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.

Notizen: Quantum Mechanical Calculation of Collision Integrals for HD

1971 ◽  
Vol 26 (11) ◽  
pp. 1926-1928 ◽  
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.

Senftleben-Beenakker Effects, Nonresonant Absorption and Collision Integrals for Gases Consisting of Symmetrie Top Molecules

1974 ◽  
Vol 29 (2) ◽  
pp. 299-305
Author(s):  
H. Moraal
Keyword(s):  
Distribution Function ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Viscosity ◽  
Tensor Polarization ◽  
Collision Integrals ◽  
Model Calculations ◽  
Dipole Moment Operator ◽  
Moment Operator ◽  
Function Density

The kinetic theories of the electric and magnetic Senftleben-Beenakker effects and of nonresonant absorption in polar symmetric top gases are reviewed, using an expansion of the distribution function-density matrix which includes the dipole moment operator μe . General expressions are given for the elastic parts of all collision integrals coupling two purely angular momentum dependent tensors. This is done for a variety of nonspherical potentials, including the dipole-dipole (DD), dipole-quadrupole (DQ) and quadrupole-quadrupole (QQ) interactions. Model calculations for the m ethyl halogenides are performed for these potentials for a number of collision integrals, namely the nonresonant cross section and three collision cross sections which are of importance for the shear viscosity Senftleben-Beenakker effects. These calculations indicate that DD, DQ and QQ interactions may all be important, that at least half of the nonresonant cross section is elastic and that the average cross section extracted by means of Levi’s theory from electric field shear viscosity Senftleben-Beenakker measurements is approximately equal to the reorientation cross section for the tensor polarization [μe](2).

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.

Experimental Studies Of Multilayer Glass Structures On Compression, Compression With Bending And Simple Bending

2019 ◽  
pp. 22-30
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Applied Load ◽  
Experimental Studies ◽  
Strength Properties ◽  
Research Topic ◽  
Normative Values ◽  
Laminated Glass ◽  
The Cross ◽  
Experimental Values

The work of multilayer glass structures for central and eccentric compression and bending are considered. The substantiation of the chosen research topic is made. The description and features of laminated glass for the structures investigated, their characteristics are presented. The analysis of the results obtained when testing for compression, compression with bending, simple bending of models of columns, beams, samples of laminated glass was made. Overview of the types and nature of destruction of the models are presented, diagrams of material operation are constructed, average values of the resistance of the cross-sections of samples are obtained, the table of destructive loads is generated. The need for development of a set of rules and guidelines for the design of glass structures, including laminated glass, for bearing elements, as well as standards for testing, rules for assessing the strength, stiffness, crack resistance and methods for determining the strength of control samples is emphasized. It is established that the strength properties of glass depend on the type of applied load and vary widely, and significantly lower than the corresponding normative values of the strength of heat-strengthened glass. The effect of the connecting polymeric material and manufacturing technology of laminated glass on the strength of the structure is also shown. The experimental values of the elastic modulus are different in different directions of the cross section and in the direction perpendicular to the glass layers are two times less than along the glass layers.

scholarly journals The 7Be(p, ?)8B Cross Section at Low Energies

1980 ◽  
Vol 33 (2) ◽  
pp. 177 ◽  
Author(s):  
FC Barker
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Solar Neutrinos ◽  
Model Calculations ◽  
Spectroscopic Factors ◽  
Low Energies ◽  
Standard Values ◽  
Experimental Values ◽  
Parameter Values ◽  
Potential Parameters

The nonresonant part of the 7Be(p, )I)8B cross section at low energies is recalculated by means of a direct-capture potential model, using parameter values determined by fitting 7Li(n, n)7Li and 7Li(n, )I)8Li data. Standard values of the potential parameters and spectroscopic factors give values of the 7Li(n,)I) cross section that are too large. Modified values that fit the thermal-neutron capture cross section predict 7Be(p,)I) cross sections that are much less than the experimental values. Also, shell model calculations predict resonant 7Be(p,)I) cross sections that are smaller than the experimental values. It is suggested that the accepted experimental values of the 7Be(p, )I) cross section may be too large, perhaps due partly to an overlarge accepted value for the 7Li(d, p)8Li cross section, which has been used for normalization purposes. A decrease in the 7Be(p,)I) cross section would reduce the calculated detection rate of solar neutrinos and lessen the discrepancy with the measured value.

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.

