Present Differential Cross Sections Research Articles

Spin polarization of electrons elastically scattered from cadmium and zinc

The authors present results for spin polarization parameters for the low-energy elastic scattering of electrons from cadmium and zinc atoms. The calculations were carried out by solving the Dirac equations for the scattered electrons. The scattering potential included the Dirac-Fock static potential for the atoms plus a non-relativistic polarization potential calculated via the polarized-orbital method. Exchange was treated exactly. The authors compare their results for the asymmetry function with recent experimental results. They also present differential cross sections in comparison with recent experimental and theoretical data for cadmium.

(e,2e) triple differential cross sections for the simultaneous ionization and excitation of helium

The authors present absolute triple differential cross sections (TDCS) measurements for ionization of helium leaving the ion in both n=1 and n=2 final states, obtained under asymmetric geometry at an incident energy approximately 5.5 keV and ejected electron energies of 5, 10 and 75 eV. The kinematics are chosen to correspond either to a constant ejection energy, or to a constant energy transfer to the target. Angular distributions are measured at both constant ejection angle ( theta a mode) and at constant scattering angle ( theta b mode). In the theta a mode experiments, the momentum transfer dependence of the n=2 triple differential generalized oscillator strength is investigated for the first time. In both modes, the n=2 angular distributions show several new features which are not present for the n=1 ones, and which tend to vanish as the ejected energy is increased. They are attributed to final state interactions between the ejected electron and the excited ion. Comparison with first-order theoretical models shows the inadequacy of a Coulomb wave representation of the ejected electron, while in the R-matrix formalism it is found that a five-state multichannel calculation qualitatively describes the shape (but not the amplitude) of the TDCS measured in the theta b mode. Comparison is also made with the photoionization in the dipolar limit where the momentum transfer approaches zero. When integrated over the ejection direction, the double differential generalized oscillator strength ratio for ionization to the n=1 and n=2 states is found to agree with an earlier first Born close coupling prediction.

Second-order approximations to laser-assisted charged-particle scattering.

Multiphoton free-free transitions within a full second-order treatment of the scattering potential are considered with two specific aims: (i) to test some widely used approximations against exact calculations; (ii) to present differential cross sections for the laser-assisted positron scattering, in the regime of intermediate field intensities (up to ${10}^{13}$ W/${\mathrm{cm}}^{2}$). In the case of a field linearly polarized along the incident particle momentum, the results clearly discriminate among the approximations, setting interesting limitations to each of them as functions of the scattering potential features and of the field parameters. Each approach shows good performance for particular scattering angle ranges, pointing to the need for improved techniques to work out fully reliable and easy-to-handle approximations.

Total (elastic plus inelastic) cross sections for electron scattering with argon and krypton atoms at energies 10-6000 eV

Total cross sections (elastic plus inelastic) are reported for electron-Ar and Kr scattering at energies 10-6000 eV. A model complex-optical-potential (COP) approach is employed in which the real and imaginary parts are expressed in terms of the target electron density. For the real part of the COP, the static potential is determined exactly at the Hartree-Fock level, the exchange potential is approximated in the free-electron-gas model and the polarisation effects are included via the parameter-free correlation polarisation potential. The imaginary part of the COP, i.e. the absorption potential, is a function of projectile energy, target charge density, mean excitation energy of the atom, and static and the exchange potential terms. The charge density of the atom is obtained accurately from the numerical self-consistent Hartree-Fock procedure. The complex potential scattering problem is solved exactly under the variable-phase-approach. Our total cross sections compare very well with the measured values at all energies considered here. We also present differential cross sections (DCS) with and without absorption effects. We found that absorption effects improve the elastic DCS at all energies above the excitation threshold.

Differential cross sections for the electron-impact excitation of He-like ions: 2 (1)S and 2 (1)P states.

Differential cross sections for the electron-impact excitation of ions are calculated and compared along the He-like isoelectronic sequence. A distorted-wave method is used to obtain the cross sections for the transitions 1 $^{1}2$ $^{1}S$ or 2 $^{1}P$ in ${\mathrm{Li}}^{+}$, ${\mathrm{O}}^{6+}$, and ${\mathrm{Si}}^{12+}$. To complete the systematic study, a comparison is also made to the cross sections for neutral He and in the limit Z\ensuremath{\rightarrow}\ensuremath{\infty} (Z being the nuclear charge). Dependence on the collision energy and comparisons to the cross sections obtained by other methods are discussed in detail. For the 2 $^{1}P$ excitation, an apparent generalized oscillator strength is derived for the ions using the present differential cross section. Their behavior is very different from the corresponding values of He.

Resonant vibrational excitation of N2 by electron impact in the 15-35 eV energy range

The authors present parameter-free differential and integral cross sections for the vibrational excitation of N2 by electron impact in the 15-35 eV range, which is dominated by a 2 Sigma u shape resonance. Their calculation is based on a static+exact exchange+local polarisation-correlation approximation of the electron-molecule interaction and on the adiabatic-nuclei approximation for the coupling with the nuclear motion.

