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NASA NTRS1995

Comparison of exact solution with Eikonal approximation for elastic heavy ion scattering

A first-order optical potential is used to calculate the total and absorption cross sections for nucleus-nucleus scattering. The differential cross section is calculated by using a partial-wave expansion of the Lippmann-Schwinger equation in momentum space. The results are compared with solutions in the Eikonal approximation for the equivalent potential and with experimental data in the energy range from 25A to 1000A MeV.

Dubey, Rajendra R.↗

NASA NTRS1981

Eikonal approximation for charge transfer from a multielectron atom to fast projectiles

The eikonal approach developed previously for calculating electron-capture cross sections for bare projectiles colliding with hydrogenic targets is extended here to allow for multielectron targets. Both the impact and wave pictures are employed and their equivalence is discussed. As a first approximation, each atomic orbital is specified by the three hydrogenic quantum numbers, an effective nuclear charge Z sub t, and an energy eigenvalue in the impact picture, or ionization potential in the wave picture. The Z sub t prime appearing in the eikonal phase factor is left undetermined because of incomplete information on the many-body target. However, analytic expressions are derived for the theoretical cross sections, and numerical values are calculated for simple choices of Z sub t prime. Those results are compared with existing experimental data for C, Ne, Ar, N2, O2, and He targets.

Ho, T. S.↗

NASA NTRS1983

Heavy-ion total and absorption cross sections above 25 MeV/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 heavy ion total and absorption cross sections at incident kinetic energies above 25 MeV/nucleon for use in cosmic ray high-energy heavy ion transport and shielding studies. Comparisons of predictions with nucleus-nucleus experimental data show excellent agreement except at the lowest energies, where the eikonal approximation may not be completely valid. Even at the lowest energies, however, agreement is typically within 20 percent.

Townsend, L. W.↗

NASA NTRS1976

Multiplicity dependence of transverse momentum in hadronic collisions

The process of secondary-particle emission in hadron-hadron collisions is analytically studied using a simple model of hadron structure. The model neglects the 'size' of the hadron constituents, considering a hadron as a continuous distribution of matter according to a step function of radius R. A version of the eikonal approximation is applied to derive the relative probability for interaction and emission of secondaries when the impact parameter b is smaller than 2R. On the basis of these assumptions, and using the uncertainty relation, an empirical parameterization is obtained for the dependence of the transverse momentum of charged secondaries on their multiplicity in the case of high-energy proton-proton collisions. Comparison with experimental data at 28 GeV/c yields agreement to within about 3%. The analysis shows that at a fixed beam momentum, the transverse momentum decreases with increasing multiplicity, and that for a given multiplicity, the transverse momentum exhibits a slow increase with beam momentum.

Saint Amand, J.↗

NASA NTRS1982

Phenomenological optical potential analysis of proton-carbon elastic scattering at 200 MeV

Differential cross sections for 200 MeV protons elastically scattered from C-12 were analyzed utilizing a local, complex, spin-dependent optical potential with a harmonic well radial dependence. Analyses were performed using the WKB and eikonal approximations. For the latter, first-order corrections to he phase shifts were incorporated to account for the spin-orbit contribution. Large disagreement between theory and experiment was observed when the usual Thomas form for the spin-orbit potential was utilized. Substantial improvement was obtained by allowing the parameters in the central and spin-orbit potential terms to vary independently.

Bidasaria, H. B.↗

NASA NTRS1985

Identification and properties of molecular systems of potential use in solar-pumped lasers

The concepts and computational tools of theortical chemistry are used to investigate molecular properties needed in direct solar-pumped lasers. Compounds of the type RR'CXY, with R and R' organic groups, and X and Y halide atoms were identified as likely candidates because of their highly enhanced absorption coefficients over compounds with a single halide atom. The use of a combination of vibrational excitation followed by electronic excitation to enhance quantum yields at certain wavelengths is indicated. A self-consistent eikonal approximation to state-to-state transitions was tested for CH3I and is useful for other problems involving electronic energy and charge transfer. An approach to calculate potential energy surfaces and transition dipoles was developed which is based on the generation of eigenstates of the nonrelativisitc Hamiltonian followed by incorporation of the spin-orbit coupling by configuration interaction.

Micha, D. A.↗

NASA NTRS1987

Ponderomotive stabilization of flute modes in mirrors Feedback control and numerical results

Ponderomotive stabilization of rigid plasma flute modes is numerically investigated by use of a variational principle, for a simple geometry, without eikonal approximation. While the near field of the studied antenna can be stabilizing, the far field has a small contribution only, because of large cancellation by quasi mode-coupling terms. The field energy for stabilization is evaluated and is a nonnegligible fraction of the plasma thermal energy. A new antenna design is proposed, and feedback stabilization is investigated. Their use drastically reduces power requirements.

Similon, P. L.↗

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 NTRS1993

Geometric model from microscopic theory for nuclear absorption

A parameter-free geometric model for nuclear absorption is derived herein from microscopic theory. The expression for the absorption cross section in the eikonal approximation, taken in integral form, is separated into a geometric contribution that is described by an energy-dependent effective radius and two surface terms that cancel in an asymptotic series expansion. For collisions of light nuclei, an expression for the effective radius is derived from harmonic oscillator nuclear density functions. A direct extension to heavy nuclei with Woods-Saxon densities is made by identifying the equivalent half-density radius for the harmonic oscillator functions. Coulomb corrections are incorporated, and a simplified geometric form of the Bradt-Peters type is obtained. Results spanning the energy range from 1 MeV/nucleon to 1 GeV/nucleon are presented. Good agreement with experimental results is obtained.

John, Sarah↗

NASA NTRS1993

Geometric model for nuclear absorption from microscopic theory

A parameter-free geometric model for nuclear absorption is derived from microscopic theory. The expression for the absorption cross section in the eikonal approximation taken in integral form is separated into a geometric contribution, described by an energy-dependent effective radius, and two surface terms which are shown to cancel in an asymptotic series expansion. For collisions of light nuclei, an expression for the effective radius is derived using harmonic-oscillator nuclear density functions. A direct extension to heavy nuclei with Woods-Saxon densities is made by identifying the equivalent half density radius for the harmonic-oscillator functions. Coulomb corrections are incorporated and a simplified geometric form of the Bradt-Peters type obtained. Results spanning the energy range of 1 MeV/nucleon to 1 GeV/nucleon are presented. Good agreement with experimental results are obtained.

John, S.↗

NASA NTRS2002

A Discontinuous Galerkin Discretization of the Eikonal Equation on Curved Piecewise Isoparametric Triangulated Manifolds

This viewgraph presentation provides information on optimizing the travel distance between two points on a curved surface. The presentation addresses the single source shortest path problem, fast algorithms for estimating the eikonal equation, fast schemes and barrier theorems, and the discontinuous Galerkin method, including hyperbolic causality, finite element method, scalars, and marching the discontinuous Galerkin Eikonal approximation.

Barth, TIm↗

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.↗

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.↗

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.↗