Strong Collision Model Research Articles

Effects of the velocity dependence of the collision frequency on the Dicke line narrowing

The effect of the velocity (v) dependence of the transport collision frequency νtrv on the Dicke line narrowing is analyzed in terms of the strong-collision model generalized to velocity-dependent collision frequencies (the so-called kangaroo model). This effect has been found to depend on the mass ratio of the resonance (M) and buffer (Mb) particles, β = Mb/M: it is at a minimum for β ≪ 1 and reaches a maximum for β ≳ 3. A power-law particle interaction potential, U(r) ∝ r−n, is used as an example to show that, compared to νtrv(v) = const (n = 4), the line narrows if νtrv(v) decreases with increasing v (n 4). At β ≳ 3, the line width can increase [compared to νtrv(v) = const] by 5 and 12% for the potentials with n = 6 and n ≳ 10, respectively; for the potentials with n = 1 (Coulomb potential) and n = 3, it can decrease by more than half and 6%, respectively. The line profile I(Ω) has been found to be weakly sensitive to νtrv(v) at some detuning Ωc of the radiation frequency Ω. Dicke line narrowing is used as an example to analyze the collisional transport of nonequilibrium in the resonance-particle velocity distribution in a laser field. The transport effect is numerically shown to be weak. This allows simpler approximate one-dimensional quantum kinetic equations to be used instead of the three-dimensional ones to solve spectroscopic problems in which it is important to take into account the velocity dependence of the collision frequency when the phase memory is preserved during collisions.

Pressure effects on bimolecular recombination and unimolecular dissociation reactions

The treatment of pressure effects on bimolecular recombinations and unimolecular dissociations is discussed. The analysis of recombination and dissociation reactions is made by showing how the nonequilibrium energy (E) and angular momentum (J)-dependent steady-state population distribution functions for the two reactions are related to each other and to the equilibrium population distribution function at the given E and J. As a special case a strong collision model is then used for the collisional rotational angular momentum transfer, and a ladder model for the collisional energy transfer. An analytical result is obtained for states below the dissociation threshold. The extension to recombinations with two exit channels is described, for application to ozone formation and isotopic effects.

Competition between Photochemistry and Energy Transfer in Ultraviolet-Excited Diazabenzenes. 3. Photofragmentation and Collisional Quenching in Mixtures of 2-Methylpyrazine and Carbon Dioxide

The quantum yield for HCN formation via 248 and 266 nm photodissociation of methylpyrazine (C5N2H6 )i s determined by IR diode probing. HCN is produced at two different dissociation rates, one of which is extremely prompt. The total quantum yield is ) 0.93 ( 0.08 for 248 nm and 0.35 ( 0.05 for 266 nm excitation. Analysis of the quenching data within the context of a gas kinetic, strong collision model allows an estimate of the rate constant for HCN production via “late” methylpyrazine photodissociation, kd1s ) 6.4 10 4 s -1 and kd1s ) 4.9 10 3 s -1 for 248 and 266 nm excitation, respectively. The rate constant for “prompt” dissociation is too large to be measured using this technique. After 266 nm excitation methylpyrazine lives more than an order of magnitude longer than after 248 nm excitation. Methylpyrazine also lives more than twice as long as pyrazine excited under identical conditions. Transient absorption measurements probing rotationally and translationally excited CO2 molecules produced following excitation of methylpyrazine are analyzed within the context of a kinetic scheme incorporating methylpyrazine photodissociation, as well as excitation of CO 2 by both translationally hot HCN and vibrationally excited methylpyrazine. This analysis indicates that vibrationally hot methylpyrazine, which has sufficient energy to dissociate, is the source of excitation in collisions imparting large amounts of rotational and translational energy to CO 2.

