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

1974 ◽  
Vol 29 (12) ◽  
pp. 1705-1716 ◽  
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.

QUASICLASSICAL TRAJECTORY STUDY OF STEREODYNAMICS FOR THE REACTIONS Li+HF/DF/TF

2013 ◽  
Vol 12 (03) ◽  
pp. 1350008
Author(s):  
JIE CHENG ◽  
XIAN-FANG YUE
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
Collision Energy ◽  
Energy Surface ◽  
Center Of Mass ◽  
Angular Distributions ◽  
Direct Reaction ◽  
Generalized Polarization ◽  
State 1 ◽  
Rotational Angular Momentum

Stereodynamics of the reaction Li + HF (v = 0,j = 0) → LiF + H and its isotopic variants on the ground electronic state (12A′) potential energy surface (PES) are studied by employing the quasiclassical trajectory (QCT) method. At a collision energy of 2.2 kcal/mol, product rotational angular momentum distributions, P(θr) and P(ϕr), are calculated in the center-of-mass (CM) frame. The results demonstrate that the product rotational angular momentum j′ is not only aligned along the direction perpendicular to the reagent relative velocity vector k, but also oriented along the negative y-axis. The four generalized polarization-dependent differential cross sections (PDDCSs) are also computed. The PDDCS00 distribution shows a sideways scattering for the reaction Li + HF and a strongly backward scattering for the reaction Li + DF . However, it displays both the forward and backward scatterings for the reaction Li + TF . These features demonstrate that the Li + HF and Li + DF reactions proceed predominantly through the direct reaction mechanism. However, the Li + TF reaction undergoes both the direct and indirect reaction mechanisms. The PDDCS21- distribution indicates that the product angular distributions are anisotropic.

THEORETICAL STUDY OF PRODUCT POLARIZATION FOR THE REACTION Ba + CH3I → BaI + CH3

2009 ◽  
Vol 08 (supp01) ◽  
pp. 1045-1051
Author(s):  
YAN QI ◽  
ZHI-XIN DUAN
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
Collision Energy ◽  
Center Of Mass ◽  
Exothermic Reaction ◽  
Classical Trajectory ◽  
Angle Distribution ◽  
Vector Correlation ◽  
Generalized Differential ◽  
Rotational Angular Momentum

Using quasi-classical trajectory (QCT) method, the vector correlation between products and reagents for the exothermic reaction Ba + CH3I → BaI + CH3 has been studied on the extended Lond–Eyring–Polanyi–Sato (LEPS) potential energy surface (PES) at three collision energies of 1.6, 3.3, and 5.6 kcal/mol. The P(θr) distribution of the products describing the k-j' correlation and the dihedral angle distribution P(ϕr) describing k-k'-j' correlation are calculated in center-of-mass (CM) frame. Four polarization dependent generalized differential cross-sections (2π/σ)(dσ00/dωt), (2π/σ)(dσ20/dωt), (2π/σ)(dσ22+/dωt), and (2π/σ)(dσ21-/dωt) have also been presented in the CM frame as well. The results indicate that the product rotational angular momentum j' is not only aligned, but also oriented along the direction perpendicular to the scattering plane. In addition, the alignment and the orientation of the BaI product rotational angular momentum depend very sensitively on the collision energy.

scholarly journals Waldmann-Snider Collision Integrals for Mixtures of Polyatomic Gases Exact and Approximate Relations

1979 ◽  
Vol 34 (11) ◽  
pp. 1255-1268
Author(s):  
W. E. Köhler ◽  
G. W. 't Hooft
Keyword(s):  
Elastic Scattering ◽  
Conservation Laws ◽  
Cross Sections ◽  
Molecular Interaction ◽  
Complete System ◽  
Collision Integrals ◽  
Polyatomic Gases ◽  
Exact Relations

Collision brackets of the linearized Waldmann-Snider collision superoperator are studied for mixtures of polyatomic gases. Properties following f r om symmetries of molecular interaction and collisional conservation laws are discussed. For a complete system of expansion tensors bracket symbol expressions for effective cross sections are given which generalize the Chapman-Cowling Ω-integrals. Exact relations between effective cross sections are derived. Approximate relations which hold for molecules with small nonsphericity and elastic scattering are also given

Quantum Mechanical Calculation of the Magnitude of the Senftleben-Beenakker Effect of the Heat Conductivity for p-H2 at Room Temperature

