Notizen: Quantum Mechanical Calculation of Collision Integrals for HD

1971 ◽  
Vol 26 (11) ◽  
pp. 1926-1928 ◽  
Author(s):  
W. E. Köhler
Keyword(s):  
Scattering Amplitude ◽  
Quantum Mechanical ◽  
Collision Term ◽  
Tensor Polarization ◽  
Collision Integrals ◽  
First Order ◽  
Relaxation Coefficient ◽  
Angular Momenta ◽  
Experimental Values ◽  
Good Agreement

The magnetic Senftleben-Beenakker effect of the viscosity is mainly determined by two collision integrals of the linearized quantum mechanical Waldmann-Snider collision term, viz. by the relaxation coefficient of the tensor polarization of the molecular rotational angular momenta and by the coefficient which couples the friction pressure tensor and the tensor polarization. Starting from a simple nonspherical potential for HD, the scattering amplitude is evaluated analytically in first order distorted wave Born approximation and the two collision integrals are calculated for room temperature. A fairly good agreement with experimental values is found.

Waldmann-Snider Collision Integrals and Nonspherical Molecular Interaction

1975 ◽  
Vol 30 (2) ◽  
pp. 117-133 ◽  
Author(s):  
W. E. Köhler
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Scattering Amplitude ◽  
Interaction Model ◽  
Tensor Polarization ◽  
Collision Integrals ◽  
Angular Momenta ◽  
Linear Molecules ◽  
Experimental Values ◽  
Amplitude Matrix

Abstract The binary scattering amplitude matrix is derived from the general interaction potential between linear molecules. The first order distorted wave Born approximation (DWBA) is used which is applicable for small nonsphericity of the interaction. The molecular cross sections determining the most important Waldmann-Snider collision integrals are calculated. In particular, the scattering cross section, the orientation cross sections for vector-and tensor polarization and the reorientation cross sections for the tensor polarization of the rotational angular momenta are treated. For a simple interaction model for HD (HT) molecules the DWBA-scattering amplitude is evaluated analytically. The relaxation cross section of the tensor polarization, σT , and the coupling cross section of friction pressure tensor and tensor polarization, ση,T, are calculated for room temperature and compared with experimental values.

Quantum Mechanical Calculation of the Magnitude of the Senftleben-Beenakker Effect of the Heat Conductivity for p-H2 at Room Temperature

1973 ◽  
Vol 28 (6) ◽  
pp. 815-823 ◽  
Author(s):  
W. E. Köhler
Keyword(s):  
Cross Sections ◽  
Heat Conductivity ◽  
Room Temperature ◽  
Scattering Amplitude ◽  
Collision Integral ◽  
Intermolecular Potential ◽  
Collision Term ◽  
Tensor Polarization ◽  
Collision Integrals ◽  
Simple Potential

The magnetic Senftleben-Beenakker effect of the heat conductivity is considered for a gas of p-H2 molecules. The magnitude of the saturation value is expressed in terms of collision integrals of the linearized Waldmann-Snider collision term. The collision integrals are, in turn, connected with molecular cross sections describing the production of a tensor polarization of the molecular rotational angular momenta. These orientation cross sections depend essentially on the nonspherical part of the intermolecular potential. For small nonsphericity of the interaction, valid in the case of H2, it is sufficient to take into account only energetically elastic collisions For a simple potential model (nearly spherical rigid ellipsoids of revolution) the scattering amplitude is analytically evaluated in first order DWBA. The relevant collision integral which describes the coupling between the rotational heat flux and the Kagan polarization is calculated for room temperature. The comparison with the experimental value shows a good agreement.

ANALYSIS OF MELTING FOR ALKALI EARTH AND ALKALI OXIDES BASED ON THE DIFFUSIONAL FORCE THEORY

2004 ◽  
Vol 18 (21n22) ◽  
pp. 1101-1107 ◽  
Author(s):  
QUAN LIU ◽  
LI-RONG CHEN
Keyword(s):  
Quantum Mechanical ◽  
Repulsive Potential ◽  
Ionic Model ◽  
Alkali Earth ◽  
Melting Temperatures ◽  
Quadrupole Interactions ◽  
Quantum Mechanical Treatment ◽  
Alkali Oxides ◽  
Experimental Values ◽  
Good Agreement

An analysis of the melting alkali earth and alkali oxides is presented using the concept of diffusional force. The calculations are performed by developing an ionic model based on Harrison's quantum mechanical treatment of overlap repulsive potential which takes into account the interactions up to second neighbors. Van der Waals dipole–dipole and dipole–quadrupole interactions calculated by more accurate methods are also included in the model. Using the formula by Fang, derived on the basis of thermodynamic analysis, the values of interionic distances for 8 alkali earth and alkali oxides at melting have been obtained. A simple model for melting is developed based on the diffusional force models. The values of Tm thus obtained are found to show fairly good agreement with experimental values of melting temperatures.

