On the K-dependence of the electrical field in a crystalline slab of oscillating charges

1981 ◽  
Vol 59 (7) ◽  
pp. 929-933 ◽  
Author(s):  
J. Grindlay
Keyword(s):  
Electric Field ◽  
Trigonometric Series ◽  
Wave Vector ◽  
Short Range ◽  
Electrical Field ◽  
Ewald Sum ◽  
Convergent Trigonometric Series ◽  
Short Range Part ◽  
Range Part

The short range part of the electric field of a crystalline slab array of oscillating charges (a) is related to the Ewald sum and (b) can be represented by a rapidly convergent trigonometric series involving the wave vector K. Values for the coefficients of the first few terms of this series are reported for lattice sites in the sc, fcc, bcc, NaCl, CsCl structures and the symmetry directions (1,0,0), (1,1,0), (1,1,1).

scholarly journals Долинно-орбитальное взаимодействие в германии, легированном донорами V группы: количественный анализ

2021 ◽  
Vol 55 (10) ◽  
pp. 901
Author(s):  
А.А. Ревин ◽  
А.М. Михайлова ◽  
А.А. Конаков ◽  
В.В. Цыпленков ◽  
В.Н. Шастин
Keyword(s):  
Short Range ◽  
Ritz Method ◽  
Orbit Interaction ◽  
Envelope Function ◽  
Triplet States ◽  
Short Range Potential ◽  
Singlet And Triplet States ◽  
Short Range Part ◽  
Range Part ◽  
Envelope Functions

In the framework of the envelope function approximation, the wave functions of electrons localized at shallow donors P, As, Sb in Ge are calculated taking into account the valley-orbit coupling caused by the donor short-range potential. It is proposed an approach that makes it possible to include inter-valley mixing in the equation for a multi-component envelope function. The calculation of the effects of the valley-orbit interaction was carried out according to the perturbation theory, while the "bare" single-valley functions were found using the Ritz method. The parameters of the short-range part of the potential and the coefficient of inter-valley mixing were found individually for each donor, making it possible to obtain the best agreement with the results of experimental measurements of the energies of the singlet and triplet states. The envelope functions of the 1s(A1) and 1s(T2) states are calculated. The parameters of the valley-orbit interaction are found for each donor. It is also shown how the functions of the excited 2s, 2p0, 2p±, 3p0 states should be modified in order to remain orthogonal to the singlet and triplet functions within the framework of a more rigorous multivalley model.

Extended excluded volume: Its origin and consequences

2012 ◽  
Vol 85 (1) ◽  
pp. 201-210 ◽  
Author(s):  
Ivo Nezbeda ◽  
Michael Rouha
Keyword(s):  
Short Range ◽  
Infinite Dilution ◽  
Structural Data ◽  
Excluded Volume ◽  
Mechanical Approach ◽  
Short Range Part ◽  
Statistical Mechanical ◽  
The Common ◽  
Nonpolar Fluids ◽  
Range Part

In contrast to the common intuitive/speculative approach based on an analysis of thermodynamic or structural data of (nonpolar) fluids, the statistical mechanical approach is used to extend the excluded volume concept to all other types of fluids. The (extended) excluded volume incorporates, in addition to common nonelectrostatic interactions defining the shape and size of the molecules, also the short-range part of the repulsive interactions between the embedded Coulombic sites. In this study we show that the extended excluded volume concept correctly predicts the behavior of the partial molar volume (PMV) at infinite dilution in different solvents and, particularly, differences between nonpolar and associating solvents. The concept is then applied to estimate the PMV of methanol in water.

scholarly journals A superformula for neutrinoless double beta decay II: the short range part

2001 ◽  
Vol 498 (1-2) ◽  
pp. 35-39 ◽  
Author(s):  
H. Päs ◽  
M. Hirsch ◽  
H.V. Klapdor-Kleingrothaus ◽  
S.G. Kovalenko
Keyword(s):  
Beta Decay ◽  
Short Range ◽  
Neutrinoless Double Beta Decay ◽  
Double Beta Decay ◽  
Short Range Part ◽  
Range Part
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