The determination of the cross sections for the reactions 27 Al( n , α ) and 56 Fe( n , p ) for 14 MeV neutrons by an absolute method

1966 ◽  
Vol 292 (1429) ◽  
pp. 180-192 ◽  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Standard Error ◽  
Particle Method ◽  
Systematic Errors ◽  
Aluminium Foil ◽  
The Mean ◽  
The Cross ◽  
Experimental Values

Measurements of the cross sections for the reactions 27 Al( n , α ) 24 Na and 56 Fe( n, p ) 56 Mn for neutrons of energy 13.5 ± 0.1 MeV have been made by a radioactivation method. The neutron flux was determined by a variant of the 'associated particle’ method, in which the α -particles produced concurrently with the neutrons from the D + T reaction were estimated in terms of the volume of helium which accumulated when they were brought to rest in an aluminium foil. Cross section values obtained at 13.5 MeV were: for 27 Al( n , α ): 118.1 ± 6.0 mb : for 56 Fe( n, p ): 106.7 ± 4.7 mb. The errors quoted include both the standard error on the mean of the experimental values and an estimate of possible residual systematic errors. The excitation functions for both reactions in the energy region 13.5 to 14.8 MeV have also been investigated, in order to provide secondary cross section values over this range of energies. At 14.8 MeV the values found were: 27 Al( n , α )103.6 ± 5.5 mb; 56 Fe( n, p )96.7 ± 4.5 mb.

Total-to-K-shell photoelectric cross-section ratios in some rare-earth and high-Z elements

1989 ◽  
Vol 67 (2-3) ◽  
pp. 139-142 ◽  
Author(s):  
S. Chandra Lingam ◽  
K. Suresh Babu ◽  
V. Prakash Kumar ◽  
D. V. Krishna Reddy
Keyword(s):  
Rare Earth ◽  
Cross Section ◽  
Atomic Number ◽  
Cross Sections ◽  
Cross Section Ratio ◽  
Section Ratio ◽  
Photoelectric Cross Section ◽  
Normal Transmission ◽  
Experimental Values ◽  
Good Agreement

The total photoelectric cross-sections in the elements gadolinium, dysprosium, erbium, lutetium, tantalum, tungsten, gold, and lead have been obtained by using the normal transmission experiments, and the results are reported. Using these total photoelectric cross sections, we have found the K-shell photoelectric cross sections, the K-jump ratios, and the total-to-K-shell photoelectric cross-section ratios at the K edges for the above elements. These values are compared with the available theoretical and experimental values. The results are in good agreement with the Storm and Israel results and the Scofield theoretical values, within the limits of experimental uncertainties. Furthermore, the variation of the total-to-K-shell photoelectric cross-section ratio with energy and atomic number is discussed.

scholarly journals The scattering of slow neutrons by ortho - and para -hydrogen

1955 ◽  
Vol 230 (1180) ◽  
pp. 19-32 ◽  
Keyword(s):  
Scattering Amplitudes ◽  
Cross Section ◽  
Cross Sections ◽  
Scattering Amplitude ◽  
Coherent Scattering ◽  
Para Hydrogen ◽  
Cavendish Laboratory ◽  
Proton Interaction ◽  
Scattering Cross Sections ◽  
Slow Neutrons

The neutron velocity selector of the Cavendish Laboratory has been used to measure the scattering cross-sections of ortho- and para -hydrogen for slow neutrons. The triplet and singlet scattering amplitudes of the neutron-proton interaction may be deduced from these cross-sections. The values obtained are a t = (0·537 ± 0·004) x 10 -12 cm, a s = -(2·373 ±0·007) x 10 -12 cm, where a t and a s are the triplet and singlet scattering amplitudes respectively. The values of the coherent scattering amplitude ƒ = 2(3/4 a +1/4 a ), and of the free proton cross-section σ ƒ = 4π(3/4 a 2 t + 1/4 a 2 s given by the above values of a t and a s , are ƒ = -(0·380 ± 0·005) x 10 -12 cm, σ ƒ = (20·41 ± 0·14) x 10 -24 cm 2 .

scholarly journals Comment on electron-impact excitation cross section measurements for He-like xenon

2019 ◽  
Vol 97 (5) ◽  
pp. 576-578
Author(s):  
J.-C. Pain ◽  
M. Comet ◽  
C.J. Fontes
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Ion Trap ◽  
Impact Excitation ◽  
Electron Impact Excitation ◽  
Experimental Investigations ◽  
State University ◽  
Electron Beam Ion Trap ◽  
Penn State ◽  
Experimental Values

We discuss lower-than-predicted collisional–excitation cross sections for helium-like xenon measured at an Electron Beam Ion Trap facility. In a review paper (H. Chen and P. Beiersdorfer. Can. J. Phys. 86, 55 (2008)), the authors find a significant effect due to the Breit interaction between the free and the bound electrons in the excitation process of He-like xenon. The authors state that the agreement between the measured and calculated cross section values can only be found when the generalized Breit interaction is included in the calculations. We have performed new calculations with a multi-configuration Dirac–Fock code, as well as with the Penn State University suite of codes, and our conclusions are that the contribution of the Breit interaction is much lower than found in the calculations presented in the abovementioned article. In fact, our predictions are subsequently almost twice as large as the experimental values. We present these considerations in hopes of motivating new experimental investigations.

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