The Reciprocal Space as a Space of Quantum Numbers

2021 ◽  
pp. 63-90
Keyword(s):  
Reciprocal Space ◽  
Quantum Numbers

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

Calculation of structure images of crystalline defects

1978 ◽  
Vol 36 (1) ◽  
pp. 282-283
Author(s):  
M.A. O'Keefe ◽  
Sumio Iijima
Keyword(s):  
Diffuse Scattering ◽  
Computing Time ◽  
Continuous Distribution ◽  
Sampling Interval ◽  
Reciprocal Space ◽  
Objective Lens ◽  
Lattice Images ◽  
Slice Method ◽  
Space Cell ◽  
Beam Lattice

We have extended the multi-slice method of computating many-beam lattice images of perfect crystals to calculations for imperfect crystals using the artificial superlattice approach. Electron waves scattered from faulted regions of crystals are distributed continuously in reciprocal space, and all these waves interact dynamically with each other to give diffuse scattering patterns.In the computation, this continuous distribution can be sampled only at a finite number of regularly spaced points in reciprocal space, and thus finer sampling gives an improved approximation. The larger cell also allows us to defocus the objective lens further before adjacent defect images overlap, producing spurious computational Fourier images. However, smaller cells allow us to sample the direct space cell more finely; since the two-dimensional arrays in our program are limited to 128X128 and the sampling interval shoud be less than 1/2Å (and preferably only 1/4Å), superlattice sizes are limited to 40 to 60Å. Apart from finding a compromis superlattice cell size, computing time must be conserved.

Decay of resonant states and determination of their quantum numbers

1970 ◽  
Vol 101 (8) ◽  
pp. 655-696 ◽  
Author(s):  
M.S. Dubovikov ◽  
Yurii A. Simonov
Keyword(s):  
Quantum Numbers ◽  
Resonant States

Time-resolved X-ray reciprocal space mapping of the crystal under external electric field

2018 ◽  
Vol 189 (02) ◽  
pp. 187-194 ◽  
Author(s):  
Nikita V. Marchenkov ◽  
Anton G. Kulikov ◽  
Ivan I. Atknin ◽  
Arsen A. Petrenko ◽  
Alexander E. Blagov ◽  
...  
Keyword(s):  
Electric Field ◽  
External Electric Field ◽  
Space Mapping ◽  
Reciprocal Space ◽  
Reciprocal Space Mapping ◽  
Time Resolved ◽  
X Ray

Ab initio structure determination of cytochrome c6 by combined reciprocal space-real space approach

2003 ◽  
Vol 218 (1) ◽  
Author(s):  
K. Chowdhury ◽  
S. Ghosh ◽  
M. Mukherjee
Keyword(s):  
Cytochrome C ◽  
Ab Initio ◽  
Structure Determination ◽  
Direct Method ◽  
Real Space ◽  
Reciprocal Space ◽  
Cytochrome C6 ◽  
Ab Initio Structure ◽  
Space Approach

AbstractThe direct method program SAYTAN has been applied successfully to redetermine the structure of cytochrome c

Debye equation versus Whole Powder Pattern Modelling: Real versus reciprocal space modelling of nanomaterials

2009 ◽  
Vol 2009 (30) ◽  
pp. 85-90 ◽  
Author(s):  
K. Beyerlein ◽  
A. Cervellino ◽  
M. Leoni ◽  
R. L. Snyder ◽  
P. Scardi
Keyword(s):  
Reciprocal Space ◽  
Powder Pattern ◽  
Equation Versus ◽  
Debye Equation

Temperature Dependences in the O + OH → O2 + H Reaction. Quasiclassical Trajectory Calculation

1993 ◽  
Vol 58 (2) ◽  
pp. 234-243 ◽  
Author(s):  
Viliam Klimo ◽  
Martina Bittererová ◽  
Stanislav Biskupič ◽  
Ján Urban ◽  
Miroslav Micov
Keyword(s):  
Temperature Dependence ◽  
Energy Surface ◽  
Analytical Form ◽  
Mean Values ◽  
Quantum Numbers ◽  
Mean Lifetime ◽  
Temperature Dependences ◽  
Quasiclassical Trajectory Calculation ◽  
The Mean ◽  
Combustion Processes

The reaction O + OH → O2 + H in conditions of combustion of hydrocarbons and polymers was modelled by using the method of quasiclassical trajectories. The potential energy surface was determined by the multiconfiguration interaction method and fitted with the analytical form of the extended LEPS function. Attention was paid to the mean values of the vibrational and rotational quantum numbers of O2 molecules and their temperature dependence. The temperature dependence of the mean lifetime of the OOH collision complex was also examined. The calculated rate constants were analyzed and compared with the experimental data over the temperature region of the combustion processes.

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