Integral Scattering Cross Sections Research Articles

Integral Electron Scattering Cross Sections from N2O for Impact Energies Ranging from 1 to 1000 eV.

Accurate total cross sections (TCS), within 5%, for electron scattering by N2O molecules have been measured with a magnetically confined electron transmission apparatus for impact energies ranging from 1 to 200 eV. For higher energies, these measurements have been complemented with our independent atom-based screening corrected additivity rule, including interference (IAM-SCAR + I) method to determine a complete reference TCS data set in the energy range (1-1000 eV). After a critical discussion that includes our calculated integral elastic and ionization cross sections and the theoretical and experimental data available in the literature, a complete set of integral elastic and inelastic (rotational, vibrational, and electronic excitation, ionization and electron attachment) cross sections, consistent with the reference TCS data, have been derived. This update on the N2O collisional database may help to improve the accuracy of radiation-induced transport models.

Potential energy surface and quantum dynamics calculation of SH2− (2A′) based on ab initio scaled external correlation correction

An accurate interatomic potential energy surface for ground state of SH2− is reported at the multireference configuration interaction level of theory using aug–cc–pVQZ basis set. The calculated ab initio energy points are utilized, after semi-empirically correcting the dynamical correlation by the many-body expansion-scaled external correlation method. To verify the accuracy of the potential energy surface, molecular reaction dynamics, including the relationship between reaction probability and collision energy, thermal rate constant, and integral scattering cross section are calculated by using the quantum time-dependent wave packet method. The final results show that our potential energy surface is accurate and the molecular reaction dynamics results are satisfactory, and the accurate potential energy surface and its dynamics results can also lay a foundation for the future experimental research of SH−-containing molecules.

Accurate time-dependent wave packet calculation for the reaction of Al(2P) + H2[formula omitted] on the AlH2(12A′) surface

The time-dependent wave packet calculation of the Al(2P) + H2X1∑g+ → H(2S) + AlHX1∑+(X1Σ+) reaction is studied on the precise global potential energy surface of AlH2(12A′). The collision energy dependence of reaction probabilities under different total angular momentum is discussed detailedly. The emphasis is on the exploration of different dynamical behaviors calculated by Coriolis coupling and centrifugal sudden approximation, which makes integral scattering cross section calculated by Coriolis coupling has a smaller oscillation intensity clearly. Moreover, the reaction is enhanced strongly by vibration excitation of H2 molecule but only weakly by rotation excitation due to the late barrier.

Absolute Differential Cross-Sections for Elastic Electron Scattering from Sevoflurane Molecule in the Energy Range from 50-300 eV.

We report the results of the measurements and calculations of the absolute differential elastic electron scattering cross-sections (DCSs) from sevoflurane molecule (C4H3F7O). The experimental absolute DCSs for elastic electron scattering were obtained for the incident electron energies from 50 eV to 300 eV, and for scattering angles from 25° to 125° using a crossed electron/target beams setup and the relative flow technique for calibration to the absolute scale. For the calculations, we have used the IAM-SCAR+I method (independent atom model (IAM) applying the screened additivity rule (SCAR) with interference terms included (I)). The molecular cross-sections were obtained from the atomic data by using the SCAR procedure, incorporating interference term corrections, by summing all the relevant atomic amplitudes, including the phase coefficients. In this approach, we obtain the molecular differential scattering cross-section (DCS), which, integrated over the scattered electron angular range, gives the integral scattering cross-section (ICS). Calculated cross-sections agree very well with experimental results, in the whole energy and angular range.

Complete Quantum Coherent Control of Ultracold Molecular Collisions.

We show that quantum interference-based coherent control is a highly efficient tool for tuning ultracold molecular collision dynamics that is free from the limitations of commonly used methods that rely on external electromagnetic fields. By varying the relative populations and phases of initial coherent superpositions of degenerate molecular states, we demonstrate complete coherent control over integral scattering cross sections in the ultracold s-wave regime of both the initial and final collision channels. The proposed control methodology is applied to ultracold O_{2}+O_{2} collisions, showing extensive control over s-wave spin-exchange cross sections and product branching ratios over many orders of magnitude.

