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. 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.

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.

Lineshapes and dipole moments in collision-induced absorption

1981 ◽  
Vol 59 (10) ◽  
pp. 1544-1554 ◽  
Author(s):  
George Birnbaum ◽  
Michael S. Brown ◽  
Lothar Frommhold
Keyword(s):  
Dipole Moment ◽  
Dipole Moments ◽  
Empirical Models ◽  
Fundamental Theory ◽  
Potential Models ◽  
Induced Absorption ◽  
Induced Dipole ◽  
Substantial Error ◽  
Argon Mixture ◽  
Helium Neon

Wave mechanical lineshapes of collision-induced absorption spectra are computed for binary mixtures of argon with helium, neon, and krypton using theoretical dipole moments as input. Comparison with measured spectra shows satisfactory agreement except for the neon–argon mixture, for which either theory or measurement is seen to be in substantial error. Empirical models of the collision-induced dipole moment which reproduce the experimental spectra more closely than the fundamental theory are also given. Best agreement between computed and experimental lineshapes is obtained when potential models which are accurate in the repulsive region are used.

Intercollisional Interference in the S Lines of H2–He Mixtures

1975 ◽  
Vol 53 (10) ◽  
pp. 954-961 ◽  
Author(s):  
J. D. Poll ◽  
J. L. Hunt ◽  
J. W. Mactaggart
Keyword(s):  
Dipole Moment ◽  
Line Shape ◽  
Short Range ◽  
Experimental Results ◽  
Strength Parameter ◽  
Free Molecule ◽  
Fundamental Band ◽  
A Value ◽  
Induced Dipole ◽  
Interference Minimum

Further experimental results on the pressure induced spectrum of normal H2–He in the region of the S(1) branch of the fundamental band are presented. These results show a well-defined minimum at the transition frequency of the free molecule. The S line is found to be the sum of two components. One of these is of essentially the same nature as the Q branch and should therefore show a pronounced intercollisional interference minimum. The second component shows the usual quadrupolar line shape without a minimum. Finally, a value for the strength parameter characterizing the short range component of the induced dipole moment is determined.

Moment analysis in collision-induced absorption: Determination of a single parameter empirical model for the induced dipole moment of He-Ar gas mixtures

2021 ◽  
pp. 1-16
Author(s):  
M.S.A. El-Kader ◽  
G. Maroulis
Keyword(s):  
Dipole Moment ◽  
Empirical Model ◽  
Adjustable Parameter ◽  
Classical Physics ◽  
Induced Absorption ◽  
Induced Dipole ◽  
Absorption Determination ◽  
Ar Gas ◽  
Good Agreement

We present a method for the construction of a one-adjustable-parameter empirical model for the induced dipole moment. The method is based on classical physics principles and relies on the first three spectral moments of the collision-induced absorption spectra at various temperatures and new interaction potentials. In this work it is applied to the spectra of He-Ar mixtures. Our values are in good agreement with the available ab initio data. The profiles calculated with these models at various temperatures are in excellent agreement with experiment.

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.

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.

On the Theory of Collision-Induced Absorption in Rare Gas Mixtures

1971 ◽  
Vol 49 (7) ◽  
pp. 837-847 ◽  
Author(s):  
S. L. Brenner ◽  
D. A. McQuarrie
Keyword(s):  
Absorption Spectrum ◽  
Dipole Moment ◽  
Far Infrared ◽  
Gas Mixtures ◽  
Moment Function ◽  
Rare Gas ◽  
Induced Absorption ◽  
Induced Dipole ◽  
Calculated Equilibrium

The observed far-infrared collision-induced absorption of helium–argon mixtures is used to determine the parameters in an induced-dipole moment function of the form[Formula: see text]It is shown that, with this form of μ(r), the values of the constants μo, ρ, and c7 that are necessary to fit the first two moments of the observed absorption contour are in disagreement with the available theoretical values of these constants. Possible explanations for this disagreement are discussed in the paper. Finally, it is shown that if μ(r) were known, it is possible to obtain an excellent representation of the entire absorption spectrum from a knowledge of only the first three moments, which are easily calculated equilibrium quantities.

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