CALCULATION OF THE PRESSURE BROADENING OF ROTATIONAL RAMAN LINES DUE TO MULTIPOLAR AND DISPERSION INTERACTION

1966 ◽  
Vol 44 (10) ◽  
pp. 2411-2430 ◽  
Author(s):  
C. G. Gray ◽  
J. Van Kranendonk
Keyword(s):  
Cross Sections ◽  
Rotational Quantum Number ◽  
Dispersion Forces ◽  
Line Broadening ◽  
Molecular Constants ◽  
Fourth Degree ◽  
Impact Theory ◽  
Experimental Values ◽  
Anisotropic Dispersion ◽  
The Impact

The impact theory of Raman line broadening is applied to the broadening of the rotational Raman lines of diatomic molecules arising from electric multipole and anisotropic dispersion forces. Expressions are derived for the elastic and inelastic optical cross sections, and these are evaluated for the self-broadening in N2, O2, CO, and CO2, using values of the molecular constants obtained from sources independent of the line-broadening experiments. Included in the calculations are the "time", or "resonant", factors in the optical cross sections, and the resulting time integrals are explicitly evaluated for arbitrary multipole interactions, and anisotropic dispersion forces of second and fourth degree in the orientations. The overall agreement between the theoretical and experimental values of the magnitude of the half-widths is satisfactory, but a discrepancy appears in the variation of the broadening with the rotational quantum number. Possible explanations of this discrepancy are suggested in view of the results on foreign-gas broadening by monatomic gases.

CALCULATION OF THE SELF-BROADENING OF RAMAN LINES DUE TO DIPOLAR AND QUADRUPOLAR FORCES

1963 ◽  
Vol 41 (3) ◽  
pp. 433-449 ◽  
Author(s):  
J. Van Kranendonk
Keyword(s):  
Phase Shift ◽  
Cross Sections ◽  
Scattered Light ◽  
Rotational Quantum Number ◽  
Intermolecular Forces ◽  
Intermolecular Potential ◽  
Radiation Process ◽  
Impact Theory ◽  
Order Of Magnitude ◽  
The Impact

The impact theory of Raman line broadening due to anisotropic intermolecular forces, developed previously, is applied to the broadening due to dipolar and quadrupolar forces. The optical cross sections are calculated assuming the isotropic intermolecular potential to be a hard-sphere potential, and neglecting the spread in velocities. Explicit expressions are derived for the phase-shift contribution to the width of the isotropic (j = 0) and anisotropic (j = 2) Raman scattered light as a function of the rotational quantum number J. For j = 2 scattering the phase shifts produced in the radiation do not vanish when the initial and final states of the radiation process are identical, and the phase-shift contribution to the width of the anisotropic components of the Q lines is of the same order of magnitude as for the S lines. In all cases the phase-shift contribution tends to zero when J becomes large compared with j. The contribution to the width of the inelastic collisions also tends to zero for large J, but this is characteristic of the long-range interactions considered here and results from the correspondingly short range of the resonance factors. The theory is compared with the available experimental data on H2 and N2. It is pointed out that quite generally an observation of the broadening of the isotropic and anisotropic Raman lines allows a determination of the lifetimes of the rotational levels and of the phase-shift contributions to the width of the anisotropic lines.

IMPACT THEORY OF RAMAN LINE BROADENING

1962 ◽  
Vol 40 (9) ◽  
pp. 1085-1100 ◽  
Author(s):  
J. Fiutak ◽  
J. Van Kranendonk
Keyword(s):  
Raman Scattering ◽  
Cross Sections ◽  
Molecular System ◽  
Electric Quadrupole ◽  
Complex Conjugate ◽  
Simple Derivation ◽  
Radiation Process ◽  
Average Value ◽  
Impact Theory ◽  
The Impact

The impact theory of Anderson for the pressure broadening of absorption and emission spectra is extended to the Raman spectra. Expressions are derived for the line shape and the optical cross sections in the classical path approximation. The central problem is the calculation of the average value of the evolution operator of the molecular system. It is shown that a simple derivation of the usual impact formula for this average value is obtained by averaging over all collisions as well as over all collision times. The perturbations of the intermediate states of the radiation processes are of importance only for resonant Raman scattering and may be neglected for non-resonant scattering. For freely rotating molecules the Raman scattering arising from electric dipole interaction can be decomposed into "isotropic", "magnetic dipole", and "electric quadrupole" scattering, corresponding to the j = 0, 1, and 2 irreducible parts of the Raman tensor. The optical cross sections for these three types of Raman scattering are different and are given by the reduced matrix elements, corresponding to j = 0, 1, and 2, of the optical cross-section operator, where j is the sum of the angular momenta in the initial and the complex conjugate of the final state of the radiation process.

scholarly journals Rotationally Resolved Rate Constant Measurements for Removal of CH(A2Δ and B2∑−) by Ketene

