A classical model for stochastic multiphoton absorption processes of anharmonic molecules

Classical power absorption of an anharmonic molecule in intense infrared radiation is calculated. A generalized damping factor and an effective random phase are introduced for the stochastic field-molecule interaction. It is shown that the over-all broadening of the power response has a fundamental lorentzian, no matter what the source of line broadening is. Excellent agreement with the quantum-mechanical results is obtained by quantizing the classical model.     

A model for a stochastic multiphoton absorption process of an anharmonic oscillator

A model of multiphoton absorption of i.r. laser radiation by an anharmonic, molecular, vibrational mode is discussed. The multiphoton absorption is described as a stochastic process for which the reservoir, including rotation and other vibrational modes, modulates the frequency of the active oscillator stochastically. The treatment of the nonlinear oscillator is based on quantization of a classical, driven anharmonic oscillator.     

A simple molecular statistical treatment of a model for cholesterics

The cholesteric state is discussed in terms of a model consisting of the Maier-Saupe and a twist interaction. The model can be easily solved in the mean field approximation. In the practical case of a large pitch analytical expressions are obtained for relevant quantities like the order parameters and the free energy. Then it appears that the pitch is temperature independent, which is a general result, and does not influence the discontinuity of the main (nematic) order parameter at the isotropic-cholesteric transition. Interactions giving rise to a temperature-dependent pitch are discussed briefly.     

High efficient system for studying multiphoton absorption

An optical arrangement for studying two-photon absorption in liquids is presented. The main feature of this new arrangement is fuller utilization of fluorescence light. This makes possible application of very low power cw laser in such experiments.     

Direct measurement of multiphoton molecular absorption of IR laser radiation by pyroelectric detector

The applicability of a pyroelectric detector (PED) to multiphoton absorption measurements (MPA) under ir laser excitation of molecules was examined. The possibility of MPA measurement of SF₆ molecules in the pressure range of 10⁻³÷10⁻¹ Torr with a time resolution of ∼ 7 μs has been shown. It has been demonstrated that the degree of vibrational relaxation of highly vibrationally excited molecules at PED surface does not depend on excitation level under the studied conditions.     

A simple model for the velocity modulation detection technique of molecular ions

We present a simple model to describe the line-profile of velocity modulated ions. This model is based on Langevin's theory of the mobility and on the independence of the electric field strength on the discharge current in the ideal positive column. A comparison of time constants responsible for the drift of the ions, the concentration, and the ignition and extinction of the discharge itself is essential for a rough understanding of the velocity modulation. The behaviour of H₃O⁺ ions in an ac glow discharge was examined. Under our experimental conditions the line-profile can be explained by a temporal dependence of the velocity which is close to a square-wave. Due to this particular temporal dependence the amplitude of the signal only depends on the concentration modulation, while the line-shape is a simple difference line-profile.     

A simple model for scalar relativistic corrections to molecular total atomisation energies

ABSTRACT

Scalar relativistic corrections to atomisation energies of first- and second-row molecules can be rationalised in terms of a simple additive model, linear in changes in atomic s populations. In a sample of 200 first-and second-row molecules, such a model can account for over 98% of the variance (99% for the first-row subset). The remaining error can be halved again by adding a term involving the change in atomic p populations: those coefficients need not be fitted but can be fixed from atomic electron affinity calculations. This model allows a fairly accurate a priori estimate for the importance of scalar relativistic corrections on a reaction energy, at essentially zero computational cost. While this is not a substitute for explicit calculation of Douglas–Kroll–Hess (DKH) or exact two-component (X2C) relativistic corrections, the model offers an interpretative tool for the chemical analysis of scalar relativistic contributions to reaction energies.     

Far infrared multiphoton absorption in p-Ge

We have calculated the far infrared multiphoton absorption coefficient in p-Ge for three different temperatures. It is shown that, under high radiation intensity, the rate of increase of the absorption coefficient changes strongly with intensity as a result of the Stark effect.     

A simple model for SmS

A simple model based on the resonant scattering theory can explain the first-order semiconductor-to-metal transition accompanied by a change of valency in SmS.     

Free-carrier multiphoton laser absorption in magnetic semiconductors

The magnon scattering by free carriers in the presence of an intense laser field is discussed. A kinetic equation for electrons is derived from which the multiphonon absorption coefficient is calculated. It is found that for very large fields the absorption coefficient is vanishing small. A physical explanation of this result is also available.     