Long jumps in the strong-collision model

The jump-length probability distribution for a classical particle diffusing in a periodic potential is calculated in the framework of a strong-collision model, where each collision of the particle with the thermal bath reequilibrates the velocity. Exact numerical results are obtained by the matrix-continued-fraction method, and two different analytical approximations are developed. In the first approximations it is assumed that an activated particle is always retrapped in the cell where it suffers the first collision; in the second approximation it is assumed that only the collisions giving a final total energy which is lower than the activation barrier are effective for retrapping. This second analytical approximation is in excellent agreement with the numerical data.

Competition between photochemistry and energy transfer in ultraviolet-excited diazabenzenes. I. Photofragmentation studies of pyrazine at 248 nm and 266 nm

The quantum yield for the formation of HCN from the photodissociation of pyrazine excited at 248 nm and 266 nm is determined by IR diode probing of the HCN photoproduct. HCN photoproducts from excited pyrazine are produced via three different dissociation channels, one that is extremely “prompt” and two others that are “late.” The total quantum yield from all reaction channels obtained at low quencher gas pressures, φ=1.3±0.2 for 248 nm and 0.5±0.3 for 266 nm, is in agreement with preliminary studies of this process as well as recent molecular beam studies. To investigate if HCN production is the result of pyrazine multiphoton absorption, this photodissociation process has been further studied by observing the HCN quantum yield as a function of total quencher gas pressure (10 mTorr pyrazine, balance SF6) and as a function of 248 nm laser fluence from 2.8 to 82 mJ/cm2. At the highest SF6 pressures, the HCN quantum yield shows strong positive correlation with laser fluence, indicating that the “prompt” channel is the result of multiphoton absorption; however, at low pressure, the HCN quantum yield is affected little by changing laser fluence, indicating that the majority of the HCN photoproducts at low pressure are produced from pyrazine which has absorbed only one UV photon. At the lowest pressures sampled, HCN produced from the one-photon “late” process accounts for more than 95% of all HCN formed (at low laser fluence). At high pressures the single photon “late” pyrazine dissociation is quenched, and HCN produced at high quencher gas pressures comes only from the multiphoton absorption channel, which can be clearly observed to depend on laser fluence. The HCN quantum yield as a function of laser intensity at high pressure has been fit to a quadratic function that can be used to determine the amount of “prompt” “unquenched” HCN produced from multiphoton photodissociation. Additionally, the information theoretic prior functions for energy disposal in the 248 nm photodissociation of pyrazine to form HCN have also been developed. Prior functions for one, two, and three-photon absorption indicate that only HCN with near room temperature translational energy comes from the one-photon process and that all HCN molecules with large amounts of translational energy are produced by multiphoton processes. Finally, analysis of the quenching data within the context of a strong collision model allows an estimate of the rate constant for HCN production from pyrazine for the major “late” channel, kd1s=1.69×105 s−1, for 248 nm excitation, and kd1s=1.33×104 s−1 for 266 nm excitation. After 266 nm excitation, pyrazine produced by the major one-photon channel lives for almost an order of magnitude longer than after 248 nm excitation.

Exact solution of the one- and three-dimensional quantum kinetic equations with velocity-dependent collision rates: Comparative analysis

The interaction of a plane monochromatic traveling wave with two-level particles suffering collisions with buffer-gas particles is considered. Collision rates are assumed to be velocity dependent. The collision integral is obtained on the basis of the strong-collision model, generalized to the case of velocity-dependent collision rates (the so-called ``kangaroo'' model). We obtained the exact analytical solution of the problem for arbitrary intensity of radiation, arbitrary ratio of homogeneous and Doppler widths of the absorption line, and arbitrary mass ratio between absorbing- and buffer-gas particles. The obtained analytical solutions of the quantum kinetic equations allowed us to analyze the spectral shape of the strong-field absorption line as well as the probe-field absorption line (the nonlinear part of the work done by the probe field) and the frequency dependence of the light-induced drift (LID) velocity. A comprehensive comparative analysis for the three- and one-dimensional versions of the model is given. On the basis of this analysis, we reach the conclusion that the one-dimensional quantum kinetic equation has quite a wide range of application. We also reveal the conditions for the strongest manifestation of the velocity dependence of the collision rates, which affects most strongly the anomalous LID.

