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

Abstract

Calculations of the integral and differential cross sections for the electronic excitation of the 2'L and 3lL states of helium are reported. The multichannel eikonal theory employing a 10-channel basis set is used. The X and x parameters for the 2'P and 3 l P states at 80 eV are also reported. A number of misprints concerning the original multichannel eikonal theory results of Flannery and McCann have occurred in the literature. These misprints are corrected in this paper. A detailed description of both the theoretical and experimental difficulties involved in the determination of the integral cross sections 01is,31s and 0 1 ~s , 3 ~D 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 3IL states of helium is given. A result of this analysis is that the experimental data on the differential cross sections for the 3'P state need to be re-interpreted in light of the experimental data of van Linden van den Heuvell e t al. A principal conclusion of this paper is that the first Born approximation undecestimates experimental data in the intermediate energy region for 'S -+ ID transitions, in contrast to the trend seen in 'S --t 'P transitions. The reason for such a reversal in I S i 'D transitions can be understood in terms of the direct (i -+ j ) , and indirect (i i n --+ j , etc) mechanisms which are important in the electronic excitation of the 3l L states of He.In particular, in this paper the importance of indirect mechanisms in the excitation of the 3IS and 3ID is shown, thereby confirming the early results of Churig and Lin and the tentative conclusions of Massey.

Electron-impact study for the and (n= 3 - 6) excitations in helium

“…There are no other experimental data obtained at an impact energy larger than 100 eV. Differences in shape and magnitude for apparent GOSs between work reported in [5, 17, 20a] at 100 eV and our work are large, for example, there is a minimum for experimental [5] and theoretical data [17] near K 2 = 0.3 au except for the DWPO data [20a]. On the other hand, the shapes of calculated apparent GOS curves at 200 eV are similar to our work, they are close to our data at K 2 0.3 au although these apparent GOSs are much smaller than our results at K 2 0.3 au.…”

“…Appropriate experimental data are only reported by Trajmar et al [5] at the impact energy of 100 eV. Appropriate calculated data are from the FBA [15a, 16], the multichannel eikonal theory (MET) at 100 and 200 eV [17,18], the distorted wave (DW) approximation at 100 eV [19], the distortedwave polarized orbital (DWPO) method at 100 and 200 eV [20a], and the first-order form of the many-body theory (FOMBT) at 100 eV [5]. Most of these data and the present results are shown in figure 2(a) which clearly shows that the present data are in good agreement with the FBA data reported by Kim and Inokuti [15a].…”

Excitation of He(31 D) by electron impact

“…At small scattering angles, the measured linear polarization P~Jn is about 60% and it remains approximately constant at this value up to about 0e = 40 ° after which is appears to display some structure and to drop to smaller values. With the exception of the DMET [17], this behaviour is not predicted by the existing theories [15,16] which show pronounced variations as a function of scattering angle. At these scattering angles, the electron charge cloud largely resembles a pure in-plane I do) state, containing little or no admixture of other substates.…”

“…The measured orientation displays large Table I [6]) and Donnelly and Crowe (v, [8]) and with DWBA-EP ((long-dashed line), [15]), DWBA-GP ((short-dashed line), [ 151), FOMBT ((dash-dotted line), [t6]), and full DMET ((solid line), [17] In conclusion, the present results for the excitation of He ((3 1/)) states by electron impact indicate that the excited wavefunction particularly at small scattering angles and at tow incident energies resembles a pure I do) state lying in the scattering plane while contributions from the other substates are relatively small. This behaviour is in qualitative agreement with the DMET but not with the DWBA and FOMBT results.…”

Differential cross sections for electron impact excitation of then= 2 states of helium at intermediate energies (80, 100 and 120 eV) measured across the complete angular scattering range (0–180°)

“…A number of theoretical models for DCS of specific interactions exist. Perturbative methods have existed for many years and include Coulomb projected Born approximation [9], first-order many-body theory (FOMBT) [10], distorted wave Born approximation (DWBA) [11], distorted-wave polarization orbital [12], multi-channel eikonal approximation [13] and second-order potential distorted-wave [14]. More recently a range of more accurate non-perturbative methods, including R-matrix with pseudostates (RMPS) [15], B-spline R-matrix (BSR) [16] and convergent close-coupling (CCC) [17], have emerged as methods that agree well with both themselves and experiment [7].…”