1994 ◽  
Vol 14 (4) ◽  
pp. 207-216 ◽  
Author(s):  
Jorge Luque ◽  
Javier Ruiz ◽  
Margarita Martin
Keyword(s):  
Quantum Number ◽  
Rate Constant ◽  
Cross Sections ◽  
Rate Constants ◽  
Rotational Quantum Number ◽  
Moderate Increase ◽  
Quantum Numbers ◽  
State Rate ◽  
Experimental Errors ◽  
Experimental Values

Rate constants for total removal of CH(A2Δ) and CH(B2∑−) in collisions with ketene were measured. For the A2Δ state, rate constants increased with vibrational quantum number; measured values were (4.5 ± 0.5) × 10-10 cm3 molec-1 s-1 and (8.0 ± 1) × 10-01 cm3 molec-1 s-1 for v′ = 0 and v′ = 2 respectively. For v′ = 0, rotational levels with quantum numbers from N′ = 4 to N′ = 16 were removed with similar rates within experimental errors; collisional disappearance of levels with higher rotational quantum numbers was faster for a factor of about 1.4. Calculations of cross sections for ketene and other fast colliders, assuming a multipole model, obtained a qualitative correlation with experimental values. CH(B2∑−) was more efficiently removed than CH(A2Δ, v′ = 0); for the lowest rotational levels a rate constant of (5.8 ± 0.3) × 10-10 cm3 molec-1 s-1 was measured and a moderate increase with rotational quantum number was observed.

THEORY OF THE IMPACT BROADENING OF RAMAN LINES DUE TO ANISOTROPIC INTERMOLECULAR FORCES

1963 ◽  
Vol 41 (1) ◽  
pp. 21-32 ◽  
Author(s):  
J. Fiutak ◽  
J. Van Kranendonk
Keyword(s):  
Raman Line ◽  
Cross Section ◽  
Raman Band ◽  
Collision Operator ◽  
Intermolecular Forces ◽  
Strong Interactions ◽  
Line Broadening ◽  
Impact Theory ◽  
Optical Cross Section ◽  
The Impact

The impact theory of Raman line broadening developed previously is applied to the broadening due to anisotropic intermolecular forces. The concept of frequency degeneracy is introduced, and its importance for the broadening of isotropic Raman lines is discussed. The components of a pure vibrational Raman band show a broadening due to the anisotropic intermolecular forces proportional to the density as long as the separation between the components is large compared with the line width. However, if the components of the vibrational band are not resolved the anisotropic forces give no further broadening with increasing density. Explicit expressions are derived for the elastic and inelastic parts of the optical cross section by expanding the collision operator in powers of the interaction responsible for the broadening and retaining only the lowest-order nonvanishing terms, but preserving the unitarity of the collision operator. The dependence of the cross section on the interaction and on the molecular diameter is shown to be quite different for weak and strong interactions.

Experimental Studies Of Multilayer Glass Structures On Compression, Compression With Bending And Simple Bending

2019 ◽  
pp. 22-30
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Applied Load ◽  
Experimental Studies ◽  
Strength Properties ◽  
Research Topic ◽  
Normative Values ◽  
Laminated Glass ◽  
The Cross ◽  
Experimental Values

The work of multilayer glass structures for central and eccentric compression and bending are considered. The substantiation of the chosen research topic is made. The description and features of laminated glass for the structures investigated, their characteristics are presented. The analysis of the results obtained when testing for compression, compression with bending, simple bending of models of columns, beams, samples of laminated glass was made. Overview of the types and nature of destruction of the models are presented, diagrams of material operation are constructed, average values of the resistance of the cross-sections of samples are obtained, the table of destructive loads is generated. The need for development of a set of rules and guidelines for the design of glass structures, including laminated glass, for bearing elements, as well as standards for testing, rules for assessing the strength, stiffness, crack resistance and methods for determining the strength of control samples is emphasized. It is established that the strength properties of glass depend on the type of applied load and vary widely, and significantly lower than the corresponding normative values of the strength of heat-strengthened glass. The effect of the connecting polymeric material and manufacturing technology of laminated glass on the strength of the structure is also shown. The experimental values of the elastic modulus are different in different directions of the cross section and in the direction perpendicular to the glass layers are two times less than along the glass layers.

The efficiency of application of virtual cross-sections method and hypotheses MELS in problems of wave signal propagation in elastic waveguides with rough surfaces

2016 ◽  
pp. 3564-3575 ◽  
Author(s):  
Ara Sergey Avetisyan
Keyword(s):  
Half Space ◽  
Cross Sections ◽  
Classical Method ◽  
Signal Propagation ◽  
Elastic Half Space ◽  
Layered Systems ◽  
Surface Layers ◽  
Inhomogeneous Surface ◽  
Wave Signal ◽  
The Impact

The efficiency of virtual cross sections method and MELS (Magneto Elastic Layered Systems) hypotheses application is shown on model problem about distribution of wave field in thin surface layers of waveguide when plane wave signal is propagating in it. The impact of surface non-smoothness on characteristics of propagation of high-frequency horizontally polarized wave signal in isotropic elastic half-space is studied. It is shown that the non-smoothness leads to strong distortion of the wave signal over the waveguide thickness and along wave signal propagation direction as well.  Numerical comparative analysis of change in amplitude and phase characteristics of obtained wave fields against roughness of weakly inhomogeneous surface of homogeneous elastic half-space surface is done by classical method and by proposed approach for different kind of non-smoothness.