First-passage times in phase space for the strong collision model

We consider the dynamics in phase space in which particles follow Newtonian trajectories that are randomly interrupted by collisions which equilibrate both the velocity and position of the particles. Collisions are assumed to be statistically independent events of zero duration and the intercollision time is a random variable with a negative exponential distribution. For this model, we derive an analytical expression for the Laplace transform of the survival probability and quadrature expressions for mean first-passage times.

A PARTIALLY CORRELATED STRONG COLLISION MODEL FOR VELOCITY- AND STATE-CHANGING COLLISIONS APPLICATION TO Ar-BROADENED HF ROVIBRATIONAL LINE SHAPE

High-resolution tunable laser measurements of rovibrational line shapes in Ar-broadened HF [A.S. Pine, J. Chem. Phys., 1994, 101, 3444] have shown the need of partially correlated Dicke narrowing models to accurately describe the observed asymmetries. A strong collision model accounting for both velocity- and state-changing mechanisms (VCD) and phase-changing ones (D), is presented. The resulting line shape justifies, on a physical basis, the empirical model previously used to interpret the observed features. The present partially correlated strong collisional model leads to a clearer interpretation of the characteristic parameters determined from the experiment for HF–Ar. Further theoretical calculations and experiments show that the residual discrepancies for the first rovibrational lines cannot be attributed to the speed dependence of the collisional line shape parameters.

Classical theories of reaction dynamics: Transition state theory, spatial diffusion controlled reactions, and the energy diffusion limit

The calculation of chemical reaction rate constants is of importance to much of chemistry and biology. Here we outline useful theoretical methods and numerical techniques for single and many dimensional systems for weak and strong collision models and discuss connections between different theories from a unified point of view.

Spectral anomalies of light-induced drift of rubidium and lithium under monochromatic excitation

The anomalous light-induced drift (LID) of atoms caused by a velocity dependence of collision frequencies has been investigated in the frame of the theory without adjustable parameters. Our results open the possibility of experimental probing of models of interatomic potentials. The extension of the strong-collision model to the case of velocity-dependent collision rates, is the basis of our approach. The obtained model describes the anomalous LID both in the case of arbitrary mass ratio of absorbing- and buffer-gas particles and in the case of arbitrary ratio of the homogeneous and Doppler widths. In particular, we applied our model to describe the anomalous LID in alkali - noble-gas mixtures (Rb - Kr and Li - Ne systems). Qualitatively another anomaly of the LID velocity was also found in the low-pressure region. As pointed out, the optical pumping effect and the hyperfine structure of the ground electronic state, but not the velocity dependence of the collision rates, are the sources of this new anomaly.

A simple model of the line mixing effect for atmospheric applications: Theoretical background and comparison with experimental profiles

We propose a new empirical method of band shape calculations which takes into account line mixing effects. The proposed shape is based on the strong collision model with attenuated interbranch coupling. Apart from the conventional set of spectral line parameters one needs only one additional parameter to account for line mixing effects in band profile calculations. This parameter depends on the perturbing gas type. It is the same for all molecular infrared absorption bands. The new shapes are shown to be successful in representing the measured absorption bands of CO 2 in nitrogen ( v 2, v 3, v 2 + 2 v 3, 2 v 2 − v 2, and 2 v 1 − v 2) and the 3.6 μm band of O 3 in nitrogen.

Stationary states and their stability for a mixture of molecular gases under velocity-selective excitation.

We consider a mixture of resonant two-level molecules under velocity-selective excitation and a buffer gas. The corresponding kinetic equations are augmented by a strong-collision model with free parameters. We obtain the equilibrium velocity distribution functions of the resonant and buffer components. We then use the Boltzmann kinetic equations to derive the H-theorem analog for this mixture (valid for arbitrary values of the collision rates \ensuremath{\nu} and the spontaneous decay rate \ensuremath{\gamma}) and discuss the implications for the stability of the stationary solutions. \textcopyright{} 1996 The American Physical Society.

