Local effective polarization and absorption potentials from cross-sections for e-atom scattering

A possibility of obtaining local, effective, energy-dependent polarization and absorption potentials from experimental cross-sections for electron scattering is investigated. Potentials have been fitted with the help of the genetic algorithm on large sets of experimental data for e-He, e-Ne and e-Ar elastic scattering at impact energies 20-3000 eV. The obtained potentials reproduce the cross-sections within experimental errors.     

Electron scattering off simple atoms for large momentum transfer collisions

In a previous paper this author examined the Born expansion and isolated those parts of the expansion that contribute most significantly to the scattering amplitude for large momentum transfer collisions in inelastic collisions from the ground state of both hydrogen and helium. It turned out that certain terms where the scattering electron interacts once with the nucleus and once with the other electron dominate. The physical reason is that large momentum transfer collisions require the nucleus to take the bulk of the incident momentum but require an interaction with the one of the bound electrons to change the state of the atom. The arguments are quite general and this paper will extend this analysis by comparing the inelastic results obtained by this method for hydrogen and helium to a close coupling calculation with many intermediate states. Further, we will extend this analysis to the correction to the 1st Born result for elastic electron-hydrogen and electron-helium collisions and provide some results for scattering from the initial metastable states of hydrogen for large momentum transfer collisions. A comparison of the results of this analytic approach will be made to the numerical close coupling approach and experiments where available. The agreement is remarkable.     

Influence of multiple elastic scattering on the shape of the elastically scattered electron peak

The influence of multiple elastic scattering on the shape of the energy distribution of elastically scattered electrons is investigated. The energy of the maximum intensity of the detected electrons differs from the probe electron beam energy due to the elastic energy loss. The experimentally observed spectrum is adequately described by a Gaussian distribution with a maximum at the elastic energy loss value. In this paper the peak-broadening mechanisms due to energy-analyzer spread function, probe beam energy distribution and atomic vibration-induced broadening are considered to be independent and of random nature. Analysis of multiple elastic scattering shows some mechanisms leading to the broadening and a shift of the elastic scattering electron energy spectrum from the value defined by single elastic scattering at the certain angle. It is revealed that the magnitude of this shift and the width of energy distribution is determined by ratio (_lin/_ltr)$(l_{\text{in}}/l_{\text{tr}})$, where _lin$l_{\text{in}}$ is inelastic mean free pass, _ltr$l_{\text{tr}}$ is the transport length.     

Effect of Polarization in （e, 2e） Ionization of Argon

The triple differential cross section of the Ar 2p orbital in a highly asymmetric geometry is calculated by using a modified distorted wave Born approximation method. A short-range polarization potential via density-functional theory is included in our calculations. It is shown that polarization potential is particularly important for calculations of the triple differential cross section.     

Dissociative attachment of low-energy electrons to vibrationally excited hydrogen molecules

Dissociative electron attachment to hot hydrogen molecules is studied in the framework of nonlocal resonance model. The method based on the use of the Bateman approximation, well known in nuclear physics, is adapted for solving the Lippmann-Schwinger integral equation of the nonlocal resonance model and applied to the calculation of cross sections of inelastic resonant electron-molecule collisions. The proposed method is compared with the Schwinger-Lanczos algorithm used extensively for the treatment of these processes. It is shown that the Bateman approximation is very useful and efficient for treating the non-separable nonlocal potentials appearing in the integral kernels of the nonlocal resonance models. The calculated cross sections for the dissociative attachment of electrons to vibrationally excited hydrogen molecules are of importance for astrophysics. This paper is dedicated to Prof. J. Bičák on the occasion of his 60th birthday.     

Modelling electron-N2 scattering in the resonant region

Quantum calculations of the resonant vibrational excitation of N₂ by electron impact are carried out using a model potential for exchange and correlation-polarization forces and exact static interaction. The inelastic process is treated within a coupled channel, space-frame formulation and final cross-sections are tested for convergence within less than of their values. Comparison with the experiments yields very good agreement with the latter data in the resonance region and suggests possible extension to calculations near the threshold openings for rovibrational inelastic processes induced by electron impact.     

Effective non-empirical absorption potentials based on quasifree-scattering model

Several recently proposed modifications and improvements of the quasifree-scattering model for absorption potentials have been tested and compared. The possibility of obtaining energy-dependent polarization potentials from these absorption potentials by the dispersion relation is investigated. Numerical calculations for the elastic scattering of electrons by neon atoms at impact energies 20–3000 eV are performed and the results are compared with experimental data.     

