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 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.

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.

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

2015 ◽  
Vol 8 (9) ◽  
pp. 3767-3787 ◽  
Author(s):  
J. Lampel ◽  
U. Frieß ◽  
U. Platt
Keyword(s):  
Raman Scattering ◽  
Inelastic Scattering ◽  
Cross Section ◽  
Cross Sections ◽  
Systematic Bias ◽  
Atmospheric Scattering ◽  
Scattering Cross ◽  
The Cross ◽  
Scattering Cross Sections ◽  
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, if the inelastic scattering happens after the absorption. 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. Inelastic scattering can also occur in liquid water, and its influence on DOAS measurements has been observed over clear ocean water. In contrast to that, vibrational Raman scattering (VRS) of N2 and O2 has often been thought to be negligible, but it also contributes. Consequences of VRS are red-shifted Fraunhofer structures in scattered light spectra and filling-in of Fraunhofer lines, additional to RRS. At 393 nm, the spectral shift is 25 and 40 nm for VRS of O2 and N2, respectively. We describe how to calculate VRS correction spectra according to the Ring spectrum. We use the VRS correction spectra in the spectral range of 420–440 nm to determine the relative magnitude of the cross-sections of VRS of O2 and N2 and RRS of air. The effect of VRS is shown for the first time in spectral evaluations of Multi-Axis DOAS data from the SOPRAN M91 campaign and the MAD-CAT MAX-DOAS intercomparison campaign. The measurements yield in agreement with calculated scattering cross-sections that the observed VRS(N2) cross-section at 393 nm amounts to 2.3 ± 0.4 % of the cross-section of RRS at 433 nm under tropospheric conditions. The contribution of VRS(O2) is also found to be in agreement with calculated scattering cross-sections. 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 3 ×10−4. Its influence on the spectral retrieval of IO, glyoxal, water vapour and NO2 in the blue wavelength range is evaluated for M91. For measurements with a large Ring signal a significant and systematic bias of NO2 dSCDs (differential slant column densities) up to (−3.8 ± 0.4) × 1014 molec cm−2 is observed if this effect is not considered. The effect is typically negligible for DOAS fits with an RMS (root mean square) larger than 4 × 10−4.

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.

Assessing the Impact of the Inlet Total Pressure Distortion on the Turbofan Thrust

2018 ◽  
pp. 19-30
Author(s):  
Yu. A. Ezrokhi ◽  
E. A. Khoreva
Keyword(s):  
Total Pressure ◽  
External Compression ◽  
Average Value ◽  
Inlet Distortion ◽  
Air Inlet ◽  
Engine Thrust ◽  
Relative Value ◽  
Main Effect ◽  
Pressure Recovery Factor ◽  
The Impact

The paper considers techniques to develop a mathematical model using a method of «parallel compressors». The model is intended to estimate the impact of the air inlet distortion on the primary parameters of the aero-engine.  The paper presents rated estimation results in the context of twin spool turbofan design for two typical cruiser modes of flight of the supersonic passenger jet. In estimation the base values σbase and the average values of the inlet ram recovery σave remained invariable. Thus, parametrical calculations were performed for each chosen relative value of the area of low-pressure region.The paper shows that an impact degree of the inlet distortion on the engine thrust for two modes under consideration is essentially different. In other words, if in the subsonic mode the impact assessment can be confined only to taking into account the influence of decreasing average values of the inlet total pressure, the use of such an assumption in the supersonic cruiser mode may result in considerable errors.With invariable values of the pressure recovery factor at the engine intake, which correspond to the speed of flight for a typical air inlet of external compression σbase, and average value σave, a parameter Δσuneven  has the main effect on the engine thrust, and degree of this effect essentially depends on a difference between σave and σbase values.

