On the Nonspherical Scattering Amplitude for Inelastic Molecular Collisions

1970 ◽  
Vol 25 (3) ◽  
pp. 336-350 ◽  
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

Rotational Angular Momentum Dependence of the Scattering Amplitude for Elastic Molecular Collisions

1968 ◽  
Vol 23 (12) ◽  
pp. 1903-1911 ◽  
Author(s):  
S. Hess ◽  
W. E. Köhler
Keyword(s):  
Angular Momentum ◽  
Interaction Potential ◽  
Scattering Amplitude ◽  
Diatomic Molecules ◽  
Spin Operator ◽  
Potential Functions ◽  
Momentum Dependence ◽  
Starting Point ◽  
Spin Tensors ◽  
Rotational Angular Momentum

The rotational angular momentum (spin) dependence of the binary scattering amplitude operator is investigated for elastic collisions of homonuclear diatomic molecules with monatomic and diatomic particles. Starting point is a formal expansion of the T-matrix (and consequently of the scattering amplitude) with respect to the nonsphericity parameter ε which essentially measures the ratio of the nonspherical and spherical parts of the interaction potential. A transscription of angle dependent potential functions into a spin operator notation is introduced. Potential functions and values for ε may be inferred from the data available in the literature for the interactions: H2—He (ε ≈ 1/4) and H2—H2 (ε ≈ 1/20). As far as elastic events are concerned, irreducible spin tensors of even rank only occur with the interaction potential and consequently with the scattering amplitude in order ε. The most important terms of the scattering amplitude of diatomic molecules are quadratic in the spins. These terms are discussed in detail. In order ε2 the scattering amplitude also contains irreducible spin tensors of odd rank. A knowledge of the orders of magnitude of the various spin — dependent terms is of interest for the SENFTLEBEN-BEENAKKER effect and for NMR in polyatomic gases.

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

1970 ◽  
Vol 25 (3) ◽  
pp. 350-362 ◽  
Author(s):  
Siegfried Hess
Keyword(s):  
Line Width ◽  
Magnetic Relaxation ◽  
Scattering Amplitude ◽  
Collision Term ◽  
Theory Approach ◽  
Molecular Scattering ◽  
Relaxation Measurements ◽  
Linear Molecules ◽  
Relaxation Coefficients ◽  
Rayleigh Light

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

Boundary Condition for the Distribution Function of a Gas of Linear Molecules

1974 ◽  
Vol 29 (12) ◽  
pp. 1723-1735
Author(s):  
J. Halbritter
Keyword(s):  
Boundary Condition ◽  
Wave Function ◽  
Distribution Function ◽  
Angular Momentum ◽  
Interaction Potential ◽  
Transition Probability ◽  
Center Of Mass ◽  
Solid Surfaces ◽  
Molecular Axis ◽  
Linear Molecules

The scattering of linear molecules by a potential wall is studied. It is assumed that the interaction potential between the molecule and the wall depends on the distance of the center of mass of the molecule from the wall and on the orientation of the molecular axis. From the wave function of the reflected molecule an expression for the transition probability for scattering into the various final molecular states is obtained. Together with a modification of Maxwell's assumption for the interaction of atoms with solid surfaces, this transition probability is used to derive a boundary condition for the distribution function of a gas of linear rotating molecules. This also takes into account the change of rotational angular momentum in the collision with the wall.

scholarly journals Temperature and angular momentum dependence of the quadrupole deformation in sd-shell

Pramana ◽  
2009 ◽  
Vol 73 (5) ◽  
pp. 839-846
Author(s):  
P. A. Ganai ◽  
J. A. Sheikh ◽  
I. Maqbool ◽  
R. P. Singh
Keyword(s):  
Angular Momentum ◽  
Quadrupole Deformation ◽  
Momentum Dependence

scholarly journals Breakdown of energy transfer gap laws revealed by full-dimensional quantum scattering between HF molecules

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Dongzheng Yang ◽  
Jing Huang ◽  
Xixi Hu ◽  
Hua Guo ◽  
Daiqian Xie
Keyword(s):  
Energy Transfer ◽  
Angular Momentum ◽  
Vibrational Energy ◽  
Energy Gap ◽  
Inelastic Collisions ◽  
Rate Coefficients ◽  
Quantum Scattering ◽  
Final States ◽  
Energy Gap Law ◽  
Quantitative Basis

Abstract Inelastic collisions involving molecular species are key to energy transfer in gaseous environments. They are commonly governed by an energy gap law, which dictates that transitions are dominated by those between initial and final states with roughly the same ro-vibrational energy. Transitions involving rotational inelasticity are often further constrained by the rotational angular momentum. Here, we demonstrate using full-dimensional quantum scattering on an ab initio based global potential energy surface (PES) that HF–HF inelastic collisions do not obey the energy and angular momentum gap laws. Detailed analyses attribute the failure of gap laws to the exceedingly strong intermolecular interaction. On the other hand, vibrational state-resolved rate coefficients are in good agreement with existing experimental results, validating the accuracy of the PES. These new and surprising results are expected to extend our understanding of energy transfer and provide a quantitative basis for numerical simulations of hydrogen fluoride chemical lasers.

scholarly journals Спектральные моменты характеристик бинарных взаимодействий между линейными молекулами

2021 ◽  
Vol 129 (3) ◽  
pp. 253
Author(s):  
А.В. Соколов ◽  
А.П. Коузов ◽  
Ж.В. Булдырева ◽  
Н.И. Егорова
Keyword(s):  
Interaction Potential ◽  
Spectral Moments ◽  
New Approach ◽  
Relaxation Matrix ◽  
Arbitrary Rank ◽  
Molecular Pair ◽  
Linear Molecules ◽  
Computer Codes ◽  
Spectral Distributions ◽  
The Way

A new approach to derive symmetrized expressions of leading classical moments of spectral distributions characterizing different anisotropic terms of the interaction potential for the case of two liear molecules is presented. The results allow to calculate diffuse shapes formed by transitions between continuous eigenstates of a molecular pair and open the way to account for the nonMarkov effects (due to finite collision durations) in the rotatonal relaxation matrix of an arbitrary rank. The approach is also applied to the spectral moments of vector and tensor characteristics determining the band intensities in the collision-induced spectra of linear molecules. Generally, the use of symmetrized expressions lead to considerably faster computer codes.

scholarly journals Three-Body Scattering Amplitude. II. Extension to Complex Angular Momentum

1964 ◽  
Vol 136 (4B) ◽  
pp. B1137-B1153 ◽  
Author(s):  
Roland L. Omnes ◽  
Victor A. Alessandrini
Keyword(s):  
Angular Momentum ◽  
Scattering Amplitude ◽  
Complex Angular Momentum ◽  
Three Body
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