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The experimental problems are summarized for measurement of inelastic differential cross sections (DCSs) for electron scattering from gases at electron impact energies near the threshold. A procedure is described and demonstrated with an example of CO.
A total of 11 scatter-free electron events from McMath plage region 8905 were observed by IMP 4 during the period from 29 July to 3 August 1967. The transit times and duration of these electron events are examined in detail. The duration of 170- to 1000-keV electrons shows a strong dependence upon the heliolongitude of the associated flare. Typical values of the duration full width at half maximum vary from 4 min at 50 deg W to 12 min at 10 deg and 90 deg W heliolongitudes. In addition, the difference in times at which the maximum intensities of the 22- to 45-keV and 170- to 1000-keV electrons occur is observed to change from 18 min near 50 deg W to 13 min at 10 deg and 90 deg W heliolongitudes. An idealized two-dimensional diffusion model for the transport of these electrons in the solar corona is proposed. The 22- to 45-keV electrons escape promptly from flare site to the feet of the interplanetary magnetic field lines, whereas 170- to 1000-keV electrons suffer slight scattering. The diffusion coefficient for 170- to 1000-keV electrons is estimated to be 3 X 10 to the 18th power sq cm/sec. Finally, a possible relation between the scatter-free and the classical diffusive-type electron events is discussed.
Nonadiabatic theory application to inelastic S-wave scattering of low energy electrons from atomic hydrogen
One version of the multichannel theory for electron-target scattering based on the Schwinger variational principle, the SMC method, requires the introduction of a projection parameter. The role of the projection parameter a is investigated and it is shown that the principal-value operator in the SMC equation is Hermitian regardless of the value of a as long as it is real and nonzero. In a basis that is properly orthonormalizable, the matrix representation of this operator is also Hermitian. The use of such basis is consistent with the Schwinger variational principle because the Lippmann-Schwinger equation automatically builds in the correct boundary conditions. Otherwise, an auxiliary condition needs to be introduced, and Takatsuka and McKoy's original value of a is one of the three possible ways to achieve Hermiticity. In all cases but one, a can be uncoupled from the Hermiticity condition and becomes a free parameter. An equation for a based on the variational stability of the scattering amplitude is derived; its solution has an interesting property that the scattering amplitude from a converged SMC calculation is independent of the choice of a even though the SMC operator itself is a-dependent. This property provides a sensitive test of the convergence of the calculation. For a static-exchange calculation, the convergence requirement only depends on the completeness of the one-electron basis, but for a general multichannel case, the a-invariance in the scattering amplitude requires both the one-electron basis and the N plus 1-electron basis to be complete. The role of a in the SMC equation and the convergence property are illustrated using two examples: e-CO elastic scattering in the static-exchange approximation, and a two-state treatment of the e-H2 Chi(sup 1)Sigma(sub g)(+) yields b(sup 3)Sigma(sub u)(+) excitation.
Electron mobility transition in infinite system of random hard core scatterers relation to switching effect in semiconductors
Low energy electron-atom and electron-molecule scattering theory
Optical potential approach to low energy electron- helium scattering
Surface scattering of electrons on metallic field effect in thin layers in theory of mean-free-path influences on conductance change
Electron velocity distribution anisotropy in reflex discharge measured by continuous wave Ar laser scattering
A generalized many-electron pseudopotential approach is presented for electron-neutral-atom scattering problems. A calculation based on this formulation is carried out for the singlet s-wave and p-wave electron-hydrogen phase shifts with excellent results. We compare the method with other approaches as well as discuss its applications for inelastic and rearrangement collision problems.