Line mixing in the infrared spectra of simple gases at moderate and high densities

A review of papers in the field of the line-mixing effect on IR absorption band shapes is presented, with most attention being paid to work carried out at the Molecular Spectroscopy Laboratory of St. Petersburg University. After general formulation of the problem, the empirical methods of rotational relaxation matrix evaluation are considered, and the strong collision model is discussed in more detail. The method of far band wing calculation, which takes into consideration both line mixing and the finite collision duration effect, shows the important role of line mixing in far wing shape formation. In the Markov approximation, line mixing is considered semiclassically. The classical distribution of the angular momentum alteration probability in collisions is used for reconstruction of Γ matrices which describe line broadening, line shifting and line mixing effects in the discrete rotational state representation. This method is shown to give acceptable results for the prediction of line mixing effects for central regions of Σ-Σ bands of diatomic and linear molecules.

Anomalous light-induced drift of potassium in Ne plus rare-gas mixtures

We report anomalous light-induced drift of potassium vapor in mixtures of Ne with another rare gas. The drift velocity versus laser frequency curve shows a strong deviation from the dispersion curve predicted by the standard theory of light-induced drift based on velocity-independent collision rates. The observed drift velocity versus frequency curves have three zero-crossings. For a qualitative explanation of the results, a strong collision model with velocity-dependent collision rates is used. The partial pressures that cancel normal light-induced drift also provide accurate ratios of cross section for potassium collisions with the various buffer gases. The observation of anomalous light-induced drift in a simple atomic system offers the opportunity to relate the results to potential curves. \textcopyright{} 1996 The American Physical Society.

The influence of molecular motion on cross-polarization in cross-linked elastomers

The effect of molecular motion on the heteronuclear cross-polarization rate for the case of the spin-lock procedure was investigated. In applying heteronuclear solid state NMR techniques to mobile elastomer systems the influence of molecular motion cannot be neglected. Starting in the slow motion regime a strong collision model was used for predicting changes of the cross-polarization rate in the dipolar spectral density function of abundant spins. The dipolar correlation time and hence the cross-polarization rate is found to scale with the inverse of the correlation time of the molecular motion. The same behavior is obtained using a second approach valid in the intermediate molecular motion regime. This is based on the effect of the motion on the homonuclear and heteronuclear van-Vleck moments and leads to a linear dependence of the cross-polarization rate on the correlation time of molecular motion. This dependence was verified experimentally by 1H 13C high-resolution cross-polarization measurements on sulfur cross-linked elastomer systems. 13C rotating frame spin-lattice relaxation rate measurements were used to corroborate these data and the approximations used to evaluate the influence of molecular motion on cross-polarization rates. The dependence of these rates on the cross-link density of the elastomer network is analyzed and it is shown that they scale with the cross-link density. The correlation of the 1H- 13C cross-polarization rates with the dynamic storage moduli was demonstrated.

Simple modeling of line-mixing effects in IR bands. II. Nonlinear molecules applications to O3 and CHClF2

A simple semiempirical approach is developed in order to model the shape of infrared absorption bands. It is based on use of the strong collision model and of a classical representation of rotational levels. The absorption coefficient then has a simple analytical expression whose wavenumber and pressure dependencies are computed by using eleven parameters which depend on the considered vibrational transition, the temperature, and the nature of the perturber only. These quantities, which are band-averaged values of the detailed spectroscopic and collisional parameters of the molecular system, can be deduced from direct fits of measured spectra. The model thus requires no previous knowledge of the characteristics of the molecules and is thus applicable to complex systems; in particular it seems a promising approach for very dense molecular spectra for which only absorption cross sections are now available. Tests are presented in the case of O3 and CHClF2 bands perturbed by N2 at room temperature for which new measurements have been made. They demonstrate the accuracy of our semiempirical approach in predicting the spectral shape in a wide range of density provided that effective parameters are used.

