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.

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

The effect of collisions on the rotational angular momentum of diatomic molecules studied using polarized light

2020 ◽  
Vol 153 (18) ◽  
pp. 184310
Author(s):  
P. T. Arndt ◽  
J. Huennekens ◽  
C. Packard ◽  
V. Tran ◽  
J. Carey ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Diatomic Molecules ◽  
Polarized Light ◽  
Rotational Angular Momentum

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.

Modified Dunham potential for rovibrational diatomic systems

1995 ◽  
Vol 73 (1-2) ◽  
pp. 59-62 ◽  
Author(s):  
Marcin Molski ◽  
Jerzy Konarski
Keyword(s):  
Angular Momentum ◽  
Quantum Number ◽  
Standard Method ◽  
Diatomic Molecules ◽  
Rotational Quantum Number ◽  
Electronic States ◽  
Rotational States ◽  
Diatomic Systems ◽  
Rovibrational States ◽  
Rotational Angular Momentum

A modified Dunham potential with parameters depending on the rotational quantum number is employed to describe the rovibrational states of diatomic molecules. This approach, applied to H81Br, 115InD, 7LiH, and 40Ar2, gives satisfactory reproduction of the observed transitions using fewer Dunham parameters than in the standard method. The results obtained indicate the possibility of introducing the local internal potentials, which, in contradiction to the global ones usually used, depend on the rotational states of a rotating–vibrating molecule. Such a J dependence may be a result of rovibronic interactions, in particular, Coriolis-type nonadiabatic interactions coupling other electronic states through the rotational angular momentum.

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 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

General Properties of Higher-Spin Fermion Interaction Currents and Their Test in πN-Scattering

2021 ◽  
Vol 57 (11) ◽  
pp. 1179
Author(s):  
Yu.V. Kulish ◽  
E.V. Rybachuk
Keyword(s):  
Angular Momentum ◽  
Partial Wave ◽  
Total Angular Momentum ◽  
Mass Shell ◽  
Present Approach ◽  
Partial Wave Analysis ◽  
Wave Analysis ◽  
Fermion Propagator ◽  
Higher Spin ◽  
Spin Tensors

The currents of higher-spin fermion interactions with zero- and half-spin particles are derived. They can be used for the N*(J) ↔ Nπ-transitions (N*(J) is thenucleon resonance with the J spin). In accordance with the theorem on currents and fields, the spin-tensors of these currents are traceless, and their products with the γ-matrices and the higher-spin fermion momentum vanish, similarly to the field spin-tensors. Such currents are derived explicitly for J=3/2and 5/2. It is shown that, in the present approach, the scale dimension of a higher spin fermion propagator equals to –1 for any J ≥ 1/2. The calculations indicate that the off-mass-shell N* contributions to the s-channel amplitudes correspond to J = JπN only ( JπN is the total angular momentum of the πN-system). As contrast, in the usually exploited approaches, such non-zero amplitudes correspond to 1/2 ≤  JπN ≤ J. In particular, the usually exploited approaches give non-zero off-mass-shell contributions of the ∆(1232)-resonance to the amplitudes S31, P31( JπN = 1/2) and P33, D33(JπN = 3/2), but our approach – to P33 and D33 only. The comparison of these results with the data of the partial wave analysis on the S31-amplitude in the ∆(1232)-region shows the better agreement for the present approach.

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