scholarly journals Elementary Statistical Models for Vector Collision-Sequence Interference Effects with Poisson-Distributed Collision Times

2010 ◽  
Vol 2010 ◽  
pp. 1-5 ◽  
Author(s):  
John Courtenay Lewis
Keyword(s):  
Dipole Moment ◽  
Poisson Process ◽  
Statistical Models ◽  
Intermolecular Force ◽  
Interference Effects ◽  
Arbitrary Power ◽  
Realistic Estimate ◽  
Induced Dipole ◽  
Using Data

In a recent paper (Lewis, 2008) a class of models suitable for application to collision-sequence interference was introduced. In these models velocities are assumed to be completely randomized in each collision. The distribution of velocities was assumed to be Gaussian. The integrated induced dipole moment μk, for vector interference, or the scalar modulation μk, for scalar interference, was assumed to be a function of the impulse (integrated force) fk, or its magnitude fk, experienced by the molecule in a collision. For most of (Lewis, 2008) it was assumed that μk∝fk and μk∝fk, but it proved to be possible to extend the models, so that the magnitude of the induced dipole moment is equal to an arbitrary power or sum of powers of the intermolecular force. This allows estimates of the infilling of the interference dip by the disproportionality of the induced dipole moment and force. One particular such model, using data from (Herman and Lewis, 2006), leads to the most realistic estimate for the infilling of the vector interference dip yet obtained. In (Lewis, 2008) the drastic assumption was made that collision times occurred at equal intervals. In the present paper that assumption is removed: the collision times are taken to form a Poisson process. This is much more realistic than the equal-intervals assumption. The interference dip is found to be a Lorentzian in this model.

Theory of Intercollisional Interference Effects. IV. Does a Zero Minimum in Induced Absorption Imply the Proportionality of the Induced Dipole Moment to the Force?

1973 ◽  
Vol 51 (23) ◽  
pp. 2455-2458 ◽  
Author(s):  
J. Courtenay Lewis
Keyword(s):  
Dipole Moment ◽  
Lorentz Gas ◽  
Intermolecular Force ◽  
Interference Effects ◽  
Induced Absorption ◽  
Induced Dipole ◽  
Interference Minimum

We show that, within the limits of the theory of intercollisional interference effects developed for collision-induced absorption by a Lorentz gas in paper I of this series, an intercollisional interference minimum which goes precisely to zero implies that the induced dipole moment is exactly proportional to the intermolecular force.

Intercollisional interference at low temperatures

1985 ◽  
Vol 63 (1) ◽  
pp. 99-103
Author(s):  
John Courtenay Lewis
Keyword(s):  
Dipole Moment ◽  
Impact Parameter ◽  
Low Temperatures ◽  
Quantum Effect ◽  
Intermolecular Force ◽  
Fundamental Band ◽  
Induced Dipole ◽  
Binary Collisions

The intercollisional interference dip in the Q-branch of the fundamental band of collision-induced spectra of H2–He mixtures partially fills in at low temperatures. In contradiction to claims that this ia a quantum effect, we show 1. that if the induced dipole moment is exactly proportional to the intermolecular force then the interference dip goes to zero at all temperatures; 2. that the filling-in of the dip is essentially a classical phenomenon and is due mainly to the discontinuity in the distance of closest approach during binary collisions as a function of impact parameter.

Theory of Intercollisional Interference Effects. I. Induced Absorption in a Lorentz Gas

1972 ◽  
Vol 50 (4) ◽  
pp. 352-367 ◽  
Author(s):  
J. Courtenay Lewis ◽  
J. Van Kranendonk
Keyword(s):  
Dipole Moment ◽  
General Theory ◽  
Kinetic Theory ◽  
Shape Function ◽  
Lorentz Gas ◽  
Intermolecular Force ◽  
Interference Effects ◽  
Exponential Functions ◽  
Series Expression ◽  
Line Shape Function

A general kinetic theory of intercollisional interference effects in induced infrared spectra is developed, in which the correlations between all the collisions in the collision sequence of a molecule are taken into account, but the effect of the ternary and higher-order collisions is neglected. The resulting series expression for the line-shape function is explicitly summed for a Lorentz gas. From this general theory expressions are derived for the depth of the intercollisional dip and the shape of the intercollisional spectrum assuming that the pair dipole moment and the intermolecular force are exponential functions with slightly different ranges. The extension of the theory to take into account the frequency dependence of the intracollisional spectrum, and the resulting inadequacy of the neglect of ternary collisions, are discussed.

Theory of intercollisional interference effects VI: an exactly solvable model exhibiting a shallow interference dip

1983 ◽  
Vol 61 (3) ◽  
pp. 440-450 ◽  
Author(s):  
John Courtenay Lewis
Keyword(s):  
Dipole Moment ◽  
Asymptotic Analysis ◽  
Closed Form ◽  
Solvable Model ◽  
Lorentz Gas ◽  
Interference Effects ◽  
Exactly Solvable Model ◽  
Induced Dipole ◽  
Exactly Solvable ◽  
The Impact

The theory of intercollisional interference effects developed in earlier publications in this series is applied to a model comprising a Lorentz gas with disks or spheres as the fixed seatterers, and a central induced dipole moment 1/R2ν varying as an inverse power of the intermolecular separation. It is shown that the integrated induced dipole moment [Formula: see text] and the relative dip height 1 – γ can be evaluated analytically and in closed form for this model. The interference dip is relatively shallow owing to a cusp in [Formula: see text] with a maximum where the impact parameter b equals the collision diameter. An asymptotic analysis indicates that the dip actually fills in as ν increases, contrary to earlier expectations. The same analysis is applied with minor modifications to an exponential induced dipole moment, and shows that the interference dip also fills in as the range goes to zero for that system. The applicability of the model to a system with more realistic interactions is discussed.

