�ber die Anwendbarkeit der statistischen Methode auf Ionengitter

Lenz, Werner

doi:10.1007/bf01342150

Cited by 183 publications

(42 citation statements)

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“…the i = j term of Eq. (12). From the figure we can differentiate two different regions of the interatomic potentials.…”

Section: Resultsmentioning

confidence: 99%

“…As observed from Eq. (12), when the projectile moves along the channel far from the surface plane, the factors of the polarization potential coming from F − and Li + have opposite signs and they compensate their contributions to order r −4 when F − and Li + ions are placed in front of each other, as it happens in the <100> direction. Furthermore, within a row model, the <100> rows -formed by alternate cations an anions -display a neutral charge, which reduces the polarization of the incident atom.…”

Section: Resultsmentioning

confidence: 99%

“…Following the Lenz energy functional [12,13], for the two types of target ions -alkali-metal and halide-the static ion-atom interaction is found to be the sum of three terms,…”

Section: Interaction Potentialsmentioning

confidence: 99%

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Influence of the polarization in grazing scattering of fast helium atoms from LiF(001) surfaces

Gravielle

Miraglia

2008

Phys. Rev. A

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Grazing scattering of neutral atoms from insulator surfaces is investigated in the intermediate velocity range, in which interference effects have been recently observed. To describe this process we introduce a distorted-wave method, based on the use of the eikonal wave function, which takes into account the phase of the scattering state along the classical projectile path. The eikonal theory is applied to evaluate the angular distribution of few keV helium atoms after impinging on a LiF(001) surface along low-index crystallographic directions. The interest focuses on the role played by the projectile polarization produced by cations and anions of the crystal surface. For the considered collision system we found a polarization channel, corresponding to the direction <110>, which is affected by this effect, while for incidence in the direction <100> the polarization contribution is nearly negligible. The proposed eikonal approach, including polarization effects, provides angular projectile spectra in good agreement with the experimental data.

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“…the i = j term of Eq. (12). From the figure we can differentiate two different regions of the interatomic potentials.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Influence of the polarization in grazing scattering of fast helium atoms from LiF(001) surfaces

Gravielle

Miraglia

2008

Phys. Rev. A

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“…However, as in classical mechanics, an explicit treatment beyond one-electron systems is elusive. This spurred the development of effective models of large Coulomb systems starting with Thomas [79], Fermi [29,30], and Lenz [46], who formulated the Thomas-Fermi model in the appropriate language of energy functionals. It asserts that in terms of the nuclear charge Z , the ground state energy of an atom is of leading order Z 7/3 .…”

Section: Introductionmentioning

confidence: 99%

The Ground State Energy of Heavy Atoms: The Leading Correction

Handrek

Siedentop

2015

Commun. Math. Phys.

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“…Let us suppose that the system is built up from N electrons with k static nuclei of charges Zj>O and locations R j corresponding to the Hamiltonian U({Zj,R)) = L ZiZ) Ri-Rjl-l. i<j The kinetic energy of the nuclei is not considered. Now, in the Thomas-Fermi theory a functional is defined (LENZ, 1932) (3.2) -…”

Section: B Phonons In Insulatorsmentioning

confidence: 99%

Vibrational Infrared and Raman Spectra of Non-Metals

Bilz¹,

Strauch²,

Wehner³

1984

Light and Matter Id / Licht Und Materie Id

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The vibrational properties of crystals determine the photon infrared absorption, inelastic neutron scattering and, to a large extent, inelastic photon scattering by phonons, i.e., Raman scattering. The interpretation of infrared and Raman spectra requires, therefore, an understanding of the basic features of lattice dynamics. The quantum theory of solids describes the crystal properties in terms of elementary excitations and their mutual interactions. Dynamic properties are represented by phonons (lattice vibrations) and their interactions mainly with other phonons (anharmonicity), electrons (electron-phonon coupling), and photons (interaction with radiation). This characterizes the scope of the article. Its emphasis is on the interrelation between theory and experiment, i.e., on the microscopic or model interpretation of experimental spectra.Work on infrared absorption and Raman scattering of non-metallic solids was summarized twenty years ago in two review articles in this Encyclopedia by LECOMTE (1958) and by MIZUSHIMA (1958). Since then, many important new experimental data have become available, thanks to very refined techniques for measuring spectra of pure and imperfect single crystals. Furthermore, the theory of the interactions of phonons and photons has been much improved, stimulated by the remarkable development of the theory of lattice vibrations and the mathematical techniques of many-body physics.In this article we describe the dispersion and absorption of infrared radiation and Raman scattering in non-metallic crystals, both perfect and containing point defects. At present, quantitative calculations are usually restricted to diatomic crystals, especially those with simple structures such as the alkali halides or germanium and its homologues, since our knowledge of lattice vibrations is still rather poor for polyatomic and low-symmetry crystals. The theory of lattice vibrations, as reviewed by COCHRAN and COWLEY (1967) in Vol. XXV /2a of this Encyclopedia, constitutes the background and the natural starting point for our investigations. There are other recent reviews by LUDWIG (1967), COCHRAN (1971), MARADUDIN et al. (1971), SINHA (1973), and several articles in: HORTON and MARADUDIN (eds., 1974). A summary of the developments during the last few years is given in Chap. B.An important part of the theory of lattice vibrations is the construction of models. A good example is the so-called shell model for phonons (see Sect. 4) which describes the adiabatic linear electron-ion interaction in terms of localized charges and coupling constants. This provides a natural explanation of some long-range ion-ion forces in insulators in terms of induced dipole forces. Anharmonic extensions of this shell model and its modifications seem very desirable, and first attempts in this direction are discussed.Models can often give a qualitatively and sometimes quantitatively correct description of certain processes in terms of a few parameters. They provide, therefore, an orientation for microscopic approaches. Furthermo...

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�ber die Anwendbarkeit der statistischen Methode auf Ionengitter

Cited by 183 publications

References 0 publications

Influence of the polarization in grazing scattering of fast helium atoms from LiF(001) surfaces

Influence of the polarization in grazing scattering of fast helium atoms from LiF(001) surfaces

The Ground State Energy of Heavy Atoms: The Leading Correction

Vibrational Infrared and Raman Spectra of Non-Metals

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