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.

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.

scholarly journals The impact of vibrational Raman scattering of air on DOAS measurements of atmospheric trace gases

2015 ◽  
Vol 8 (3) ◽  
pp. 3423-3469 ◽  
Author(s):  
J. Lampel ◽  
U. Frieß ◽  
U. Platt
Keyword(s):  
Raman Scattering ◽  
Inelastic Scattering ◽  
Cross Section ◽  
Cross Sections ◽  
Scattered Light ◽  
Optical Absorption Spectroscopy ◽  
Systematic Bias ◽  
Atmospheric Scattering ◽  
Sensing Applications ◽  
The Impact

Abstract. In remote sensing applications, such as differential optical absorption spectroscopy (DOAS), atmospheric scattering processes need to be considered. After inelastic scattering on N2 and O2 molecules, the scattered photons occur as additional intensity at a different wavelength, effectively leading to filling-in of both solar Fraunhofer lines and absorptions of atmospheric constituents. Measured spectra in passive DOAS applications are typically corrected for rotational Raman scattering (RRS), also called Ring effect, which represents the main contribution to inelastic scattering. In contrast to that, vibrational Raman scattering (VRS) of N2 and O2 has often been thought to be negligible, but also contributes. Consequences of VRS are red-shifted Fraunhofer structures in scattered light spectra and filling-in of Fraunhofer lines, additional to RRS. We describe how to calculate VRS correction spectra in analogy to the Ring spectrum. We discuss further the impact of VRS cross-sections for O2 and N2 on passive DOAS measurements. The relevance of VRS is shown for the first time in spectral evaluations of Multi-Axis DOAS data. This measurement data yields in agreement with calculated scattering cross-sections, that the observed VRS cross-section amounts to 2.2 ± 0.4% of the cross-section of RRS under tropospheric conditions. It is concluded, that this phenomenon has to be included in the spectral evaluation of weak absorbers as it reduces the measurement error significantly and can cause apparent differential optical depth of up to 2.5 × 10−4. Its influence on the spectral retrieval of IO, Glyoxal, water vapour and NO2 in the blue wavelength range is evaluated. For measurements with a large Ring signal a significant and systematic bias of NO2 dSCDs up to (−3.8 ± 0.4) × 1014 molec cm−2 at low elevation angles is observed if this effect is not considered.

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.

scholarly journals Non-LTE modelling of cyanoacetylene: evidence for isomer-specific excitation

2020 ◽  
Vol 501 (2) ◽  
pp. 1911-1919
Author(s):  
Cheikh T Bop ◽  
François Lique ◽  
Alexandre Faure ◽  
Ernesto Quintas-Sánchez ◽  
Richard Dawes
Keyword(s):  
Radiative Transfer ◽  
Cross Sections ◽  
Emission Spectra ◽  
Abundance Ratio ◽  
Rate Coefficients ◽  
Close Coupling ◽  
Circumstellar Gas ◽  
Order Of Magnitude ◽  
Rotational Transitions ◽  
The Impact

ABSTRACT Cyanoacetylene molecules are widespread in the interstellar medium (ISM) and several of its isomers have been detected in cold molecular clouds and circumstellar gas. Accurate estimates of the abundance ratio of cyanoacetylene isomers may provide deep insight into their environment. Such knowledge requires rigorous modelling of the emission spectra based on non-local thermodynamic equilibrium (LTE) radiative transfer calculations. To this end, we computed excitation cross-sections of HC2NC and HNC3 induced by collision with para- and ortho-H2, using a quantum mechanical close-coupling method. Then, by thermally averaging these data, we derived rate coefficients for the first 31 low-lying rotational levels of each isomer for temperatures up to 80 K. For the para-H2 collider, the propensity rules are in favour of rotational transitions involving Δj1 = 2 for both isomers, while for the ortho-H2 collider, Δj1 = 2 and Δj1 = 1 rotational transitions are favoured for HC2NC and HNC3, respectively. A comparison of rate coefficients for the HC3N isomers shows differences up to an order of magnitude, especially at low temperatures. Finally, we performed non-LTE radiative transfer calculations to assess the impact of such variations in the analysis of observations. Our simulation suggests that the lack of collisional data specific to each isomer could lead to errors up to a factor of 2–3 in the excitation temperatures. We expect that these data could help in better understanding the cyanoacetylene chemistry and constraining the nitrogen chemistry in the ISM.

