Wavelength, many-electron

Approximations have been reviewed in the case of short deBroglie wavelengths for the nuclei to derive coupled quantal-semiclassical computational procedures, by choosing different types of many-electron wavefunctions. Time-dependent Hartree-Fock and time-dependent multiconfiguration Hartree-Fock formulations are possible, and lead to the Eik/TDHF and Eik/TDMCHF approximations, respectively. More generally, these can be considered special cases of an Eik/TDDM approach, in terms of a general density matrix for many-electron systems. 

Although Dirac s equation does not directly admit of a completely self-consistent single-particle interpretation, such an interpretation is physically acceptable and of practical use, provided the potential varies little over distances of the order of the Compton wavelength (h/mc) of the particle in question. It allows, for instance, first-order relativistic corrections to the spectrum of the hydrogen atom and to the core-level densities of many-electron atoms. The latter aspect is of special chemical importance. The required calculations are invariably numerical in nature and this eliminates the need to investigate central-field solutions in the same detail as for Schrodinger s equation. A brief outline suffices. 

It is not absolutely necessary to have accurate interatomic potentials to perform reasonably good calculations because the many collisions involved tend to obscure the details of the interaction. This, together with the fact that accurate potentials are only known for a few systems makes the Thomas-Fermi approach quite attractive. The Thomas-Fermi statistical model assumes that the atomic potential V(r) varies slowly enough within an electron wavelength so that many electrons can be localized within a volume over which the potential changes by a fraction of itself. The electrons can then be treated by statistical mechanics and obey Fermi-Dirac statistics. In this approximation, the potential in the atom is given by ... 

Photoinduced ionization (or simply photoionization ) is the complete separation of an electron from a molecule. In the gas phase (isolated molecules) this requires considerable energy. Since there are many electrons in a molecule the ionization potential (IP) refers to the energy needed to separate to infinity the least tightly bound electron. The energies are such that only light in the far UV or in the vacuum UV (this refers to wavelengths below 180 nm) can directly ionize molecules in the gas phase. 

An approach briefly presented here is based on a combination of the eikonal (or short wavelength) approximation for nuclei, and time-dependent Hartree-Fock states for the many-electron system, in what we have called the Eikonal/ TDHF approach.[13] A similar description can be obtained with narrow wavepackets for the nuclear motions. Several other approaches have recently been proposed for doing first principles dynamics, a very active area of current research. [39, 11, 15]... 

Perhaps the most interesting application of electron-electron covariance mapping relates to the question of the major mode of multiple ionization of atoms and molecules. Luk et al. [34] studied the multiple ionization process in Xe using a laser of 193 nm wavelength and 10 ps pulse length and conventional ion TOP spectroscopy they suggested that it was direct (a collective, instantaneous emission of many electrons). Lambropoulos [35] pointed out that, with a laser of such modest rise time, the ionization must proceed sequentially. In fact L Huillier et al. [36] had also studied Xe at 532 nm and observed a knee in the curve of log (ion counts) vs log (laser intensity) for Xe that they attributed to direct double ionization. 

Since the transport in chromia is by electron transfer, chromia does not exhibit the Hall effect, photoconductivity, or carrier injection. Inconsistent results have been obtained from direct measurements of the diffusion of chromic ions in chromia 191,192). The dielectric constant was measured by Fang and Brower 193). The energy distribution curve of the photoelectrons emitted by chromia shows a spread of many electron volts 194), as is typical of insulators. The adsorption of gases such as ethanol shifts the limit of the photoeffect to longer wavelengths 195). Photoconductivity was not detected in chromia 196). Chemisorption of oxygen on chromia was not influenced by a previous nuclear irradiation in vacuo 189). 

Atomic vapor-absorption bands can be used to produce a high-performance notch filter [57-65]. As its name suggests, this type of filter relies on the absorption of specific wavelengths by electron orbital transitions in an atomic vapor. The filter is based on a metal vapor (e.g., rubidium [65]), which is often held in a transparent glass cell. Such filters can produce fair attenuation (3-5 optical density) over a very narrow bandwidth (less than 1 cm ) [63]. Their principal drawbacks are their relative complexity, their many closely spaced absorption peaks that can interfere with the data of interest, and the fact that the absorption peaks are not necessarily coincident with common laser wavelengths. Because the filter s absorption bands are so extremely narrow, if the laser shifts frequency even minutely, it will fall outside the absorption peak and will not be blocked. These challenges reduce the general applicability and attractiveness of this type of filter for Raman systems. 

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