Electron-helium Collisions Research Articles

Laser-assisted singly and doubly ionizing electron-helium collisions at high impact energy and large momentum transfer

SynopsisElectron-impact single and double ionization of a helium atom in the presence of laser radiation with low frequency and intensity is studied theoretically. The kinematical regime of high impact energy and large momentum transfer, with two fast electrons in the final channel, is considered. Fully differential cross sections corresponding to the laser-assisted (e, 2e) and (e, 3e) processes are calculated for different models of the target state. The laser-assisted cross sections are found to be more sensitive to the electron-electron correlations in helium than the field-free ones.

Electron- and positron-impact atomic scattering calculations using propagating exterior complex scaling

Calculations are reported for four-body electron-helium collisions and positron-hydrogen collisions, in the S-wave model, using the time-independent propagating exterior complex scaling (PECS) method. The PECS S-wave calculations for three-body processes in electron-helium collisions compare favourably with previous convergent close-coupling (CCC) and time-dependent exterior complex scaling (ECS) calculations, and exhibit smooth cross section profiles. The PECS four-body double-excitation cross sections are significantly different from CCC calculations and highlight the need for an accurate representation of the resonant helium final-state wave functions when undertaking these calculations. Results are also presented for positron-hydrogen collisions in an S-wave model using an electron-positron potential of V12 = − (8 + (r1 − r2)2)−1/2. This model is representative of the full problem, and the results demonstrate that ECS-based methods can accurately calculate scattering, ionization and positronium formation cross sections in this three-body rearrangement collision.

Laser-assisted electron-impact ionization of atoms

Fast, 1 keV electron–helium collisions performed in an intense ( 4 × 1 0 12 W/cm 2), non-resonant laser field were investigated realizing the first experiment for laser-assisted ionization. The resulting double- and triple-differential cross-sections for the single ionization show significant differences in comparison to the field-free cross-sections. Our quantum-mechanical calculation, using a First-Born approximation (FBA) to describe the collision and Volkov states for the continuum electrons, cannot explain the measured cross-sections.

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.

Light polarization effects in laser-assisted elastic electron-helium collisions: a Sturmian approach

We study the scattering of fast electrons by atoms in the presence of a strong laser field. Our method takes into account the `dressing' of the target states by including the laser-atom interaction to first order, while the laser-projectile interaction is treated to all orders. The interaction of the fast incident electron with the target atom is treated in the first-Born approximation. Detailed calculations are performed for the `elastic' scattering of 500 eV electrons by helium accompanied by the transfer of photons. We discuss the influence of the laser polarization on the differential cross sections as a function of the scattering angle, laser frequency and intensity.

Production of cold orthohelium in counter propagating helium and electron beams

Inelastic electron-helium collisions with zero center of mass momentum are discussed as a potential method of production of low energy metastable helium suitable for magnetic trapping.

Double- and triple-differential cross sections for electron-impact ionization of helium.

Triple- (TDCS) and double- (DDCS) differential cross sections have been calculated for single ionization in electron-helium collisions for asymmetric geometry at intermediate and medium high energies. The TDCS and DDCS results have been presented for different kinematical situations and have been compared with the corresponding experiments. In the present prescription, the final-state wave function involves the correlation between the two continuum electrons and satisfies the three-body asymptotic boundary condition (for asymmetric geometry), which is an important criterion for reliable ionization cross sections. The sensitivity of the ionization cross sections (particularly of the TDCS) with respect to the choice of the bound-state wave function of the He atom has also been studied, using two different forms of wave function of the He atom. The binary-to-recoil peak intensity ratio against momentum transfer in TDCS is found to be in closer agreement with the experiment for the simple Hylleraas wave function than for the Hartree-Fock wave function. The DDCS results are found to be in good agreement with the experimental data of Mueller-Fiedler {ital et} {ital al}. [J. Phys. B 19, 1211 (1986)] for lower ejected energy ({ital E}{sub 2}), while for higher {ital E}{sub 2} the results are closer to the measurementsmore » of Shyn {ital et} {ital al}. [Phys. Rev. A 19, 557 (1979)] and Avaldi {ital et} {ital al}. [Nuovo Cimento D 9, 97 (1987)].« less

Pseudostate bases including an L2 description of the continuum for use in e--He collision calculations