Spectra of H2–Ne and D2–Ne Van der Waals Complexes in the Collision-Induced Fundamental Bands of Hydrogen and Deuterium

1972 ◽  
Vol 50 (13) ◽  
pp. 1458-1464 ◽  
Author(s):  
A. R. W. McKellar ◽  
H. L. Welsh
Keyword(s):  
Quantum Number ◽  
Direct Evidence ◽  
Van Der Waals ◽  
Rotational Quantum Number ◽  
Intermolecular Forces ◽  
The Other ◽  
Van Der Waals Complexes ◽  
Intermolecular Potential ◽  
Rare Gas ◽  
Potential Well

Spectra of H2–Ne and D2–Ne Van der Waals complexes accompanying transitions in the collision-induced fundamental bands of hydrogen and deuterium have been obtained with an absorption path of 110 m at temperatures around 27 K in a specially designed multiple-traversal cell. The observed structure is similar to that of H2– and D2–Ar, Kr, and Xe complexes studied earlier, but the number of lines observed for the Ne complexes is fewer because of the shallower intermolecular potential. Well-resolved R and P branches (Δl= ±1, where l is the rotational quantum number of the complex) accompanying the overlap-induced Q1 (0) transitions are analyzed directly to give rotational (B) and centrifugal stretching (D) constants for the complexes. Unlike the other H2– rare gas complexes the spectra accompanying quadrupole-induced transitions show no direct evidence of anisotropy of the intermolecular forces.

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.

Pound Wise and Penny Foolish? Weight Loss and The Dynamics of Health Care Spending

2011 ◽  
Vol 14 (2) ◽  
Author(s):  
Thomas G Koch
Keyword(s):  
Weight Loss ◽  
Cost Savings ◽  
Cost Effective ◽  
Economic Consequences ◽  
Health Care Spending ◽  
Order Of Magnitude ◽  
Dynamic Measures ◽  
The Cost ◽  
The Impact ◽  
The Relationship

Current estimates of obesity costs ignore the impact of future weight loss and gain, and may either over or underestimate economic consequences of weight loss. In light of this, I construct static and dynamic measures of medical costs associated with body mass index (BMI), to be balanced against the cost of one-time interventions. This study finds that ignoring the implications of weight loss and gain over time overstates the medical-cost savings of such interventions by an order of magnitude. When the relationship between spending and age is allowed to vary, weight-loss attempts appear to be cost-effective starting and ending with middle age. Some interventions recently proven to decrease weight may also be cost-effective.

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 The Impact of the Electric Field on Surface Condensation of Water Vapor: Insight from Molecular Dynamics Simulation

Nanomaterials ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 64 ◽  
Author(s):  
Qin Wang ◽  
Hui Xie ◽  
Zhiming Hu ◽  
Chao Liu
Keyword(s):  
Molecular Dynamics ◽  
Water Vapor ◽  
Electric Field ◽  
Intermolecular Forces ◽  
Dynamics Simulation ◽  
Water Molecules ◽  
Attraction Force ◽  
Condensation Rate ◽  
Shape Transformation ◽  
The Impact

In this study, molecular dynamics simulations were carried out to study the coupling effect of electric field strength and surface wettability on the condensation process of water vapor. Our results show that an electric field can rotate water molecules upward and restrict condensation. Formed clusters are stretched to become columns above the threshold strength of the field, causing the condensation rate to drop quickly. The enhancement of surface attraction force boosts the rearrangement of water molecules adjacent to the surface and exaggerates the threshold value for shape transformation. In addition, the contact area between clusters and the surface increases with increasing amounts of surface attraction force, which raises the condensation efficiency. Thus, the condensation rate of water vapor on a surface under an electric field is determined by competition between intermolecular forces from the electric field and the surface.

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