Total Differential Scattering Cross Sections Research Articles

Regge pole description of scattering of gravitational waves by a Schwarzschild black hole

We revisit the problem of plane monochromatic gravitational waves impinging upon a Schwarzschild black hole using complex angular momentum techniques. By extending our previous study concerning scalar and electromagnetic waves [A. Folacci and M. Ould El Hadj, Phys.\, Rev.\, D {\bf 99}, 104079, (2019), arXiv:1901.03965], we provide complex angular momentum representations and Regge pole approximations of the helicity-preserving and helicity-reversing scattering amplitudes and of the total differential scattering cross section. We show, in particular, that for high frequencies (i.e., in the short-wavelength regime), a small number of Regge poles permits us to describe numerically with very good agreement the black hole glory and the orbiting oscillations and we then provide a semiclassical approximation that unifies these two phenomena.

Laser-assisted electron scattering on a nano-sphere

We investigate the scattering of electrons on a hard sphere in the presence of a laser field of arbitrary intensity. We use spherical Gordon–Volkov states, and we present a novel method for the computation of a key quantity in this theory. We compute and analyze some additional results regarding the total differential scattering cross sections in the case of the weak field limit.

Inelastic scattering of electrons at real metal surfaces

A theory is presented to calculate the electron inelastic scattering cross section for a moving electron near the surface region at an arbitrary takeoff angle. The theory is based on using a bulk plasmon-pole approximation to derive the numerically computable expression of the electron self-energy in the random-phase approximation for a surface system, through the use of experimental optical constants. It is shown that the wave-vector-dependent surface dielectric function satisfies the surface sum rules in this scheme. The theory provides a detailed knowledge of electron self-energy depending on the kinetic energy, distance from surface, and velocity vector of an electron moving in any metal of a known dielectric constant, accommodating the formulation to practical situation in surface electron spectroscopies. Numerical computations of the energy-loss cross section have been made for Si and Au. The contribution to the total differential scattering cross section from each component is analyzed. The depth dependence informs us in detail how the bulk excitation mode changes to a surface excitation mode with an electron approaching the surface from the interior of a medium.

Potential Energy Surfaces for Unsaturated Hydrocarbons from Crossed Molecular Beams

The total differential scattering cross sections for several important unsaturated hydrocarbon molecules with common atmospheric gases were measured in a crossed molecular beam apparatus. The experiments show quantum interferences which relate to potential energy surface parameters, such as the well depth and radial minimum. The damping of the quantum features, over contributions from experimental resolutions, provides information on the angular and radial anisotropies present in the potential energy surfaces. We have investigated two areas: (1) the role of the probe partner in determining the interaction strength for a given hydrocarbon target, and (2) the effect of increasing the overall length of the hydrocarbon molecule for a fixed probe. By comparing results for a class of scattering systems, we can identify chemical and physical trends that determine the van der Waals potential energy surfaces of larger molecules. We expect these results to aid in the prediction and interpretation of complementary experimental measurements on the high resolution infrared spectroscopy of weakly bound complexes.

Ab initio and scaled potential energy surfaces for Ar–C2H2: Comparison with scattering and spectroscopic experiments

New coupled-cluster ab initio potential energy surfaces (PES’s) were determined for the interaction of Ar with a rigid acetylene molecule. These PES’s were in addition modified by scaling the correlation energy. Based on both the original and scaled PES’s, close-coupled calculations of the total differential scattering cross section were carried out. Rovibrational energy levels of the Ar–C2H2 complex were computed variationally. In addition, we simulated the ir spectra corresponding to excitation of the upper diad of the ν3/ν2+ν4+ν5 excited molecular vibrational states. The comparison of all these quantities with experiment shows generally good agreement for the several scaled PES’s. In addition, the sensitivity of the PES to the experimental data are investigated by varying the scaling factor. The original and scaled PES’s are also compared with several phenomenological PES’s and a previously published ab initio PES [F.-M. Tao, S. Drucker, and W. Klemperer, J. Chem. Phys. 102, 7289 (1995)].

An improved potential energy surface of Ar–C2H2

The intermolecular interaction of the Ar–C2H2 system was investigated using the coupled-states approximation to analyze the scattering process at a collision energy of 649.5 cm−1 (80.5 meV) and a close-coupling method to predict bound state energy levels. In both cases, the acetylene molecule is treated as a rigid rotor. A primary rainbow peak observed in the total differential scattering experiment provides useful information on the well depth while dimer rotational frequencies give accurate information on the shape around the minimum of the ground state potential. Four existing potentials for the system were tested against the total differential scattering cross section and rotational spectroscopic measurements. No one potential showed good agreement with both measurements. An improved potential energy surface was obtained by fitting simultaneously both scattering and spectroscopic data.