The centrifugal sudden distorted wave method for calculating cross sections for chemical reactions: Angular distributions for Cl + HCl → ClH + Cl

We describe a method for calculating cross sections for atom plus diatom reactive collisions based on the centrifugal sudden distorted wave (CSDW) approximation. This method is nearly exact at low energies where reactive cross sections are small. Representative CPU times are given for applications of the CSDW method to the Cl + HCl → ClH + Cl reaction using CDC 7600, Cyber 176, Cyber 205, Cray X-MP and Cray-2 computers. We also present differential cross sections for the Cl + HCl reaction and apply a simple semiclassical model which relates these cross sections to the partial wave reaction probabilities, and to the energy dependence of the reaction probabilities for zero total angular momentum. This model explains why the differential cross sections are backward peaked, and why the oscillatory cross sections seen in earlier, more approximate infinite order sudden calculations are not found in the present results at low energy.

A complex phaseshift analysis for elastic scattering of 54.4 eV electrons from sodium

Elastic differential cross section data for 54.4 eV electrons scattered off sodium atoms have been obtained and then analysed by a complex phaseshift technique. Values of the total elastic, total reaction and complete total cross sections derived from the differential cross section are presented. The values of the total cross sections are consistent with what one would expect from experimental data and theoretical calculations. This is a strong indication that the present differential cross section is physically reasonable.

EBS triple differential cross sections for the coplanar asymmetric ionisation of H(2s) by fast electrons

The authors present first Born, second Born, EBS and EBS' triple differential cross sections for the ionisation of H(2s) by fast electrons, for the case of a coplanar asymmetric geometry. Detailed calculations are preformed for an incident of 250 eV, and ejected electron energy of 5 eV and several scattering angles. Their results are markedly different from the corresponding ones obtained for the ionisation of H(1s). Second-order and third-order effects are significant, but not higher-order effects.

Inelastic scattering of electrons from sodium

Differential cross sections for the excitation of the 32P state in sodium have been measured over the angular range 2<or= theta <or=130 degrees at incident electron energies of 22.1 and 54.4 eV. The present measurements resolve the conflict between the previous data of Buckman et al. (1979) and of Srivastava et al. (1980). The present differential cross sections demonstrate the inadequacy of current theories in the prediction of large-angle scattering cross sections and indicate the need for the development of more sophisticated theories. The authors have also measured the alignment parameter lambda in the angular range 3<or= theta <or=15 degrees at incident energies of 22.1, 30 and 54.5 eV. These data are compared with the forward-angle predictions of several theories and the limitations of this parameter as a test of the theory of the excitation of the 32P state in sodium is discussed.

Elastic scattering and excitation of the 1s to 2s and 1s2p transitions in atomic hydrogen by electrons to medium to high energies

Multi-pseudostate close coupling is used to investigate 1s to 1s, 1s to 2s and 1s to 2p scattering at energies from 54.4 to 350 eV. Two sets of pseudostates are considered. The first is that of Fon et al. (1981); the second is an improved set. In constructing the improved pseudostates emphasis is placed upon getting the second Born term right. Target states of angular symmetries not included in the pseudostate bases are taken into account by using the distorted-wave second Born approximation of Kingston and Walters (1980). Results for elastic scattering are satisfactory; it is estimated that the present elastic differential cross sections are accurate to better than 5% at any angle at 200 and 300 eV. For the 2s and 2p excitations the theoretical picture is not so clear. Here there are significant differences between our results and the experiments of Williams (1975) and of Williams and Willis (1975). Some other theoretical calculations are in better accord with these experiments, although the authors believe the present work to be on firmer ground. Cases where the theoretical approximations are unanimously in disagreement with experiment suggest the presence of inaccuracies in the measurements and highlight the need for further experimental investigation. Of special interest are the angular correlation parameters of the 1s to 2p excitation; their results are in reasonable agreement with the main experiment at 54.4 eV in the angular range up to 70 degrees ; beyond 70 degrees there are still problems to be resolved.

Triple and double differential cross sections for electron impact ionisation of helium for 'energy-sharing' kinematics

The triple differential cross sections for electron impact ionisation of helium are investigated for 'energy-sharing' kinematics. A comparison is made with results of the simplified eikonal impulse approximation (EIA). Over the electron impact energy range from 200-2000 eV the authors also present absolute double differential cross sections for electron impact ionisation, in which only one existing electron is detected. It is shown that these cross sections are closely related to triple differential cross sections, in which two electrons are detected, for some scattering geometries. A model, which includes Rutherford scattering by the nucleus, is suggested, in order to explain the large discrepancy between the integrated EIA and the experimental data for very asymmetric energy disposition between the outgoing electrons.

Elastic and inelastic scattering of electrons by Na

Utilising a crossed-electron-beam-metal-atom-beam scattering technique differential excitation cross sections at 10, 20, 40 and 54.4 eV incident energies and at scattering angles ranging from 10 to 120 degrees have been measured for the following transitions: (i) elastic scattering, and (ii) excitation from ground state (32S) to (a) 32P, (b) 42S, (c) 32D+42P and (d) 42D+42F+52P+52S states in Na. Comparisons with recent theoretical and experimental results have been made. Using previous theoretical and experimental results as guides the present differential cross sections have been extrapolated between angular regions of 0-10 degrees and 120-180 degrees . Integral and momentum cross sections have been computed from these cross sections.

Ab initio cross sections for the excitation of the b3σu+state of H2by electron impact in the distorted-wave approximation

The authors present differential cross sections for the x 1Σg → b 3Σu transition in H2 at 15 eV incident electron energy. The cross sections are computed in the distorted-wave approximations, using the random-phase approximation for the electronic transition density and a discrete basis set technique for obtaining the distorted waves. The cross sections are found to be in good agreement with experimental data.