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 Raman scattering in high-refractive-index nanostructures

Nanophotonics ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Søren Raza ◽  
Anders Kristensen
Keyword(s):  
Raman Spectroscopy ◽  
Refractive Index ◽  
Raman Scattering ◽  
Bound States ◽  
Stimulated Raman Scattering ◽  
Dielectric Materials ◽  
High Refractive Index ◽  
Surface Enhanced Raman Spectroscopy ◽  
Raman Enhancement ◽  
The Impact

AbstractThe advent of resonant dielectric nanomaterials has provided a new path for concentrating and manipulating light on the nanoscale. Such high-refractive-index materials support a diverse set of low-loss optical resonances, including Mie resonances, anapole states, and bound states in the continuum. Through these resonances, high-refractive-index materials can be used to engineer the optical near field, both inside and outside the nanostructures, which opens up new opportunities for Raman spectroscopy. In this review, we discuss the impact of high-refractive-index nano-optics on Raman spectroscopy. In particular, we consider the intrinsic Raman enhancement produced by different dielectric resonances and their theoretical description. Using the optical reciprocity theorem, we derive an expression which links the Raman enhancement to the enhancement of the stored electric energy. We also address recent results on surface-enhanced Raman spectroscopy based on high-refractive-index dielectric materials along with applications in stimulated Raman scattering and nanothermometry. Finally, we discuss the potential of Raman spectroscopy as a tool for detecting the optical near-fields produced by dielectric resonances, complementing reflection and transmission measurements.

scholarly journals Considerations of the Scale of Radiocarbon Offsets in the East Mediterranean, and Considering a Case for the Latest (Most Recent) Likely Date for the Santorini Eruption

Radiocarbon ◽  
2012 ◽  
Vol 54 (3-4) ◽  
pp. 449-474 ◽  
Author(s):  
Sturt W Manning ◽  
Bernd Kromer
Keyword(s):  
Time Horizon ◽  
Weighted Average ◽  
17Th Century ◽  
Data Sets ◽  
East Mediterranean ◽  
Average Value ◽  
Accuracy And Precision ◽  
Wide Range ◽  
The Impact ◽  
East Mediterranean Region

The debate over the dating of the Santorini (Thera) volcanic eruption has seen sustained efforts to criticize or challenge the radiocarbon dating of this time horizon. We consider some of the relevant areas of possible movement in the14C dating—and, in particular, any plausible mechanisms to support as late (most recent) a date as possible. First, we report and analyze data investigating the scale of apparent possible14C offsets (growing season related) in the Aegean-Anatolia-east Mediterranean region (excluding the southern Levant and especially pre-modern, pre-dam Egypt, which is a distinct case), and find no evidence for more than very small possible offsets from several cases. This topic is thus not an explanation for current differences in dating in the Aegean and at best provides only a few years of latitude. Second, we consider some aspects of the accuracy and precision of14C dating with respect to the Santorini case. While the existing data appear robust, we nonetheless speculate that examination of the frequency distribution of the14C data on short-lived samples from the volcanic destruction level at Akrotiri on Santorini (Thera) may indicate that the average value of the overall data sets is not necessarily the most appropriate14C age to use for dating this time horizon. We note the recent paper of Soter (2011), which suggests that in such a volcanic context some (small) age increment may be possible from diffuse CO2emissions (the effect is hypothetical at this stage and hasnotbeen observed in the field), and that "if short-lived samples from the same stratigraphic horizon yield a wide range of14C ages, the lower values may be the least altered by old CO2." In this context, it might be argued that a substantive “low” grouping of14C ages observable within the overall14C data sets on short-lived samples from the Thera volcanic destruction level centered about 3326–3328 BP is perhaps more representative of the contemporary atmospheric14C age (without any volcanic CO2contamination). This is a subjective argument (since, in statistical terms, the existing studies using the weighted average remain valid) that looks to support as late a date as reasonable from the14C data. The impact of employing this revised14C age is discussed. In general, a late 17th century BC date range is found (to remain) to be most likelyeven ifsuch a late-dating strategy is followed—a late 17th century BC date range is thus a robust finding from the14C evidence even allowing for various possible variation factors. However, the possibility of a mid-16th century BC date (within ∼1593–1530 cal BC) is increased when compared against previous analyses if the Santorini data are considered in isolation.

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