Proton and Hydrogen Transport through Hydrogen Environments: Ionization and Stripping

Abstract Data are presented over a wide range of impact energies describing the ionization or stripping probability, projectile energy loss, and ejected electron and recoiling target energies and angles for proton and hydrogen passage through hydrogen astrophysical environments. These kinematic and reaction data are tabulated at three levels of detail for use in heavy-particle (H+, H) and secondary-electron transport simulations: (1) the integral scattering cross section and average values of the distributions of energy and angle of the particles, (2) the singly differential cross sections as a function of particle energy and angle, and (3) a subset of the many possible doubly differential cross sections as functions of the particle energy and angle chosen to be most relevant to transport simulations.

Corrections to the Thomson cross section caused by relativistic effects and by the presence of the drift velocity of a classical charged particle in the field of a monochromatic plane wave

An approach to the solution of the relativistic problem of the motion of a classical charged particle in the field of a monochromatic plane wave with an arbitrary polarization (linear, circular, or elliptic) is proposed. It is based on the analysis of the 4-vector equation of motion of the charged particle together with the 4-vector and tensor equations for the components of the electromagnetic field tensor of a monochromatic plane wave. This approach provides analytical expressions for the time-averaged square of the 4-acceleration of the charge, as well as for the averaged values of any quantities periodic in the time of the reference frame. Expressions for the integral power of scattered radiation, which is proportional to the time-averaged square of the 4-acceleration of the charge, and for the integral scattering cross section, which is the ratio of the power of scattered radiation to the intensity of incident radiation, are obtained for an arbitrary inertial reference frame. An expression for the scattering cross section, which coincides with the known results at the circular and linear polarizations of the incident waves and describes the case of elliptic polarization of the incident wave, is obtained for the reference frame where the charged particle is on average at rest. An expression for the scattering cross section including relativistic effects and the nonzero drift velocity of a particle in this system is obtained for the laboratory reference frame, where the initial velocity of the charged particle is zero. In the case of the circular polarization of the incident wave, the scattering cross section in the laboratory frame is equal to the Thompson cross section.

Electron impact excitation of helium in Debye plasma

The probability, differential, and integral scattering cross sections of the 11S→21S and 11S→21P transitions of helium have been calculated in the first Born approximation. The projectile-target interactions depending on the temperature and the density of plasma are described by the Debye-Hückel model. Wave functions of the target before and after collision were modeled by non orthogonal Hartree-Fock orbitals. The wave functions parameters are calculated with the Ritz variational method. We improve our unscreened first Born approximation integral cross sections by using the BE-scaled (B stands for binding energy and E excitation energy) method. The second Born approximation has also been used to calculate the excitation cross sections in Debye plasma. Our calculations are compared to other theoretical and experimental results where applicable.

Electron scattering cross sections from anthracene over a broad energy range (0.00001–10,000 eV)

We report a computational investigation of electron scattering by anthracene (C14H10) in the gas phase. Integral and differential cross sections have been calculated by employing two distinct ab-initio quantum scattering methods: the symmetry adapted–single centre expansion method (ePOLYSCAT) and a screening corrected form of the independent atom model (IAM–SCAR) at low and high energies, respectively. After a detailed evaluation of the current results, we present a complete set of integral scattering cross sections from 0.00001 to 10,000eV.

Integral and Momentum Cross Sections for Electron Elastic and Vibrational Excitation Scattering with Nitrogen in the Energy Range 5–30 eV

Integral and momentum transfer cross sections are calculated in the energy range from 5 to 30 eV and compared with other calculated and measured data. The overall agreement between our present results and various theoretical and experimental results are obtained. The present results are obtained by solving integrodifferential body-frame vibrational close-coupling equations. Distributed spherical Gaussian correlation-polarization model potentials with high-order terms and exact exchange effects in a single-configuration Slater determinant are used. The analytic Born completion method is also used to calculate high-order scattering matrix elements.