A simple mathematical model for TTS

Published data on Temporary Threshold Shift (TTS) suggest that in many cases the rms pressure at threshold during and after exposure to noise varies in a simple exponential manner, and that the ultimate shift of pressure threshold for exposure to steady noise is dependent on the mean square pressure of that noise. This response could occur if some part of the hearing mechanism were heated by exposure to noise and were at the same time subject to Newtonian cooling, and if the change in the pressure threshold were proportional to the change of temperature. This model can explain the shapes of many growth and recovery curves given in dB, why time constants found for recovery from TTS appear greater than those for growth and why threshold shifts on ears with elevated thresholds appear smaller than those for ears with low thresholds. Because of individual variation, averaged dB results mask the nature of the processes involved. Hence, for a better understanding of TTS, individual ears should be studied separately, and, if possible, measurements should be made in rms Pa instead of dB.     

A simple model for diffuse reflection

Diffuse reflection from a matte nonabsorbing inhomogeneous medium such as white paint or paper can be described by a simple model in which light rays enter the volume of medium and then undergo a random walk until they reemerge from the surface. Lambert's law of diffuse reflection is an immediate consequence of the random walk. Another consequence of the volume interaction is that the light emerges from a different point than where it enters. This spreading of the light was measured for BaSO₄ white reflectance paint and for several kinds of paper. The random walk model implies a diffusion equation which makes predictions that are in reasonable agreement with the experiments. The spreading is proportional to an interaction length which, in this model, represents the range of distances that light rays penetrate before beginning their random walk.     

A simple model for metamagnetic percolation

An Ising model with both antiferromagnetic and randomly diluted, infinitely strong ferromagnetic interactions is studied on a Bethe lattice. The results are used to interpret recent experimental data on the phase diagram of Fe_xMg_1-xCl₂.     

A simple model for radiation damping

Increasing interest has been shown in the method of matched asymptotic expansions for the construction and solution of the equations of motion in general relativity. This paper discusses a simple model which can, in principle, be solved exactly. A comparison of the two solutions shows that the matched asymptotic expansion technique determines correctly the final damping rate and frequency (at least to fourth order in a small parameter), but the phase information is spurious.     

A simple model for surface relaxations

A simple model for surface relaxations is developed based on short-ranged two-body forces and a pressure applied to a crystal surface. Interplanar displacements are calculated as an elastic response to unresolved surface stresses which arise during the creation of the surface. For α-iron, the first-neighbor force is dominant at the surface and is significantly stronger than in the bulk, and surface pressure is stronger than the bulk Cauchy pressure and acts primarily on the outermost plane of atoms.     

A simple molecular theory for photo-induced smectic phase

The response of liquid crystals to light is very important for applications of liquid crystals in display and memory devices. Recently experiments have been carried out on liquid crystals doped with photoactive azo compounds. It is seen that UV rays incident on such systems can lower the nematic isotropic transition temperature T _NI . Also, in some mixtures, a photo-induced smectic phase is observed. This is attributed to the change in the trans (longer) isomer to cis (shorter) isomer of the photoactive dopant. We have earlier developed a molecular mean-field model assuming the medium to consist of inter-converting anti-parallel and parallel pairs to explain the molecular origin of “two lengths”. The model was used to explain double re-entrance, the effect of electric field on T _NI , etc. This model is modified to include the change of trans to cis isomer which is equivalent to an increase of fraction of parallel (shorter) pairs. The calculated phase diagram with respect to incident UV radiation energy shows an induced smectic phase. This is in qualitative agreement with experimental trends.     

Fundamental quantum limit to the multiphoton absorption rate for monochromatic light

The local multiphoton absorption rate for an arbitrary quantum state of monochromatic light, taking into account the photon number, momentum, and polarization degrees of freedom, is shown to have an upper bound that can be reached by coherent fields. This surprising result rules out any quantum enhancement of the multiphoton absorption rate by momentum entanglement.     

A simple model for planar dechanneling calculations

In this letter a simple procedure for calculating the initial dechanneling of ion is presented. The calculations show good agreement with both experimental data and computer simulation data on planar dechanneling.     

A simple model for the Kapitza conductance

A simple model is suggested which views the Kapitza resistance in terms of individual atomic collisions at a solid-HeII boundary.