Kinetic Theory of Nonequilibrium Alignment Phenomena in Atomic Vapors

1973 ◽  
Vol 28 (10) ◽  
pp. 1543-1553
Author(s):  
W. E. Köhler ◽  
S. Hess
Keyword(s):  
Cross Sections ◽  
Scattering Amplitude ◽  
Flow Birefringence ◽  
Optical Methods ◽  
Tensor Polarization ◽  
First Order ◽  
Atomic Vapors ◽  
Reacting Mixtures ◽  
Order Of Magnitude ◽  
Special Case

Nonequilibrium alignment phenomena in gases of polyatomic molecules (Senftleben-Beenakker effect, flow birefringence) have been studied extensively during the last decade. Similar effects should also exist for atoms with nonzero electronic orbital angular momentum. The Waldmann- Snider equation (considered as Boltzmann equation for reacting mixtures) is used to derive an expression for the tensor polarization caused by a flow field in such atomic vapors. As a simple special case 2P-atoms are treated as an effective two level system (fine structure doublet). They can be tensor-polarized in the state with j = 3/2. An ansatz is made for the nonspherical interaction potential between 2P-atoms. The scattering amplitude is calculated in first order Born approximation which is reasonable for the high temperatures necessary. The relevant cross sections and collision integrals are evaluated. The temperature dependence of the alignment and its order of magnitude are discussed. Although the effect is rather small it should be detectable by optical methods (flow birefringence). The connection of flow birefringence and collisional alignment is elucidated.

Systematic calculations of energy levels and transitions rates in Mo XXVIII

2020 ◽  
Vol 75 (8) ◽  
pp. 739-747
Author(s):  
Feng Hu ◽  
Yan Sun ◽  
Maofei Mei
Keyword(s):  
Energy Levels ◽  
Oscillator Strengths ◽  
Atomic Data ◽  
Data Sets ◽  
Electron Systems ◽  
Excitation Energies ◽  
Experimental Values ◽  
Qed Effects ◽  
Hyperfine Structures ◽  
Good Agreement

AbstractComplete and consistent atomic data, including excitation energies, lifetimes, wavelengths, hyperfine structures, Landé gJ-factors and E1, E2, M1, and M2 line strengths, oscillator strengths, transitions rates are reported for the low-lying 41 levels of Mo XXVIII, belonging to the n = 3 states (1s22s22p6)3s23p3, 3s3p4, and 3s23p23d. High-accuracy calculations have been performed as benchmarks in the request for accurate treatments of relativity, electron correlation, and quantum electrodynamic (QED) effects in multi-valence-electron systems. Comparisons are made between the present two data sets, as well as with the experimental results and the experimentally compiled energy values of the National Institute for Standards and Technology wherever available. The calculated values including core-valence correction are found to be in a good agreement with other theoretical and experimental values. The present results are accurate enough for identification and deblending of emission lines involving the n = 3 levels, and are also useful for modeling and diagnosing plasmas.

Analysis of the First Order and Slowly Varying Motions of an Axisymmetric Floating Body in Bichromatic Waves

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
João Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Drift Motion ◽  
First Order ◽  
Motion Responses ◽  
Simple Geometry ◽  
Good Agreement

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and biharmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axisymmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in biharmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

scholarly journals DFT calculation and assignment of vibrational spectra of aryl and alkyl chlorophosphates

2014 ◽  
Vol 12 (2) ◽  
pp. 153-163
Author(s):  
Viktor Anishchenko ◽  
Vladimir Rybachenko ◽  
Konstantin Chotiy ◽  
Andrey Redko
Keyword(s):  
Vibrational Spectra ◽  
Basis Sets ◽  
Heavy Atoms ◽  
Wide Range ◽  
Complete Assignment ◽  
Key Factor ◽  
Polarization Functions ◽  
Experimental Values ◽  
Semi Empirical ◽  
Good Agreement

AbstractDFT calculations of vibrational spectra of chlorophosphates using wide range of basis sets and hybrid functionals were performed. Good agreement between calculated and experimental vibrational spectra was reached by the combination of non-empirical functional PBE0 with both middle and large basis sets. The frequencies of the stretching vibrations of the phosphate group calculated using semi-empirical functional B3LYP for all basis sets deviate significantly from the experimental values. The number of polarization functions on heavy atoms was shown to be a key factor for the calculation of vibrational frequencies of organophosphates. The importance of consideration of all the stable rotamers for a complete assignment of fundamental modes was shown.