The possibility of constructing a distorted-wave second Born approximation model for electron-helium collisions at energies above 30 eV is examined. It is proposed to calculate the second Born term by analytic integration over the intermediate momentum of the colliding electron and by replacing the infinite sum over intermediate target states by a finite sum over a pseudostate expansion. A method is proposed for obtaining pseudostate bases which approximately reproduce known bound-state contributions to the oscillator strength sum rules for n3,1S to n3,1P transitions and polarizabilities of the 11S, 21S and 23S states. These bases are composed of 'exact' n3,1S, n3,1P and n3,1D states up to n=3 and of a restricted number of 3,1S, 3,1P and 3,1D L2-type pseudostates. Certain of the latter lie in the continuum and their energies are adjusted to correspond to quadrature points for Gauss-Laguerre integration, this in order to easily evaluate the continuum contributions to oscillator strength sums, polarizabilities and second Born terms.

The multichannel eikonal theory of electron-helium collisions. I. Excitation of He(11S)

Calculations of the integral and differential cross sections for the electronic excitation of the 21L and 31L states of helium are reported. The multichannel eikonal theory employing a 10-channel basis set is used. The lambda and chi parameters for the 21P and 31P states at 80 eV are also reported. A number of misprints concerning the original multichannel eikonal theory results of Flannery and McCann (1975) have occurred in the literature. These misprints are corrected in the paper. A detailed description of both the theoretical and experimental difficulties involved in the determination of the integral cross sections sigma 11S to 31S and sigma 11S to 31D is provided. In addition, a critique of the assumptions made in previous experimental determinations of the differential cross sections (both composite and magnetic sublevel) for the 21L states of helium is given. A principal conclusion of the paper is that the first Born approximation underestimates experimental data in the intermediate energy region for 1S1D transitions, in contrast to the trend seen in 1S1P transitions. In the paper the importance of indirect mechanisms in the excitation of the 31S and 31D is shown, thereby confirming the early results of Chung and Lin (1968, 1969) and the tentative conclusions of Massey (1969, 1974).

Angular dependence of autoionisation linewidths due to post-collision interaction in e-He collisions

In this paper the authors present measurements of energy positions and widths of ejected- and scattered-electron profiles in electron-helium collisions. The energy of the incoming electrons is chosen such that following the excitation and the subsequent autoionisation of a doubly excited helium atom the ejected and the scattered electrons have roughly the same energy. An angle-dependent broadening of the ejected-electron profiles is observed; this may be caused by post-collision interaction (PCI) between the two electrons. The experimental results are in qualitative agreement with a semiclassical description of PCI in this energy region.

Strong coulomb interactions in atomic physics

The efficacy of diagonalising the Hamiltonian in all prevailing Coulomb interactions is stressed, as is the associated Wu Li concept of correlation whether of particles or events or both. The continuum distorted wave (CDW) theory is derived as a connected perturbation series using transparent generalised nonorthogonal coordinates. The target version is applied to K-K electron capture in proton-Ar collisions. Convergence properties are illustrated by CDW2 and CDW3 examples. Correlated CDW is applied to double resonant capture in He 2+-He collisions. The rôle of CDW in describing ionization and capture to the continuum is stressed and a new phase-integral variational CDW half-way house theory of coupled equations is presented. Some highly correlated Wannier effects in quantal threshold ionization are illustrated for electron-helium collisions.

Orientation and alignment parameters for e-He (11S to 31D) collisions

A ten-channel eikonal treatment of electron-helium collisions is performed for a basis set of (11S, 21S, 21P, 31S, 31P and 31D) target states to yield the first theoretical results for the orientation and alignment parameters for the 31D level of helium. Good agreement with recent measurements is obtained.

Computation of scattering functions in second-order many-body theory

A noniterative method is discussed for solving the electron-atom scattering equation derived in second-order many-body theory. The incident electron energy is taken to lie above the first inelastic threshold of the target atom. The method is applied to electron-helium collisions and elastic phase shifts for s-, p-, and, d-wave scattering, computed in various models arising from the formalism, are tabulated.

Momentum-transfer cross section for electron-helium collisions in the range 4-12 eV

Drift velocities of electrons in helium at 293 K have been measured in the range $2.5\ensuremath{\le}\frac{E}{N}\ensuremath{\le}7.0$ Td (1 Td = ${10}^{\ensuremath{-}17}$ V/${\mathrm{cm}}^{2}$), and analyzed to determine the momentum-transfer cross section between 4 and 12 eV. The estimated error bounds on the cross section are \ifmmode\pm\else\textpm\fi{}3% in the range $4\ensuremath{\le}\ensuremath{\epsilon}\ensuremath{\le}7$ eV and \ifmmode\pm\else\textpm\fi{}5% in the range $7l\ensuremath{\epsilon}\ensuremath{\le}12$ eV. The implications of the new result to the problem of determining standard cross sections for electron-helium scattering below the first excitation threshold are discussed.