The anisotropic potential energy surfaces of H2, N2, and Ar with C2H2 from total differential scattering experiments

The total differential scattering cross sections for H2, N2, and Ar with C2H2 were measured on an in-plane crossed molecular beam apparatus at collision energies of 1051, 1056, and 929 K, respectively. Well resolved rainbow oscillations for N2 and Ar, and diffraction oscillations for H2, showed two interference effects. Effective spherical and anisotropic potentials were obtained from analysis using single channel and infinite-order-sudden (IOS) methods, based on the semiclassical Jeffreys–Wentzel–Kramers–Brillouin (JWKB) approximation. The damping of oscillations showed the importance of anisotropy in the pair potentials. Total differential scattering cross sections calculated using the IOS method were in excellent agreement with the experimental data.

Screened Rutherford backscattering cross sections for heavy ion and low energy backscattering analysis

The energy dependence of the total differential scattering cross section of 20–180 keV H +, D + and He + ions, as well as 100–350 keV C 2+ and O 2+ ions, backscattered through a laboratory angle of 161.2° by monolayer-thick Au targets was measured. The ratio of the measured cross section to the Rutherford cross section ranged from 0.91 for 180 keV H 4 to 0.44 for 100 keV O 2+. The results were found to be in excellent agreement with exact classical calculations of the scattering cross section performed using Dirac-Fock atomic potentials. A comprehensive review of all previous measurements of the screened Rutherford backscattering cross section has been performed for comparison with the present results.

Classical trajectory calculation of transport and relaxation properties for N2–Ne mixtures

A detailed comparison of the predictive powers of two recently determined potential energy surfaces [J. Chem. Phys. 88, 5465 (1988); 89, 3505 (1988)] for the N2–Ne interaction has been carried out. In particular, the following has been tested: calculations using these two surfaces against experimental values of the total differential scattering cross section at 75.8 meV, the temperature dependence of the interaction second virial coefficient over the range 90 K to 323 K, the temperature dependence of the binary diffusion coefficient and the mixture viscosity over the range 280 K to 973 K, the mixture thermal conductivity at 300 K, and viscosity and thermal conductivity field-effects, rotational relaxation, and collision-broadening of the depolarized Rayleigh line over a restricted temperature range. Forty-five effective cross sections that determine the bulk transport and relaxation phenomena have been calculated by classical trajectory methods for temperatures varying from 77.5 K to 973 K. Second-approximation calculations of the mixture transport phenomena using these calculated cross sections give impressive agreement with the experimental results over a wide temperature range for both potential surfaces. While one potential gives better agreement with the scattering data, the second virial coefficient data, the bulk transport data, and the depolarized Rayleigh collision-broadening data than does the other potential, the opposite is true for the rotational relaxation and field-effect data.

A study of molecular correlations observed in the small-angle photon scattering distributions of 60 keV photons interacting with low-atomic-number media

A variant of the multisection filter and annular target geometry, with a designed angular acceptance of ±0.5°, has been utilised in measuring accurate. O(5%), absolute total differential scattering cross sections of 60 keV photons for H 2O, methyl methacrylate (C 5H 8O 2) n and nylon-6 (C 12H 22O 3N 2) n in the angular scattering range of 2°–10°. The effects of molecular correlations manifest, to varying degree, in strong forward peaking of the scattered photon distribution. Comparison is made with available experiment and theory.

Total differential scattering cross section of Ar +-Ar at 15 to 400 keV

We report on the measurement of the total differential scattering cross section of Ar +-Ar at laboratory energies between 15 and 400 keV. Using an ab initio relativistic molecular program which calculates the interatomic potential energy curve with high accuracy, we are able to reproduce the detailed structure found in the experiment.

Total differential scattering cross sections for hydrogen scattered from nitrogen and hydrogen fluoride

In-plane total differential scattering cross sections for H2 scattered from N2 and HF are reported. The data are analyzed in terms of spherical and anisotropic potentials using single channel and IOS methods for calculating the differential cross sections. In the case of H2/HF the diffraction oscillations are highly damped at small angles, suggesting that the anisotropy is large.

The methane-methane total differential scattering cross section

An in-plane crossed molecular beam apparatus has been used to measure the methane-methane total differential scattering cross section. A clearly resolved rainbow oscillation enables an effective isotropic well depth to be determined rather accurately. The data is analysed using a number of spherical and anisotropic potential functions and is also fitted to an analytic semiempirical spherical model. None of the potentials currently in the literature give scattering cross sections and second virial coefficients which are in good agreement with experimental data.