Differential cross sections for Coulomb scattering of electrons without atomic excitation from thin aluminum targets for incident energies from 0.1 to 3.0 mev
Applications of the hybrid theory to the scattering of electrons from Ile+ and Li++ and resonances in these systems, A. K. Bhatia, NASA/Goddard Space Flight Center- The Hybrid theory of electron-hydrogen elastic scattering [I] is applied to the S-wave scattering of electrons from He+ and Li++. In this method, both short-range and long-range correlations are included in the Schrodinger equation at the same time. Phase shifts obtained in this calculation have rigorous lower bounds to the exact phase shifts and they are compared with those obtained using the Feshbach projection operator formalism [2], the close-coupling approach [3], and Harris-Nesbet method [4]. The agreement among all the calculations is very good. These systems have doubly-excited or Feshbach resonances embedded in the continuum. The resonance parameters for the lowest ' S resonances in He and Li+ are calculated and they are compared with the results obtained using the Feshbach projection operator formalism [5,6]. It is concluded that accurate resonance parameters can be obtained by the present method, which has the advantage of including corrections due to neighboring resonances and the continuum in which these resonances are embedded.
The P-wave hybrid theory of electron-hydrogen elastic scattering [Phys. Rev. A 85, 052708 (2012)] is applied to the P-wave scattering from He ion. In this method, both short-range and long-range correlations are included in the Schroedinger equation at the same time, by using a combination of a modified method of polarized orbitals and the optical potential formalism. The short-correlation functions are of Hylleraas type. It is found that the phase shifts are not significantly affected by the modification of the target function by a method similar to the method of polarized orbitals and they are close to the phase shifts calculated earlier by Bhatia [Phys. Rev. A 69, 032714 (2004)]. This indicates that the correlation function is general enough to include the target distortion (polarization) in the presence of the incident electron. The important fact is that in the present calculation, to obtain similar results only a 20-term correlation function is needed in the wave function compared to the 220- term wave function required in the above-mentioned calculation. Results for the phase shifts, obtained in the present hybrid formalism, are rigorous lower bounds to the exact phase shifts. The lowest P-wave resonances in He atom and hydrogen ion have been calculated and compared with the results obtained using the Feshbach projection operator formalism [Phys. Rev. A, 11, 2018 (1975)]. It is concluded that accurate resonance parameters can be obtained by the present method, which has the advantage of including corrections due to neighboring resonances, bound states and the continuum in which these resonance are embedded.
A single scattering theory is used to directly derive the D(r) result of Cassinelli et al (1987) and to investigate the extent to which it can be generalized to nonuniform spherical light sources, nonspherical light sources, arbitrary spatial distributions of scattering electrons, and scattering particles other than electrons. Expressions are also obtained for the factor by which the total scattered (as well as polarized) intensity is modified by finite size light sources, which is relevant to the case where the much stronger direct unpolarized starlight is eclipsed.
Measurement of the angular distribution of electrons elastically scattered from N2 as a function of energy, utilizing a crossed-beam technique. Measurements have been made of monoenergetic electrons with energies between 5 and 90 eV scattered from a collimated beam of N2 at angles from -114 to +160 deg. The wide angular range of the measurements has enabled the determination of the total elastic-scattering and momentum-transfer cross sections. The measurements are relative and have been normalized to Fisk's (1936) theoretical calculation at 5 eV. The results generally agree well with other published measurements and with theory.
The scattering of low energy electrons and positrons is described for the liquid phase and compared and contrasted with that for the gas phase. Similarities as well as differences are noted. The loci of scattering sites, called spurs in the liquid phase, are considered in detail. In particular, their temporal and spatial evolution is considered from the point of view of scattering. Two emphases are made: one upon the stochastic calculation of the distribution of distances required for slowing down to thermal velocities, and the other upon the calculation of cross sections for energy loss by means of quantum mechanics.
Quasi-stationary techniques for calculating energies and widths of resonances occurring in electron-atom and electron-molecule scattering
The asymptotic effective potential for electron- or positron-hydrogen elastic scattering is derived, correct to order x to the -7th, where x is the positron projectile coordinate, using the Feshbach optical potential as a starting point in the manner of Kleinman et al (1968). To order x to the -6th the potential agrees with the close-coupling results of Seaton and Steenman-Clark (1977) but not to order x to the -7th, where the present calculation gives the result + or - 213/2(x to the 7th) for electron and positron respectively. This coefficient differs considerably from the approximate value of Seaton and Steenman-Clark, and the discrepancy is traced to the omission of d states in their calculation.