Elastic scattering of electrons and positrons by atomic hydrogen and helium at intermediate and high energies

The eikonal Born series (EBS) method is used to analyse the elastic scattering of fast electrons and positrons by atomic hydrogen and helium. The properties of the terms of the Born and Glauber series are discussed, and in particular the dependence of these terms as a function of the (large) incident wavenumber k and the magnitude Delta of the momentum transfer. A more precise EBS treatment of small-angle scattering is presented by improving the calculation of the second Born term in this angular region. The EBS results agree very well with the recent absolute measurements of elastic differential cross sections, both for electron-atomic-hydrogen and electron-helium collisions.

Electron-photon angular correlations in electron-helium collisions for 31P excitations

Electron-photon angular correlations have been measured by detecting, in delayed coincidence, electrons inelastically scattered from helium and photons emitted in decays from the 31P level. The measurements have been carried out using both the 31P-11S (53.7 nm) line and the 31P-21S (501/6 nm) line. Analysis of the data yields the ratio of differential cross sections for exciting 31P magnetic sublevels lambda and the absolute value of the relative phase mod chi mod between the corresponding excitation amplitudes for electron scattering angles between 10 degrees and 30 degrees at incident electron energies in the range 50 eV to 150 eV. Data on the atomic orientation is also presented. The results are compared with the predictions of the first Born approximation and a recent multichannel eikonal calculation.

Measurement of elastic-scattering relative differential cross sections for electron-helium collisions at low energies and small angles

The experiment presented measures the relative differential cross sections in helium for the energies between 1.0 and 10.0 eV and at the angles 10\ifmmode^\circ\else\textdegree\fi{}, 15\ifmmode^\circ\else\textdegree\fi{}, 20\ifmmode^\circ\else\textdegree\fi{}, 25\ifmmode^\circ\else\textdegree\fi{}, and 30\ifmmode^\circ\else\textdegree\fi{}. The results are compared to the experiments of others and are also compared to the present theories. Since experiments do not overlap very well in this region, conclusions are difficult to draw. It is easier, however, to make comparisons to the theoretical predictions. It is shown that the results of this experiment do not agree well with the theoretical predictions.

Electron-photon angular correlations in electron-helium collisions: measurements of complex excitation amplitudes, atomic orientation and alignment

Electron-photon angular correlations were measured by delayed coincidences between electrons scattered inelastically from helium and 58.4 nm photons emitted in the decay of 2 1P state. The ratio of the differential cross sections for exciting the degenerate magnetic sublevels and the relative phase of the corresponding excitation amplitudes for electron scattering angles between 16 degrees and 40 degrees and for incident electron energies in the range 40 to 200 eV is deduced. The data show that a high degree of atomic orientation is produced by collisions in this range of energy and angle. The orientation increases rapidly towards its theoretical limit as the scattering angle is increased, and higher incident energy produces, in general, greater orientation at a fixed scattering angle. The data also show that the alignment of the atomic dipole radiation pattern can depart significantly from the direction of linear momentum transfer at the larger scattering angles. The results are compared with the predictions of the first Born and Glauber approximations, and good agreement is obtained with a recent distorted wave calculation.

Eikonal theory of electron-atom collisions

The application of eikonal methods to electron-atom scattering is reviewed. After recalling the basic features of the eikonal approximation, we discuss the Glauber theory, the eikonal-Born series method, the eikonal optical model theory and the eikonal distorted wave approach. We also give a survey of recent results obtained for electron-hydrogen and electron-helium collisions at intermediate energies.

Measurements of Complex Excitation Amplitudes in Electron-Helium Collisions by Angular Correlations Using a Coincidence Method

Angular correlations were measured by delayed coincidences between electrons of incident energy about 80 eV scattered inelastically from helium and photons from excited $3^{1}P$ and $2^{1}P$ states. From the angular correlation in each case we deduce the ratio of the differential cross sections for exciting the magnetic sublevels of the excited state and the phase between the corresponding excitation amplitudes. We compare the atomic radiation patterns with those predicted by the Born approximation.