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. II. Induced Absorption in a Real Gas

1972 ◽  
Vol 50 (22) ◽  
pp. 2881-2901 ◽  
Author(s):  
J. Courtenay Lewis
Keyword(s):  
Kinetic Theory ◽  
Upper Bound ◽  
Shape Function ◽  
Lorentz Gas ◽  
Exponential Model ◽  
Interference Effects ◽  
Mass Ratio ◽  
Real Gas ◽  
Interference Minimum ◽  
Line Shape Function

The kinetic theory of intercollisional interference effects in induced infrared spectra developed in the first publication of this series for a Lorentz gas is extended to a real gas.A principal conclusion is that intercollisional interference in absorption is always destructive in the systems considered. Though the theory is mathematically less tractable for the real gas than for the Lorentz gas, a useful upper bound to the intercollisional interference dip minimum is obtained. This upper bound is evaluated for the exponential model developed previously, for all values of the mass ratio m1/m2. The intercollisional interference minimum itself is calculated for this model with m1 = m2. Finally, a simplification of the expression for the line-shape function is discussed.

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.

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.

ON THE TEMPERATURE DEPENDENCE OF THE SHAPE OF PARAMAGNETIC RESONANCE LINES

1960 ◽  
Vol 38 (9) ◽  
pp. 1168-1186 ◽  
Author(s):  
Malcolm McMillan ◽  
W. Opechowski
Keyword(s):  
Thermal Expansion ◽  
General Theory ◽  
Temperature Dependence ◽  
Shape Function ◽  
Temperature Dependent ◽  
Paramagnetic Resonance ◽  
Effective Spin ◽  
Spin Lattice ◽  
Second Moments ◽  
Line Shape Function

A theory of the temperature dependence of the shape of paramagnetic resonance lines is developed for temperatures sufficiently low to make the effects of the spin–lattice interaction and thermal expansion negligible. General expressions for the first and second moments of the line shape function as functions of the temperature are obtained, and the approximations used are discussed in detail. These expressions are applied to the case of effective spin [Formula: see text] and 1. As an illustration of the general theory numerical results are given for the paramagnetic resonance lines of nickel fluosilicate. In this case the moments become strongly temperature dependent below 10 °K.

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.

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.

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.

ON THE TEMPERATURE DEPENDENCE OF PARAMAGNETIC RESONANCE IN THE CASE OF THE ISING MODEL

1961 ◽  
Vol 39 (12) ◽  
pp. 1733-1737 ◽  
Author(s):  
Y. Y. Lee
Keyword(s):  
Ising Model ◽  
Temperature Dependence ◽  
Approximation Method ◽  
Line Shape ◽  
Theoretical Study ◽  
Shape Function ◽  
Paramagnetic Resonance ◽  
One Dimensional ◽  
The One ◽  
Line Shape Function

The adequacy of the approximation method used by McMillan and Opechowski in their theoretical study of the temperature dependence of the paramagnetic resonance line shape function is very difficult to ascertain for the case of a typical paramagnetic crystal. For this reason the approximation method has been investigated for the very simple case of the one-dimensional Ising model. Exact expressions for the line shape function of the model are compared with expressions obtained by the approximation method mentioned above. The agreement between the two expressions is found to be very good in general, and extremely good at very low temperatures.

scholarly journals Wormhole modeling in R2 gravity with linear trace term

2020 ◽  
Vol 35 (08) ◽  
pp. 2050045
Author(s):  
Nisha Godani ◽  
Gauranga C. Samanta
Keyword(s):  
General Relativity ◽  
General Theory ◽  
Significant Contribution ◽  
Shape Function ◽  
Exotic Matter ◽  
Geometric Configuration ◽  
Energy Conditions ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Traversable Wormholes

Morris and Thorne1 proposed traversable wormholes, hypothetical connecting tools, using the concept of Einstein’s general theory of relativity. In this paper, the modification of general relativity (in particular [Formula: see text] theory of gravity defined by Harko et al.2) is considered, to study the traversable wormhole solutions. The function [Formula: see text] is considered as [Formula: see text], where [Formula: see text] and [Formula: see text] are controlling parameters. The shape and redshift functions appearing in the metric of wormhole structure have significant contribution in the development of wormhole solutions. We have considered both variable and constant redshift functions with a logarithmic shape function. The energy conditions are examined, geometric configuration is analyzed and the radius of the throat is determined in order to have wormhole solutions in absence of exotic matter.

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