Continuum multiple scattering

Smith IM, Thompson DG, Blum K (1998) Chiral effects in electron scattering by molecules using a continuum multiple scattering method. J Phys B 31 4029... 

In Figure 4 our calculated cross sections for the 3cTg level are compared with the results of the Stleltjes moment theory (STHT) approach (25) and of the continuum multiple scattering model (CMSM)... 

Briefly, XANES is associated with the excitation process of a core electron to bound and quasibound states, where the bound states interacting with the continuum are located below the ionization threshold (vacuum level) and the quasibound states interacting with the continuum are located above or near the threshold. Thus, XANES contains information about the electronic state of the x-ray absorbing atom and the local surrounding structure. However, as stated above, unhke EXAES, since the excitation process essentially involves multielectron and multiple scattering interactions, interpretation of XANES data is substantially more complicated than that of EXAFS data. 

The spectral features of XANES have been interpreted as the result of multiple-scattering resonances of the low kinetic energy photoelectrons. Examples of the strong and sharp XANES peaks above the continuum threshold and below the beginning of the weak EXAFS oscillations in the absorption spectra of condensed molecular complexes, are shown in Fig. 4.6. 

This part introduces variational principles relevant to the quantum mechanics of bound stationary states. Chapter 4 covers well-known variational theory that underlies modern computational methodology for electronic states of atoms and molecules. Extension to condensed matter is deferred until Part III, since continuum theory is part of the formal basis of the multiple scattering theory that has been developed for applications in this subfield. Chapter 5 develops the variational theory that underlies independent-electron models, now widely used to transcend the practical limitations of direct variational methods for large systems. This is extended in Chapter 6 to time-dependent variational theory in the context of independent-electron models, including linear-response theory and its relationship to excitation energies. 

In extreme cases a multiple-scattering, sharp resonant structure can result in which the electron is in a quasi-bound state (155). One example is the white line, which is among the most spectacular features in X-ray absorption and is seen in spectra of covalently bonded materials as sharp ( 2eV wide) peaks in absorption immediately above threshold (i.e., the near continuum). The cause of white lines has qualitatively been understood as being due to a high density of final states or due to exciton effects (56, 203). Their description depends upon the physical approach to the problem for example, the LiUii white lines of the transition metals are interpreted as a density-of-states effect in band-structure calculations but as a matrix-element effect in scattering language. 

The shape of the white line is affected by multiple-scattering excitations and by the fact that the L-shell transition is degenerate in energy with a continuum of transitions. The continuum may cause the white line to become skewed at the high-energy side, as in the case of Pt, where a tailing of up to 30 eV past the edge is observed. 

Molecular-orbital approaches to edge structures differ for semiconducting and isolating molecular complexes. The latter and transition-metal complexes allow one to minimize solid-state effects and to obtain molecular energy levels at various degrees of approximation (semiempirical, Xa, ab initio). The various MO frameworks, namely, multiple-scattered wave-function calculations (76, 79, 127, 155) and the many-body Hartree-Fock approach (13), describe states very close to threshold (bound levels) and continuum shape resonances. 

Third, while these Ideas were developed (36) In the context of molecular photolonlzatlon, the continuum elgenchannel concept carries over without any fundamental change to electron-molecule scattering. Finally, while we have used one-electron wavefunctlons here, obtained with the multiple-scattering model, we emphasize that the elgenchannel concept Is a general one and we look forward to Its use In the analysis of more sophisticated, many-electron molecular continuum wavefunctlons. 

The direction of the continuum radiation is related to the velocity of the decelerated electron, so principally it is related to the initial beam direction, but as a result of the multiple scattering this direction preference is lose. A peak of the signal in the direction of the electron beam comes from absorption phenomena inside the specimen as is the case for the characteristic radiation. 

The region in the continuum where multiple scattering processes are relevant is called the XANES region. 

The extraction of the variation of the interatomic distances in unknown systems is complicated by the determination of = (ii/2 m(E — Eg -b V) because V, the average interstitial potential in the muffin tin approximation, is unknown. In order to overcome the problem of V, which cannot be determined experimentally, it has been pointed out that the energy separation of a multiple scattering resonance in the continuum from a bound state at threshold AE = (E,. — E ) can be used to determine the variation of the interatomic distance. 

Dell Ariccia M, Gargano A, Natoli CR, Bianconi A (1984) A calculation of C. -shell X-ray absorption spectra of C2Hn (n = 2, 4, 6) oriented molecules correlation between position of the multiple scattering resonance in the continuum and the C-C bond length. LNF-INFN Report LNF-84-51 (P)... 

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