Elastic electron scattering from the antimony atom in the spin-polarized optical potential approach

This is the first theoretical study of elastic scattering of electrons on antimony atoms in a broad range of low and intermediate collision energies from 0.1 eV to 1 keV. A complex optical potential (OP) in the spin-polarized approximation is used for the calculation of differential (DCSs) and integral scattering cross sections as well as a spin exchange asymmetry parameter. It is shown that for this atom the spin dependence of not only exchange interaction, but also polarization interaction should be taken into account at the asymmetry calculation. Two types of absorption potential are used: a non-empirical potential within the quasi-free electron scattering approximation and a McCarthy-type empirical potential. The calculations are also performed without taking account of absorption effects, i.e. in the approximation of solely the parameter-free real part of the OP. Characteristics of the antimony atom and spin correlation–polarization potentials are found using the local spin density approximation. Energy and angular positions of 11 critical minima in the DCSs are found. The highest energy minimum among them is located at [663.2 eV; 132.02°]. In the angular vicinities of the critical minima, spin polarization parameters, the Sherman function S(θ) and the U(θ) function are calculated. The present DCSs and S(θ) are compared with other available theoretical and experimental data.

Collisions of paramagnetic molecules in magnetic fields: An analytic model based on Fraunhofer diffraction of matter waves

We investigate the effects of a magnetic field on the dynamics of rotationally inelastic collisions of open-shell molecules ($^{2}\ensuremath{\Sigma}$, $^{3}\ensuremath{\Sigma}$, and $^{2}\ensuremath{\Pi}$) with closed-shell atoms. Our treatment makes use of the Fraunhofer model of matter wave scattering and its recent extension to collisions in electric [M. Lemeshko and B. Friedrich, J. Chem. Phys. 129, 024301 (2008)] and radiative fields [M. Lemeshko and B. Friedrich, Int. J. Mass. Spec. 280, 19 (2009)]. A magnetic field aligns the molecule in the space-fixed frame and thereby alters the effective shape of the diffraction target. This significantly affects the differential and integral scattering cross sections. We exemplify our treatment by evaluating the magnetic-field-dependent scattering characteristics of the He-CaH $(X\phantom{\rule{0.2em}{0ex}}^{2}\ensuremath{\Sigma}^{+})$, He-${\mathrm{O}}_{2}$ $(X\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{--})$, and He-OH $(X\phantom{\rule{0.2em}{0ex}}^{2}\ensuremath{\Pi}_{\ensuremath{\Omega}})$ systems at thermal collision energies. Since the cross sections can be obtained for different orientations of the magnetic field with respect to the relative velocity vector, the model also offers predictions about the frontal-versus-lateral steric asymmetry of the collisions. The steric asymmetry is found to be almost negligible for the He-OH system, weak for the He-CaH collisions, and strong for the He-${\mathrm{O}}_{2}$. While odd $\ensuremath{\Delta}M$ transitions dominate the He-OH $[J=3∕2,f\ensuremath{\rightarrow}{J}^{\ensuremath{'}},e/f]$ integral cross sections in a magnetic field parallel to the relative velocity vector, even $\ensuremath{\Delta}M$ transitions prevail in the case of the He-CaH $({X}^{2}{\ensuremath{\Sigma}}^{+})$ and He-${\mathrm{O}}_{2}$ $(X\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{\ensuremath{-}})$ collision systems. For the latter system, the magnetic field opens inelastic channels that are closed in the absence of the field. These involve the transitions $N=1,J=0\ensuremath{\rightarrow}{N}^{\ensuremath{'}}$, ${J}^{\ensuremath{'}}$ with ${J}^{\ensuremath{'}}={N}^{\ensuremath{'}}$.