scholarly journals A note on the relations between elastic and inelastic interactions and increasing ratio σel(s)/σtot(s) at the LHC

2019 ◽  
Vol 34 (32) ◽  
pp. 1950259 ◽  
Author(s):  
S. M. Troshin ◽  
N. E. Tyurin
Keyword(s):  
Elastic Scattering ◽  
Energy Dependence ◽  
Impact Parameter ◽  
Cross Sections ◽  
Parameter Dependence ◽  
Slope Parameter ◽  
Short Notice ◽  
Inelastic Interactions ◽  
The Impact ◽  
Mode A

We comment briefly on relations between the elastic and inelastic cross-sections valid for the shadow and reflective modes of the elastic scattering. Those are based on the unitarity arguments. It is shown that the redistribution of the probabilities of the elastic and inelastic interactions (the form of the inelastic overlap function becomes peripheral) under the reflective scattering mode can lead to increasing ratio of [Formula: see text] at the LHC energies. In the shadow scattering mode, the mechanism of this increase is a different one, since the impact parameter dependence of the inelastic interactions probability is central in this mode. A short notice is also given on the slope parameter and the leading contributions to its energy dependence in both modes.

scholarly journals Charged current Drell-Yan production at N3LO

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Claude Duhr ◽  
Falko Dulat ◽  
Bernhard Mistlberger
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Production Cross Section ◽  
Production Cross ◽  
Hadron Collider ◽  
Charge Asymmetry ◽  
Charged Current ◽  
Leading Order ◽  
Neutrino Pair ◽  
The Impact

Abstract We present the production cross section for a lepton-neutrino pair at the Large Hadron Collider computed at next-to-next-to-next-to-leading order (N3LO) in QCD perturbation theory. We compute the partonic coefficient functions of a virtual W± boson at this order. We then use these analytic functions to study the progression of the perturbative series in different observables. In particular, we investigate the impact of the newly obtained corrections on the inclusive production cross section of W± bosons, as well as on the ratios of the production cross sections for W+, W− and/or a virtual photon. Finally, we present N3LO predictions for the charge asymmetry at the LHC.

scholarly journals Simulation Tests of a Cow Milking Machine—Analysis of Design Parameters

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1358
Author(s):  
Ewa Golisz ◽  
Adam Kupczyk ◽  
Maria Majkowska ◽  
Jędrzej Trajer
Keyword(s):  
Mathematical Model ◽  
Simplified Model ◽  
Design Parameters ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Local Loss ◽  
Linear Drag ◽  
Milking Machine ◽  
Machine Analysis ◽  
The Impact

The objective of this paper was to create a mathematical model of vacuum drops in a form that enables the testing of the impact of design parameters of a milking cluster on the values of vacuum drops in the claw. Simulation tests of the milking cluster were conducted, with the use of a simplified model of vacuum drops in the form of a fourth-degree polynomial. Sensitivity analysis and a simulation of a model with a simplified structure of vacuum drops in the claw were carried out. As a result, the impact of the milking machine’s design parameters on the milking process could be analysed. The results showed that a change in the local loss and linear drag coefficient in the long milk duct will have a lower impact on vacuum drops if a smaller flux of inlet air, a higher head of the air/liquid mix, and a higher diameter of the long milk tube are used.

Dependence of Diffusion Paths on Thermodynamic Factors in Ternary Systems

2008 ◽  
Vol 277 ◽  
pp. 119-124 ◽  
Author(s):  
Ü. Ugaste ◽  
J. Priimets ◽  
Tony Laas
Keyword(s):  
Approximate Equation ◽  
Ternary Systems ◽  
Diffusion Path ◽  
Tracer Diffusion ◽  
Diffusion Paths ◽  
Slope Function ◽  
Experimental Values ◽  
The Impact ◽  
Tracer Diffusion Coefficients ◽  
Thermodynamic Factors

The impact of thermodynamic factors on deviation from linearity of diffusion path in the ternary system Cu-Fe-Ni is analyzed. For that the slope function of the diffusion path for the diffusion couples 65Ni30Cu5Fe –29.5Ni16.5Cu54Fe, 49.5Ni50.5Fe – 51Ni49Cu and 84Cu16Ni – 50Ni50Fe, annealed at 1000°C for 196h, were calculated by an approximate equation using only thermodynamic data. Results of the calculation were compared with the values of the slope function obtained directly from experimental data. It is shown that despite of the fact that the tracer diffusion coefficients of the components in the system Cu-Fe-Ni are not equal the coincidence between the calculated and experimental values of the slope function is remarkable. This allows us to conclude that at least in this case the deviation of the diffusion path from linearity depends mainly on the thermodynamic properties of the system.

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