Spectral line transfer modelling in collisionally pumped X-ray lasers

Results of calculations on spectral profiles of a laser line propagating along collisionally pumped X-ray lasers are presented. The strong collision model and density matrix components are used to describe the active medium kinetics. Propagation is modelled with the standard radiative transport equation. The results are related to other calculations and to limited experimental data. Arbitrary broadening is assumed and the resulting Voigt profile is calculated by the adapted Kielkopf approximation method, enabling considerably faster calculations.

Simple modeling of line-mixing effects in IR bands. I. Linear molecules: Application to CO2

A simple approach is developed in order to model the influence of collisions on the shape of infrared absorption by linear molecules. It accounts for line-mixing effects within, as well as between, the different branches (P,Q,R) of the band. It is based on use of the strong collision model, of a classical representation of rotational levels, and of the rigid rotor approximation. The absorption coefficient then has a very simple analytical expression; its wave number and pressure dependencies are computed by using eight parameters which depend on the considered vibrational transition, the temperature, and the nature of the perturber only. These quantities are band-averaged values of the detailed spectroscopic and collisional parameters of the molecular system. Tests of the model are presented in the ν3 and 3ν3 bands of CO2 perturbed by He and Ar at elevated pressures. They demonstrate the accuracy of our approach in accounting for the effects of collisions on the spectral shape in a wide density range; indeed, the superposition of Lorentzian individual lines at low pressure, as well as the collapse (narrowing) of the band at very high pressure are satisfactory predicted.

Muon-spin-resonance study of muonium dynamics in Si and its relevance to hydrogen.

The dynamics of transitions among muonium (Mu) states in Si have been studied by radio-frequency (rf) muon-spin-resonance techniques. A total of ten samples doped to roughly ${10}^{15}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ p type and to ${10}^{16}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ n type were investigated at temperatures from 10 to 500 K. The normalized rf asymmetry for the ionized center in the p-type samples is well described by a three-state strong-collision model involving ${\mathrm{Mu}}_{\mathrm{BC}}^{+}$, ${\mathrm{Mu}}_{\mathrm{BC}}^{0}$, and ${\mathrm{Mu}}_{\mathit{T}}^{0}$. Addition of ${\mathrm{Mu}}_{\mathit{T}}^{\mathrm{\ensuremath{-}}}$ and related transitions complicates the model for intermediate n-type concentrations; however, at higher n-type levels a modified three-state model with ${\mathrm{Mu}}_{\mathit{T}}^{\mathrm{\ensuremath{-}}}$ replacing ${\mathrm{Mu}}_{\mathrm{BC}}^{+}$ successfully describes the charged-state intensities. Observed features are assigned to seven separate transition processes and a single set of parameters, obtained primarily from fits to two samples, provide an excellent description over the full doping range. The Mu results correlate well with the few analogous hydrogen measurements and imply rapid transitions among several hydrogen states under typical experimental conditions.

Theory of avoided level-crossing relaxation dynamics for axial muonated radicals

A calculation encompasing the dynamics of rotational motion, electron spin relaxation and chemical reactions at an avoided level crossing resonance (ALCR) of muonated radicals with axial hyperfine anisotropy is presented. The main emphasis is directed toward the rotational diffusive motion, assumed to be isotropic, which is treated with the stochastic Liouville formalism. Inter-resonance interactions, electron and chemical relaxation effects are incorporated using a multistate version of the strong collision model, derived from the above formalism in the appropriate spin space. A central finding of the calculation concerns the role of the inter-resonance interactions. It will be shown that over the range where dynamical mechanisms broaden the ΔM = 1 ALCR line to the extent that there is overlap with the ΔM = 0, 2 lines, then these transitions are strongly supressed.