Intercollisional interference effects in pressure-induced infrared spectra

1968 ◽  
Vol 46 (10) ◽  
pp. 1173-1179 ◽  
Author(s):  
J. Van Kranendonk
Keyword(s):  
Spectral Density ◽  
Infrared Spectra ◽  
Interference Effect ◽  
Dipole Moments ◽  
Intermolecular Force ◽  
Interference Effects ◽  
Anisotropic Part ◽  
Induced Dipole ◽  
Binary Collisions ◽  
Zero Frequency

The dip observed in the Q branch of the pressure-induced vibrational spectra at high densities is shown to be an interference effect due to the correlations existing between the dipole moments induced in successive binary collisions. A similar dip is predicted to exist in the translational spectra of inertgas mixtures at zero frequency. This intercollisional interference effect has the same origin as the dip in the spectral density of the intermolecular force, discussed by Purcell in connection with nuclear electric dipole relaxation. The effect does not occur for the anisotropic part of the induced dipole moments, and this explains the observed absence of any splitting of the S lines and of the QQ component of the Q branch of the induced infrared spectra.

DIRECTIONAL DIFFUSION OF K ATOMS ON A GaAs(110) SURFACE

2006 ◽  
Vol 05 (06) ◽  
pp. 895-900 ◽  
Author(s):  
NOBUYUKI ISHIDA ◽  
AGUS SUBAGYO ◽  
KAZUHISA SUEOKA
Keyword(s):  
Dipole Moment ◽  
Electric Field ◽  
Radial Direction ◽  
Negative Sample ◽  
Directional Diffusion ◽  
Sample Bias ◽  
Induced Dipole ◽  
High K ◽  
Scanning Area ◽  
The Relationship

We performed STM measurements on the K/GaAs (110) surface with high K coverage. The K atoms gradually disappeared while scanning the tip over the surface at negative sample bias voltage. The phenomenon strongly occurred over the scanning area and can be explained by the field-induced surface diffusion from the scanning area to radial direction. Considering the interaction between the dipole moment of the adsorbed K atoms and the electric field, we discuss the relationship between the static and induced dipole moment of K atoms on a GaAs (110) surface.

Interference effects in the spectrum of HD: I. The fundamental band of pure HD

1983 ◽  
Vol 61 (12) ◽  
pp. 1648-1654 ◽  
Author(s):  
N. H. Rich ◽  
A. R. W. McKellar
Keyword(s):  
Absorption Spectrum ◽  
Dipole Moment ◽  
Phase Shift ◽  
Electric Dipole Moment ◽  
Electric Dipole ◽  
High Density ◽  
Line Profiles ◽  
Interference Effects ◽  
Permanent Electric Dipole Moment ◽  
Precise Interpretation

The absorption spectrum of the ν = 1 ← 0 band of HD has been investigated at a temperature of 77 K and for densities in the range of 15 to 140 amagat. The band consists of two components: a broad collision-induced quasi continuum arising from dipoles induced during molecular collisions; and a dipole-allowed part arising from the small permanent electric dipole moment of the free HD molecule. The interference effects which occur between these two components were studied for the dipole-allowed R1(0) and R1(1) transitions. These transitions exhibited increasingly large asymmetries and changes in intensity at high density, but their behaviours were quite different from each other. The shape of each transition could be well represented by a series of Fano line profiles, and the evolution of shape and intensity with density could be accounted for by the formulation of Herman, Tipping, and Poll. However, the precise interpretation of the phase shift parameters arising in the theory is not clear.

scholarly journals Iterative solution of quadratic tensor equations for mutual polarisation

2002 ◽  
Vol 32 (5) ◽  
pp. 301-312 ◽  
Author(s):  
Wynand S. Verwoerd
Keyword(s):  
Dipole Moment ◽  
Linear Approximation ◽  
Iterative Solution ◽  
Second Order ◽  
Local Fields ◽  
Bulk Materials ◽  
Tensor Equation ◽  
Order Tensor ◽  
Intrinsic Values ◽  
Induced Dipole

To describe mutual polarisation in bulk materials containing high polarisability molecules, local fields beyond the linear approximation need to be included. A second order tensor equation is formulated, and it describes this in the case of crystalline or at least locally ordered materials such as an idealised polymer. It is shown that this equation is solved by a set of recursion equations that relate the induced dipole moment, linear polarisability, and first hyperpolarisability in the material to the intrinsic values of the same properties of isolated molecules. From these, macroscopic susceptibility tensors up to second order can be calculated for the material.

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