A spherical potential for hydrogen from solid state and scattering data

Calculations of the ground state energy and pressure of solid hydrogen, and of the total differential scattering cross section for D2+H2, are used to assess existing isotropic potentials for the hydrogen pair interaction. Although several of the models give consistent results in the region of the potential minimum, they differ significantly at short distances. A comparison with solid state and scattering data indicates that ab initio calculations are in error and that there is a lack of consistency between this data and second virial coefficient measurements. The results are used to recommend a potential surface that is consistent with the experimental data.

A comparison of the predictions of various model N2–He potential energy surfaces with experiment

Predictions of beam scattering and bulk gas phenomena based upon five different model potential energy surfaces for the N2–He system are compared with experiment. The surfaces considered are our recent HFD1 and HFD2 surfaces based on the Hartree–Fock plus damped dispersion (HFD) model, the surface of Habitz, Tang, and Toennies (HTT) based upon the Tang–Toennies model, the surface of Keil, Slankas, and Kuppermann (KSK) and a modification (KKM3) of the KSK surface. The physical observables against which these surfaces are tested include total differential scattering cross sections, state-to-state inelastic differential scattering cross sections, interaction second virial coefficients, shear viscosity and binary diffusion coefficients, and the relaxation cross section for the Senftleben–Beenakker effect on the shear viscosity. None of the surfaces is in complete agreement with all of these observables. For the interaction second virial coefficients, the shear viscosity and binary diffusion coefficients, the HFD1 surface is the only one to predict values within most of the experimental error bars. The relaxation cross section is correctly predicted only by the KKM3 surface which was essentially fitted to it. The HFD1, HFD2, and HTT surfaces are all in good agreement with the state-to-state inelastic cross sections. The KSK surface gives the best agreement with the total differential cross section. It appears that an accurate N2–He surface cannot be obtained from simple models, and its determination will require multiproperty fits.

Elastic differential cross sections for small-angle scattering of 25-, 50-, and 100-keV protons by helium atoms

The first measurements of elastic differential cross sections have been carried out for 25-, 50-, and 100-keV protons scattered through very small angles by helium atoms. The University of Missouri\char22{}Rolla energy-loss spectrometer provided the required high angular resolution and also separated the elastically scattered ions from the inelastically scattered ions. The data are compared to our Born, Glauber, and classical calculations as well as a four-state calculation. All of the measured elastic differential cross sections are more sharply peaked than theory for the smallest scattering angles. At the larger scattering angles all of the measured elastic differential cross sections are below the theoretical calculations. However, if the classical calculation is interpreted as a total differential scattering cross section, it compares well with our estimate of the sum of the elastic, charge-transfer, and inelastic differential cross sections.

Total differential scattering cross sections for ArHCl

The total differential cross sections for AlHC1 are measured. A coupled state calculation was performed to find a potential surface to reproduce the measured data.(AIP)

Experimental study of effective interatomic potentials

Total differential scattering cross sections for ion-atom collisions are measured and compared with predictions from various interatomic potentials. Ions with atomic numbers $6\ensuremath{\le}{Z}_{1}\ensuremath{\le}54$ and energies 2.5-400 keV are scattered by xenon through 1-6\ifmmode^\circ\else\textdegree\fi{}. For closest separations, $\ensuremath{\le}1.5{a}_{0}$, the scattering behaves nearly elastically with universal scaling properties, and individual statistical potentials give successful predictions including peak structures. For larger separations a strong ${Z}_{1}$ dependence appears and statistical potentials fail.

Effect of molecular anisotropy on beam scattering measurements

Within the energy sudden approximation the total integral and total differential scattering cross sections are given by the angle average of scattering cross sections computed at fixed rotor orientations. Using this formalism we have examined the effect of molecular anisotropy on scattering of He by HCl and by CO. Comparisons with accurate close coupling calculations indicate that this approximation is quite reliable, even at very low collision energies, for both of these systems. Comparisons are also made with predictions based on the spherical average of the interaction. For HCl the anisotropy is rather weak and its main effect is a slight quenching of the oscillations in the differential cross sections relative to predictions of the spherical averaged potential. For CO the anisotropy is much stronger, so that the oscillatory pattern is strongly quenched and somewhat shifted. It appears that the sudden approximation provides a simple yet accurate method for describing the effect of molecular anisotropy on scattering measurements.

Experimental Determination of the Charge Density of the Bond-Forming Electrons inN2

High-precision total differential scattering cross sections for 40-keV electrons incident on N/sub 2/ have been measured. In order to observe binding effects in the scattering cross sections, the data have been compared to a theoretical set of intensities based on scattering from noninteracting nitrogen atoms placed in the proper geometric relation. The resulting difference function has been Fourier transformed according to the procedures described by Kohl and Bartell. The charge-density-difference map which is the result of this deconvolution process is compared with the Hartree-Fock model. (AIP)