Absolute Electron Scattering Cross Sections for theCF2Radical

Using a crossed electron-molecular beam experiment, featuring a skimmed nozzle beam with pyrolytic radical production, absolute elastic cross sections for electron scattering from the CF2 molecule have been measured. A new technique for placing measured cross sections on an absolute scale is used for molecular beams produced as skimmed supersonic jets. Absolute differential cross sections for CF2 are reported for incident electron energies of 30-50 eV and over an angular range of 20-135 deg. Integral cross sections are subsequently derived from those data. The present data are compared to new theoretical predictions for the differential and integral scattering cross sections, as calculated with the Schwinger multichannel variational method using the static-exchange and static-exchange plus polarization approximations.

The resonance structures in the cross sections of slow electron interaction with barium atoms: a fully relativistic R-matrix study

A 23-state close-coupling calculation on the slow electron interaction with barium atoms is carried out by using a fully relativistic R-matrix method. The results for the slow electron scattering and photodetachment of the negative atomic barium ions are presented. An apparent relativistic fine-structure split is produced for both the bound states of the negative ion and the shape resonance states of the free electron. The electron affinities for the 6s26p2Po3/2 level and the 6s26p2Po1/2 level are obtained to be 183 meV and 240 meV, respectively. The 57 meV fine-structure split of the 6p orbital is very close to the experimental value. The fine-structure split of the d-wave shape resonance above the elastic threshold is predicted to be 31 meV. The calculated integral scattering cross sections from 0 to 10 eV show that including the relativistic effects cannot eliminate the large discrepancies between theory and the existing experiment.

Very low energy electron scattering in nitromethane, nitroethane, and nitrobenzene

Absolute total integral and total backward scattering cross sections are reported for CH 3 NO 2 , C 2 H 5 NO 2 , and C 6 H 5 NO 2 at electron-impact energies from 30 meV to several eV, with some additional data at higher energies. These experimental data extend the range of species studied in low-energy electron scattering to include target molecules with dipole moments large enough to support dipole-bound states. Data provide a further test of the validity of the Born point-dipole approximation for the calculation of rotationally inelastic scattering cross sections for polar molecules, which are of importance in modeling the chemical and physical characteristics of industrial and natural plasmas. For CH 3 NO 2 and C 2 H 5 NO 2 , large cross sections are found, monotonically increasing with decreasing electron energy in qualitative and to some degree quantitative agreement with theory based on the Born model. As in earlier studies other polar species, the Born model is found to underestimate significantly backward-scattering cross sections. C 6 H 5 NO 2 shows a powerful dip in the total integral scattering cross sections <200 meV, a feature not found in the backward-scattering cross section and totally at variance with any simple theory. The suggestion is made that this behavior, in common with ClO 2 and Cl 2 O, may arise through interference between direct Born-type rotational excitation and an indirect channel involving temporary negative ion states in the continuum.

Very low energy electron scattering in C6H5F, C6H5Cl, C6H5Br and C6H5I

Integral and backward scattering cross sections are reported for the scattering of electrons from C6H5F, C6H5Cl, C6H5Br and C6H5I over the energy range between 10 and 20 meV to 10 eV. The measurements were made in transmission experiments using a synchrotron radiation photoionization apparatus with an energy resolution in the incident electron beam of ~3.5 meV (FWHM). The absolute accuracy of the cross sections is limited by experimental difficulties with respect to strong rotationally inelastic forward scattering, due to the dipolar nature of the target molecules. Integral scattering cross sections are found to rise to more than 1500 Å2 at the lowest energies in C6H5F, C6H5Cl and C6H5Br and to more than 2000 Å2 in C6H5I due to an additional contribution from electron attachment. At low energy, both integral and backward scattering cross sections are very similar in C6H5F, C6H5Cl and C6H5Br. Data are interpreted in terms of rotationally inelastic scattering, with values of cross sections essentially dictated by the correspondingly similar dipole moments (1.6-1.7 D) of these three species. The Born model for rotationally inelastic scattering consistently underestimates the experimental cross sections and overestimates the degree of forward scattering. Our data illustrate the limitations of the Born model for the estimation of low-energy scattering cross sections for plasma modelling.

