Spectrum of the Depolarized Rayleigh Light Scattered by Gases of Linear Molecules

The spectrum of the depolarized Rayleigh light scattered by a gas of linear molecules is calculated by a kinetic theory approach based on the Waldman-Snider equation. Collisional and diffusional broadening are studied. The line width is related to relaxation coefficients which are collision brackets obtained from the linearized Waldmann-Snider collision term involving the binary molecular scattering amplitude and its adjoint. It is shown under which conditions the relaxation coefficients characterizing the line width can be compared with data obtained from Sentfleben- Beenakker effect and nuclear magnetic relaxation measurements

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On the Nonspherical Scattering Amplitude for Inelastic Molecular Collisions

Zeitschrift für Naturforschung A ◽

10.1515/zna-1970-0304 ◽

1970 ◽

Vol 25 (3) ◽

pp. 336-350 ◽

Cited By ~ 5

Author(s):

W. E. Köhler ◽

S. Hess ◽

L. Waldmann

Keyword(s):

Angular Momentum ◽

Bulk Viscosity ◽

Interaction Potential ◽

Scattering Amplitude ◽

Inelastic Collisions ◽

Momentum Dependence ◽

Molecular Collisions ◽

Molecular Scattering ◽

Polarized Beam ◽

Linear Molecules

The rotational angular momentum dependence of the nonspherical scattering amplitude is investigated for inelastic collisions of linear molecules. As far as the approximation of small nonsphericity can be applied, this dependence is obtained from the angular momentum dependence of the nonspherical interaction potential. The connection between the nonspherical scattering amplitude and observables that can be measured by molecular scattering experiments involving a polarized beam is discussed. Some qualitative remarks are made on collision brackets occurring in the theoretical expressions for the bulk viscosity and for the Senftleben-Beenakker effect for H2 and HD

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Notizen: Kinetic Theory for the Broadening of the Depolarized Rayleigh Line

Zeitschrift für Naturforschung A ◽

10.1515/zna-1969-1136 ◽

1969 ◽

Vol 24 (11) ◽

pp. 1852-1853

Author(s):

Siegfried Hess

Keyword(s):

Kinetic Theory ◽

Theory Approach ◽

Rayleigh Line ◽

Linear Molecules ◽

Rayleigh Light

Abstract Collisional and diffusional broadening of the depolarized Rayleigh light scattered by a gas of linear molecules are studied by a kinetic theory approach based on the Waldmann-Snider equation.

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Broadening of the Fine-Structure Raman Lines in Gaseous Oxygen

Zeitschrift für Naturforschung A ◽

10.1515/zna-1971-1012 ◽

1971 ◽

Vol 26 (10) ◽

pp. 1639-1643

Author(s):

S. Hess ◽

H. F. P. Knaap

Keyword(s):

Fine Structure ◽

Relaxation Frequency ◽

Collision Term ◽

60 Ghz ◽

Pressure Broadening ◽

Gaseous Oxygen ◽

Molecular Potential ◽

Electronic Spin ◽

Anti Stokes ◽

Rayleigh Light

Abstract Due to the coupling between the rotational angular momentum and the electronic spin, the depolarized Rayleigh light scattered from gaseous oxygen shows Stokes and anti-Stokes satellites shifted by about 60 GHz. The broadening of these fine-structure Raman lines is investigated theoretically for high and medium pressures where the linewidth is determined by two contributions, one proportional and the other inversely proportional to the pressure, p. The linewidth in the pressure broadening region is given by a relaxation frequency which is obtained from the Waldmann-Snider collision term. The p-1 contribution to the linewidth is determined by the ratio of the second moment of the fine-structure freqencies (with respect to the center of the shifted line) and another relaxation frequency. Both relaxation frequencies are sensitive to the nonspherical part of the inter-molecular potential.

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Simulation of magnetic relaxation measurements of tetragonal and thin films

Superconductor Science and Technology ◽

10.1088/0953-2048/11/11/008 ◽

1998 ◽

Vol 11 (11) ◽

pp. 1241-1250 ◽

Cited By ~ 1

Author(s):

M Holiastou ◽

M Pissas ◽

D Niarchos ◽

P Haibach ◽

U Frey ◽

...

Keyword(s):

Thin Films ◽

Magnetic Relaxation ◽

Relaxation Measurements

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Magnetic relaxation measurements on tissue mimicking phantoms: comparison between different fitting algorithms in MRI T2 calculations

Physica Medica ◽

10.1016/j.ejmp.2014.07.337 ◽

2014 ◽

Vol 30 ◽

pp. e118-e119

Author(s):

G. Kalaitzakis ◽

L. Kavroulakis ◽

T. Boursianis ◽

S. Veneti ◽

L. Kontopodis ◽

...

Keyword(s):

Magnetic Relaxation ◽

Relaxation Measurements

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Waldmann-Snider Collision Integrals and Nonspherical Molecular Interaction. I. Collision Integrals for Pure Gases

Zeitschrift für Naturforschung A ◽

10.1515/zna-1974-1202 ◽

1974 ◽

Vol 29 (12) ◽

pp. 1705-1716 ◽

Cited By ~ 21

Author(s):

W. E. Köhler

Keyword(s):

Angular Momentum ◽

Cross Sections ◽

Molecular Interaction ◽

Scattering Amplitude ◽

Collision Operator ◽

Positive Definiteness ◽

Collision Integrals ◽

General Properties ◽

Relaxation Coefficients ◽

Rotational Angular Momentum

Collision integrals of the linearized Waldmann-Snider collision operator for pure gases are defined. General properties due to invariances of the molecular interaction are discussed. Effective cross sections are introduced and expressed in terms of convenient bracket symbols. The positive definiteness of the relaxation coefficients is proved. The approximation of small nonsphericity for the scattering amplitude is explained and consequences for the collision integrals are investigated. Molecular cross sections describing the orientation and reorientation of the molecular rotational angular momentum are defined. Expressions for effective cross sections relevant for the various nonequilibrium alignment phenomena are presented.

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Notizen: Quantum Mechanical Calculation of Collision Integrals for HD

Zeitschrift für Naturforschung A ◽

10.1515/zna-1971-1123 ◽

1971 ◽

Vol 26 (11) ◽

pp. 1926-1928 ◽

Cited By ~ 7

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.

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Messung kernmagnetischer Relaxationszeiten in Hochauflösung mittels schneller adiabatischer Passagen

Zeitschrift für Naturforschung A ◽

10.1515/zna-1970-1117 ◽

1970 ◽

Vol 25 (11) ◽

pp. 1674-1680

Author(s):

Hans Lütje

Keyword(s):

High Resolution ◽

Polyethylene Oxide ◽

Magnetic Relaxation ◽

Chemical Shifts ◽

Signal To Noise Ratio ◽

Relaxation Times ◽

Resonance Signal ◽

Additional Equipment ◽

Relaxation Measurements ◽

Fast Passage

Abstract The nuclear magnetic relaxation times T1 and T2 may be determined by observing the relaxation that follows after a stop of an adiabatic fast passage at different points of the resonance signal. High resolution measurements are possible with external proton stabilization during the relaxation process if the chemical shifts are larger than 1 ppm and the relaxation times are longer than 1 sec. If no high resolution is required the lower limit is 0.2 seconds. Relaxation measurements are possible using conventional NMR-spectrometers without additional equipment. Since the signal to noise ratio is favourable, rather dilute solutions may be investigated. Relaxation measurements on benzene, on 4 different protons of 4-dimethylamino-benzaldehyde and on polyethylene oxide in solution are reported.

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