Low-energy electron scattering from copper

Differential cross sections for the elastic scattering of electrons from the ground states of copper for the configuration 3d¹⁰ 4s and the excitation state ²D with the configuration 3d⁹ 4s² have been calculated. Local density approximations to the exchange and correlation potentials have been used in these calculations, and it is confirmed that Hara exchange coupled with a Hedin-Lundqvist electron-gas-type correlation potential joined to an adiabatic polarization potential gives good predictions for differential cross sections. A comparison of the calculated results with other experimental and theoretical data are presented and discussed.     

Electron scattering by formic acid in the gas phase: comparing measured and computed angular distributions

Elastic differential cross-sections are measured over a broad range of energy values and the results are compared with quantum calculations for the same process. The agreement between measured and computed data turns out to be fairly good and calculations further allow the separation of the cis and trans conformer behavior and to compare it with the angular distributions for scattering from the dimer at the same energies.     

Studies on vibrational excitation differential cross-sections of low-energy electron scattering from N2 molecule

The vibrational excitation differential cross-sections (DCS) of low-energy electron-N₂ scattering are studied using vibrational close-coupling (VCC) method and vibrational scattering potentials which include static, exchange and polarization contributions. By including the contributions of 18 partial waves, 20 vibrational states, and 16 molecular symmetries (up to Λ=7), the converged vibrational excitation (0↦2, 0↦3, 0↦4) DCS agree well with experimental results. Also obtained are converged vibrational (1↦0, 1↦1, 1↦2, 1↦3) DCS, with the impact energies being those of the main resonant peaks (1.92 eV, 1.90 eV, 1.62 eV, 1.63 eV).     

Electron Scattering by C4H10 and C6H6 in the Energy Range 100--1000eV

We investigate the applicability of the independent atom model （IAM） to elastic electron scattering from complex polyatomic molecules, namely C4H10 and C6H6, in the energy range 100-1000eV. The cross sections of the elastic electron scattering are calculated by employing the IAM together with the relativistic partial waves. The incorporation of both the modified absorption potential and the extended structural factor in the IAM makes the elastic differential cross sections and momentum transfer cross sections have a good agreement with the available experimental data. The present simple model seems to be insensitive to the complexity of the target molecules so that the proposed procedure can be quite useful for calculation of electron scattering from bio-molecules.     

Low-energy electron scattering from gaseous CS<Subscript>2</Subscript>: angular distributions and effect of exchange forces

Ab initio calculations are reported for the quantum scattering of electrons from CS₂ molecules in the gas phase and for energies which range from near threshold up to about 100 eV. Angular distributions are examined in detail and an extensive comparison is made with existing experiments and earlier calculations. The agreement found with the latter data is fairly good and results are further discussed in terms of a physical mechanism of “exchange level shifting" to explain the disappearance of a Π_u resonance suggested by earlier studies.     

Elastic scattering of low-energy electrons by NO

We report elastic integral, momentum transfer and differential cross sections for electron scattering by N₂O for energies up to 50 eV. These results were obtained at the static-exchange approximation with the Schwinger Multichannel Method with Pseudopotentials [M.H.F. Bettega, L.G. Ferreira and M.A.P. Lima, Phys. Rev. A 47, 1111 (1993)]. In general our results show good agreement with experimental data and with other theoretical results but some discrepancies are found. We have also found a shape resonance around 4 eV in agreement with previous calculations using the R-matrix Method of Sarpal et al. [J. Phys. B 29, 857 (1996)]. On the other hand, the existence of a resonance at about 13 eV, clearly seen by the Schwinger Variational Iterative Method [Michelin et al., J. Phys. B 29, 2115 (1996)], can not be confirmed by our calculations. At this energy, our cross sections show a broad bump with no clear resonant behavior given by the eigenphase sum. Received: 13 November 1997 / Revised: 13 March 1998 / Accepted: 9 April 1998     

Electron-Helium Scattering in a Bichromatic Laser Field in the Second-Order Born Approximation

The elastic scattering of electrons in atomic helium assisted by a bichromatic laser field is investigated in the second order Born approximation. The target atom is approximated by a simple screening potential. The dependence of the differential cross section on the relative phase between the two laser components is calculated, and compared with the recent results of first order Born approximation [Sun J F, Liang M C and Zhu Z L 2007 Chin. Phys. Lett. 24 2572].     

Photodetachment of HF- in an Electric Field

Photdetachment of a negative HF^- ion in an electric field is studied by using the two-centre model and the closed orbit theory. An analytic formula is presented for the electron flux of HF^- in the presence of an electric field. The results show that the oscillation in the electron flux distribution is caused by the rescattering effect of the molecular ion core and the interference between the two nuclei. In addition, the interference between the orbits passing through the given spatial point also plays an important role in the electron flux distribution. This study provides a new understanding of the photodetachment of polar molecules in the presence of external field.     