Absolute Integral and Differential Cross Sections for the Reactive Scattering of H- + D2 and D- + H2

For the two reactions H- + D2 → D- + HD and D- + H2 → H- + HD, absolute integral and differential cross sections have been determined in a guided ion beam (GIB) apparatus. From the effective cross sections, measured in the translational energy range ET = 0.1−10 eV, thresholds for the onset of the reactions have been derived, indicating effective barrier heights of 350 ± 60 meV for H- + D2 and 330 ± 60 meV for D- + H2. These values are substantially lower than previously reported experimental and theoretical data. Comparison of the integral cross sections for the two isotopic variants reveals a significant isotope effect. The collision of the light ion with the heavy molecule leads to a cross section which is almost a factor of 2 smaller than for D- reacting with H2. Possible experimental effects discriminating D- versus H- are discussed. The recently reported differential cross section for H- + D2 which has been obtained with a crossed beam experiment is in good accordance with the present data determined with the GIB technique. A new result is that, at small collision energies, the angular dependence is very similar for both isotopic variants. In view of the quite large isotopic effect for the integral cross sections this is not self-evident. All these detailed results pose a challenge to full quantum dynamical scattering theory of the H3− collision system.

Leptoquark pair production in hadronic interactions

The scalar and vector leptoquark pair production cross sections in hadronic collisions are calculated. In a model independent analysis we consider the most general C and P conserving couplings of gluons to both scalar and vector leptoquarks described by an effective low-energy Lagangian which obeys SU(3)c invariance. Analytical expressions are derived for the differential and integral scattering cross sections including the case of anomalous vector leptoquark couplings, K G and ΛG, to the gluon field. Numerical predictions are given for the kinematic range of the TEVATRON and LHC. The pair production cross sections are also calculated for the resolved photon contributions to at HERA and LEP ⊗ LHC, and for the process at possible future e + e − linear colliders and γγ colliders. Estimates of the search potential for scalar and vector leptoquarks at present and future high energy colliders are given.

Summary of existing information on the incoherent scattering of photons, particularly on the validity of the use of the incoherent scattering function

X-ray scattering by individual atomic electrons is known as Compton scattering if the simplifying approximation is invoked that the target electrons are initially free and rest, in which case the differential and integral scattering cross sections can be computed using the compact analytical expressions given by Klein and Nishina in 1929. In real atoms the electrons are neither free nor at rest, resulting in departures from the Klein-Nishina expressions. These departures have been estimated theoretically in varying degrees of sophistication, with correspondingly varying degrees of ease in applying these corrections to the free electron model. At present the most widely used treatment of these departures is via the incoherent scattering function S( x, Z) in which x is a momentum transfer variable dependent on the incident photon energy and the scattered-photon deflection angle, and Z is the atomic number of the atom associated with the target electron. The incoherent scattering function S( x, Z) also enters into calculations of the cross section for electron-positron pair production in the fields of the atomic electrons, known also as triplet production. This report includes a historical survey of experimental and theoretical work on the Compton effect and on the incoherent scattering function. The validity of the use of the incoherent scattering function is examined and discussed.

Scattering of rotationally aligned oxygen molecules and the measurement of anisotropies of van der Waals forces.

Measurements are reported for the scattering of molecular oxygen with both a hot rotational energy distribution and cooled at its ground rotational state with a controlled alignment of the rotational angular momentum. The cooling and control of the alignment are achieved using supersonic expansion in beams of molecular oxygen seeded in various mixtures of Ne, He, and ${\mathrm{H}}_{2}$ and monitored by a Stern-Gerlach magnetic deflection technique. It is shown by the example of integral scattering cross section with Xe in the glory energy range that information can be obtained on the isotropic and anisotropic components of intermolecular van der Waals interactions.