nucleus). The extended MV model can serve as the initial condition for the helicity generalization of the JIMWLK evolution equation constructed in our previous paper, as well as for calculation of helicity-dependent observables in the quasi-classical approximation to QCD.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Considering nonlocality in the optical potentials within eikonal models

Background: For its simplicity, the eikonal method is the tool of choice to analyze nuclear reactions at high energies (E > 100 MeV/nucleon), including knockout reactions. However, so far, the effective interactions used in this method are assumed to be fully local. Purpose: Given the recent studies on nonlocal optical potentials, in this work we assess whether nonlocality in the optical potentials is expected to impact reactions at high energies and then explore different avenues for extending the eikonal method to include nonlocal interactions. Method: We compare angular distributions obtained for nonlocal interactions (using the exact R-matrix approach for elastic scattering and the adiabatic distorted wave approximation for transfer) with those obtained using their local-equivalent interactions. Results: Our results show that transfer observables are significantly impacted by nonlocality in the high-energy regime. Because knockout reactions are dominated by stripping (transfer to inelastic channels), nonlocality is expected to have a large effect on knockout observables too. Three approaches are explored for extending the eikonal method to nonlocal interactions, including an iterative method and a perturbation theory. Conclusions: None of the derived extensions of the eikonal model provide a good description of elastic scattering. Here, this paper suggests that nonlocality removes the formal simplicity associated with the eikonal model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