1973 ◽  
Vol 28 (6) ◽  
pp. 815-823 ◽  
Author(s):  
W. E. Köhler
Keyword(s):  
Cross Sections ◽  
Heat Conductivity ◽  
Room Temperature ◽  
Scattering Amplitude ◽  
Collision Integral ◽  
Intermolecular Potential ◽  
Collision Term ◽  
Tensor Polarization ◽  
Collision Integrals ◽  
Simple Potential

The magnetic Senftleben-Beenakker effect of the heat conductivity is considered for a gas of p-H2 molecules. The magnitude of the saturation value is expressed in terms of collision integrals of the linearized Waldmann-Snider collision term. The collision integrals are, in turn, connected with molecular cross sections describing the production of a tensor polarization of the molecular rotational angular momenta. These orientation cross sections depend essentially on the nonspherical part of the intermolecular potential. For small nonsphericity of the interaction, valid in the case of H2, it is sufficient to take into account only energetically elastic collisions For a simple potential model (nearly spherical rigid ellipsoids of revolution) the scattering amplitude is analytically evaluated in first order DWBA. The relevant collision integral which describes the coupling between the rotational heat flux and the Kagan polarization is calculated for room temperature. The comparison with the experimental value shows a good agreement.

Waldmann-Snider Collision Integrals and Nonspherical Molecular Interaction

1975 ◽  
Vol 30 (2) ◽  
pp. 117-133 ◽  
Author(s):  
W. E. Köhler
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Scattering Amplitude ◽  
Interaction Model ◽  
Tensor Polarization ◽  
Collision Integrals ◽  
Angular Momenta ◽  
Linear Molecules ◽  
Experimental Values ◽  
Amplitude Matrix

Abstract The binary scattering amplitude matrix is derived from the general interaction potential between linear molecules. The first order distorted wave Born approximation (DWBA) is used which is applicable for small nonsphericity of the interaction. The molecular cross sections determining the most important Waldmann-Snider collision integrals are calculated. In particular, the scattering cross section, the orientation cross sections for vector-and tensor polarization and the reorientation cross sections for the tensor polarization of the rotational angular momenta are treated. For a simple interaction model for HD (HT) molecules the DWBA-scattering amplitude is evaluated analytically. The relaxation cross section of the tensor polarization, σT , and the coupling cross section of friction pressure tensor and tensor polarization, ση,T, are calculated for room temperature and compared with experimental values.

THEORETICAL STUDY OF STEREO-DYNAMICS FOR THE REACTION C(3P) + CH(2II) → C2 + H ON THE THREE LOWEST POTENTIAL ENERGY SURFACES

2010 ◽  
Vol 09 (06) ◽  
pp. 1065-1073 ◽  
Author(s):  
ZUOYE LIU ◽  
BITAO HU
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
Potential Energy Surfaces ◽  
Three Dimensional ◽  
Angular Distributions ◽  
Potential Surfaces ◽  
Positive Direction ◽  
Classical Trajectories ◽  
Energy Surfaces ◽  
Rotational Angular Momentum

Based on the global three-dimensional adiabatic potential surfaces (PESs) 12 A ′, 22 A ′, 12 A ″ [Boggio-Pasqua et al., Phys Chem Chem Phys2:1693, 2000], the stereo-dynamics of the reaction C + CH → C 2 + H has been investigated by using the quasi-classical trajectories (QCT) method. The four polarization-dependent differential cross sections (PDDCSs) and the angular distributions of P(θr), P(ϕr), P(θr, ϕr) have been calculated at the collision energy 0.1 eV on the three PESs, respectively. The calculated results indicate that the distribution of the product C2 is backward-forward scattering on the 12 A ′ and 12 A ″ PESs and backward scattering on the 22 A ′ PES. The product rotational angular momentum is strongly aligned along the perpendicular direction to the reagent relative velocity k on the three PESs. The orientation of the product C 2 rotational angular momentum tends to point to the positive direction of the y-axis on the 12 A ′ PES but the negative direction on the 22 A ′ and 12 A ″ PESs.

Cross sections for transfer of rotational angular momentum in CO2from13C spin relaxation studies in the gas phase

1987 ◽  
Vol 86 (5) ◽  
pp. 2717-2722 ◽  
Author(s):  
Cynthia J. Jameson ◽  
A. Keith Jameson ◽  
Nancy C. Smith ◽  
Karol Jackowski
Keyword(s):  
Angular Momentum ◽  
Gas Phase ◽  
Spin Relaxation ◽  
Cross Sections ◽  
Relaxation Studies ◽  
Rotational Angular Momentum

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.

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