Geometric shielding corrections for total cross section calculations of electron scattering by CH4, C2H6, C2H3F3, C2H4, C2F4, C2Cl4 and C2Cl2F2 from 30–5000?eV

To quantify the changes in the geometric shielding effect in a molecule as the incident electron energy varies, an empirical fraction, which represents the total cross section contributions of shielded atoms in a molecule at different energies, is presented. Using this empirical fraction, the total cross sections for electron scattering by CH₄, C₂H₆, C₂H₃F₃, C₂H₄, C₂F₄, C₂Cl₄ and C₂Cl₂F₂ are calculated over a wide energy range from 30 to 5000 eV by the additivity rule model at the Hartree-Fock level. The quantitative total cross sections are compared with those obtained by experiment and other theories where available. Good agreement is attained above 100 eV.     

Scattering of electrons from gas-phase N2O(1Σ): Computed cross-sections and angular distributions in comparison with experiments

Ab initio calculations are reported for the quantum scattering of electrons from N₂O molecules in the gas phase and for energies which range from near threshold up to about 100 eV. Elastic integral cross-sections and angular distributions are examined in detail and an extensive comparison is made with existing experiments. The agreement found with the latter data is fairly good and results are further discussed to explain the physical mechanisms at work for this polar target.     

Modified effective-range theory for low energy ${\sf e}$-N2 scattering

We analyze the low-energy e-N₂ collisions within the framework of the modified-effective range theory (MERT) for the long-range potentials, developed by O’Malley et al. [J. Math. Phys. 2, 491 (1961)]. In comparison to the traditional MERT we do not expand the total cross-section in the series of the incident momentum ?k, but instead we apply the exact analytical solutions of the Schrödinger equation for the long-range polarization potential, as proposed in the original formulation of O’Malley et al. This extends the applicability of MERT up to few eV regime, as we confirm using some simplified model potential of the electron-molecule interaction. The parameters of the effective-range expansion (i.e. the scattering length and the effective range) are determined from experimental, integral elastic cross-sections in the 0.1–1.0 eV energy range by fitting procedure. Surprisingly, our treatment predicts a shape resonance that appears slightly higher than experimentally well known resonance in the total cross-section. Agreement with the experimentally observed shape-resonance can be improved by assuming the position of the resonance in a given partial wave. Influence of the quadrupole potential on resonances is also discussed: we show that it can be disregarded for N₂. In conclusion, the modified-effective range formalism treating the long-range part of the potential in an exact way, reproduces well both the very low-energy behavior of the integral cross-section as well as the presence of resonances in the few eV range.     

Elastic scattering of electrons from tetrahydrofurfuryl alcohol

Differential cross-sections (DCSs) for elastic scattering of electrons from tetrahydrofurfuryl alcohol (THFA), which can be considered as an analogue molecule to DNA sugar deoxyribose, were determined using crossed beam measurements for incident energies from 40 eV to 300 eV and scattering angles from 30° to 110°. The relative DCSs were measured both as a function of incident electron energy and scattering angle, allowing absolute calibration of the whole data set via normalization to a single point. The absolute calibration has been performed according to calculated absolute DCSs obtained by the corrected independent atom method using an improved quasifree absorption model. The calculated data-set includes DCSs and integral elastic and inelastic cross-sections in the incident energy range from 5 eV to 5000 eV. The theoretical results agree very well with the experimental ones, regarding the shape of DCSs. Moreover, the same theoretical procedure has been used to obtain DCSs for elastic electron scattering from a simpler deoxyribose analogue tetrahydrofuran (THF), which agree very well, both in shape and on the absolute scale, with the recent experimentally obtained absolute DCSs [A.R. Milosavljević et al., Eur. Phys. J. D 35, 411 (2005)]. The present results are also compared with the recent theoretical data for THF and THFA. Finally, according to both experimental and theoretical data, the DCSs for elastic electron scattering from THFA and THF molecules appear to be very similar both in shape and absolute scale.     

The viscosity cross-section for elastic electron-xenon collisions including electron spin polarization

The results of the evaluation of the viscosity cross-section for elastic electron-xenon collisions, taking into account the spin-orbit interaction of the continuum electron, in the energy interval from 0.1 eV to 50 eV are presented and discussed. The calculations are performed on the basis of three theoretically derived sets of phase shift data obtained by different authors and on the deduced relativistic expression for the viscosity cross-section in terms of phase shifts discerning the spin-up and spin-down states of the scattered electrons. Comparison with viscosity cross-sections, as evaluated from non-relativistic phase shifts extracted from experiments, strongly favours the relativistic results. The assumption of isotropic scattering is critically examined and the error induced by its use is shown to persist to the same extent as in non-relativistic calculations, at least in the energy region considered. Received: 22 April 1998 / Received in final form: 16 December 1998