Vulcanization of Elastomers. 23. The Chemical Kinetics of Vulcanization Reactions and The Physical Properties of The Vulcanizates. I

1960 ◽  
Vol 33 (2) ◽  
pp. 335-341
Author(s):  
Walter Scheele ◽  
Karl-Heinz Hillmer
Keyword(s):  
Activation Energy ◽  
Physical Properties ◽  
Chemical Kinetics ◽  
Kcal Mole ◽  
First Order ◽  
Equilibrium Swelling ◽  
Kinetics Of ◽  
Kinetics Of Vulcanization ◽  
Limiting Value ◽  
Good Agreement

Abstract As a complement to earlier investigations, and in order to examine more closely the connection between the chemical kinetics and the changes with vulcanization time of the physical properties in the case of vulcanization reactions, we used thiuram vulcanizations as an example, and concerned ourselves with the dependence of stress values (moduli) at different degrees of elongation and different vulcanization temperatures. We found: 1. Stress values attain a limiting value, dependent on the degree of elongation, but independent of the vulcanization temperature at constant elongation. 2. The rise in stress values with the vulcanization time is characterized by an initial delay, which, however, is practically nonexistent at higher temperatures. 3. The kinetics of the increase in stress values with vulcanization time are both qualitatively and quantitatively in accord with the dependence of the reciprocal equilibrium swelling on the vulcanization time; both processes, after a retardation, go according to the first order law and at the same rate. 4. From the temperature dependence of the rate constants of reciprocal equilibrium swelling, as well as of the increase in stress, an activation energy of 22 kcal/mole can be calculated, in good agreement with the activation energy of dithiocarbamate formation in thiuram vulcanizations.

Models for New Corrugated and Porous Solar Air Collectors under Transient Operation

2017 ◽  
Vol 42 (1) ◽  
Author(s):  
Qahtan Adnan Abed ◽  
Viorel Badescu ◽  
Adrian Ciocanea ◽  
Iuliana Soriga ◽  
Dorin Bureţea
Keyword(s):  
Climatic Conditions ◽  
Meteorological Conditions ◽  
Bias Error ◽  
First Order ◽  
Solar Air Collector ◽  
Section Surface ◽  
South Eastern Europe ◽  
Main Components ◽  
Theoretical Results ◽  
Good Agreement

AbstractMathematical models have been developed to evaluate the dynamic behavior of two solar air collectors: the first one is equipped with a V-porous absorber and the second one with a U-corrugated absorber. The collectors have the same geometry, cross-section surface area and are built from the same materials, the only difference between them being the absorbers. V-corrugated absorbers have been treated in literature but the V-porous absorbers modeled here have not been very often considered. The models are based on first-order differential equations which describe the heat exchange between the main components of the two types of solar air heaters. Both collectors were exposed to the sun in the same meteorological conditions, at identical tilt angle and they operated at the same air mass flow rate. The tests were carried out in the climatic conditions of Bucharest (Romania, South Eastern Europe). There is good agreement between the theoretical results and experiments. The average bias error was about 7.75 % and 10.55 % for the solar air collector with “V”-porous absorber and with “U”-corrugated absorber, respectively. The collector based on V-porous absorber has higher efficiency than the collector with U-corrugated absorber around the noon of clear days. Around sunrise and sunset, the collector with U-corrugated absorber is more effective.

scholarly journals Structural elastic and thermal properties of SrxCd1−x O mixed compounds — a theoretical approach

2014 ◽  
Vol 32 (3) ◽  
pp. 350-357
Author(s):  
Purvee Bhardwaj
Keyword(s):  
Phase Transition ◽  
Vibrational Energy ◽  
Zero Point ◽  
Study Phase ◽  
Energy Effect ◽  
Phase Transition Pressure ◽  
Vegard’S Law ◽  
Extended Interaction ◽  
Experimental Values ◽  
Good Agreement

AbstractIn the present paper, the structural and mechanical properties of alkaline earth oxides mixed compound SrxCd1−x O (0 ≤ x ≤ 1) under high pressure have been reported. An extended interaction potential (EIP) model, including the zero point vibrational energy effect, has been developed for this study. Phase transition pressures are associated with a sudden collapse in volume. Phase transition pressure and associated volume collapses [ΔV (Pt)/V(0)] calculated from this approach are in good agreement with the experimental values for the parent compounds (x = 0 and x = 1). The results for the mixed crystal counterparts are also in fair agreement with experimental data generated from the application of Vegard’s law to the data for the parent compounds.

Sign in / Sign up

Export Citation Format

Share Document