Electron-atom scattering

Peng, L.-M., Ren, C., Dudarev, S.L. and Whelan, M.J. (1996) Robust parameterization of elastic and absorptive electron atomic scattering factors, Acta Cryst. A, 52, 257-276. 

Byron Jr., F.W. and Joachain, C.J. (1973). Elastic electron-atom scattering at intermediate energies. Phys. Rev. A 8 1267-1282. 

P. Krylstedt, N. Elander, E. Brandas, A Complex Dilated Study of Shape Resonances and Negative Ions in Electron-Atom Scattering, within an Asymptotic Complete Form of Continuum Exchange, J. Phys. B At. Mol. Opt. Phys. 22 (1989) 1623. 

R.K. Nesbet, Variational Methods in Electron-Atom Scattering Theory, Plenum, New... 

In the variety of excitation or de-excitation processes that allow the preparation and/or observation of the system via the participation of the continuous spectrum, the dominant and most interesting characteristics are generated by the transient formation of nonstationary or unstable states. For example, the excitation may be caused by the absorption of one or of many photons during the interaction of an initial atomic or molecular state with pulses of long or of short duration. Or, the transient formation and influence on the observable quantity may occur during the course of electron-atom scattering or of chemical reactions. 

Domcke, W. and Cederbaum, L.S. (1977). Theory of the vibrational structure of resonances in electron-atom scattering, Phys. Rev. A 16, 1465-1482. 

In terms of location, the primary process may be concentrated at one atom, as in an electron-atom scattering in LEED or in electron emission from core levels. It may also be delocalized over many atoms, as in photoelectron emission from a delocalized valence band level. The latter case is again of value to obtain molecular orientations directly. The polarization of the incident electron may also be used to determine molecular orientations, through its effect on the primary process. 

In section 2.3 we have decomposed various surface-sensitive techniques into a small set of more elementary processes. In this section we shall present appropriate formalisms that describe these individual processes. Namely, we shall discuss the theoretical treatment of the propagation of electrons in the surface region, as well as the treatment of elastic and inelastic electron-atom scattering, photoelectron emission and of Auger electron emission. These parts... 

The interference effects resulting from electron propagation are responsible for providing the desired structural information in all the techniques discussed here. The extraction of structural information, therefore, requires a knowledge of the electron wavelengths and of any phase shifts that may occur in electron emission and electron-atom scattering. Failure to understand these processes can result in quite erroneous results. 

Electron-atom scattering is central to all techniques under discussion here. As we have mentioned, electron-atom scattering at surfaces has been treated almost exclusively by means of the muffin-tin model. 

The formalism of electron-atom scattering has been extensively dealt with elsewhere./27,28,29/ We shall only recall its main features here. Because of the assumed spherical symmetry, the partial-wave scattering approach is convenient. Namely, an incoming spherical wave h[2 kr) y/ (r), (—can scatter only into the outgoing spherical wave hf kr) Y/"(r) (here hf and hf2 are Hankel functions of the first and second kinds, k = 2n/h(2mE) i, E is the kinetic energy and r — r ). This occurs with amplitude t( (f is an element of the diagonal atomic <-matrix), which is related to the phase shifts 6l through... 

Some of the early calculations of electron—atom scattering assumed that the potential was small compared with the total energy so that it is a good approximation to iterate the Lippmann—Schwinger equation (6.73). Using the notation (6.65,6.71) the resultant series... 

Use of the potential (7.35) in solving the coupled Lippmann—Schwinger equations (6.73,6.87) corresponding to (7.24) is a unique and numerically-valid description of the electron—atom scattering problem in the context of formal scattering theory. 

The Lippmann—Schwinger equations (6.73) are written formally in terms of a discrete notation i) for the complete set of target states, which includes the ionisation continuum. For a numerical solution it is necessary to have a finite set of coupled integral equations. We formulate the coupled-channels-optical equations that describe reactions in a channel subspace, called P space. This is projected from the chaimel space by an operator P that includes only a finite set of target states. The entrance channel 0ko) is included in P space. The method was first discussed by Feshbach (1962). Its application to the momentum-space formulation of electron—atom scattering was introduced by McCarthy and Stelbovics... 

The / -matrix method is a multichannel generalisation of the calculation of potential scattering described in section 4.4.3. It was introduced by Wigner and Eisenbud (1947) to describe neutron-nucleus reactions at low energy. Its application to electron—atom scattering has been described by Burke and Robb (1975). 

Nesbet R. L. In "Variational Methods in Electron-Atom Scattering Theory," Plenum Press, New York, 1980, p. 25. 

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