General Line Shape Research Articles

Quantum interference among competing unimolecular decay channels: Asymmetric S D2CO decay profiles

The dynamics of a state undergoing decay to a manifold of states coupled to a dissociative continuum is investigated in the weak coupling limit. The decay rate is found to be composed of terms symmetric and asymmetric in the relative energy difference between the initial state and the states in the manifold. The well-known symmetric terms arise from resonantly enhanced decay of the initial state through each state in the manifold to the continuum. The newly identified asymmetric terms arise from interfering couplings of the initial state to the continuum through different states in the manifold, i.e., from off-diagonal elements of the width matrix Γkk′ of the effective Hamiltonian describing dissociation of the states in the manifold. The general line shape derived here is used to fit asymmetric features in Stark level-crossing spectra of D2CO. Statistical properties of the width matrix are summarized, and the relation between diagonal and off-diagonal matrix element magnitudes is derived.

A unified approach to line-shape analysis in polymer crystallography

General line shapes in the diffraction patterns of polymeric crystalline systems have been investigated on the basis of the interaction among the scattering units. A perturbation term has been incorporated into the Hamiltonian of the harmonic molecular lattice and the corresponding intensity distribution has been deduced from first principles with the assumption of elastic scattering. The various line broadenings, formerly interpreted as results of microlattice strains within a crystal or paracrystallinity, have been shown to be special cases of the general consequence of the higher-order interactions. Finally, the explicit temperature dependence of a line width was deduced and verified against experimental work on polyethylene single crystals.

Effect of pump fluctuations on line shapes in coherent anti-Stokes Raman scattering

The theory of coherent anti-Stokes Raman scattering (CARS) is extended to include the effect of pump fluctuations. The intensities and spectra of lines in resonant CARS are calculated to all orders in fields assuming a phase-diffusion model for waves at the two pump frequencies. The bandwidth of the two lasers enters in a much more complicated way than following a simple scaling of ${T}_{1}$ or ${T}_{2}$. Various resonances in CARS spectra due to dynamic splitting of the energy levels are discussed for a range of detunings, field intensities, and bandwidths. In contrast to the usual spectra in strong fields, the Rabi sidebands appear as dispersion-shaped structures. The laser linewidth is shown to change dramatically the CARS line shape. The case of no saturation is also treated, thus allowing for the inclusion of more general line shapes and fluctuations of the pump waves and the nonlinear susceptibility tensor ${\ensuremath{\chi}}^{(3)}$. Gaussian statistics of the pump field are shown to lead to enhancement factors in CARS intensity, similar to those appearing in the context of multiphoton absorption processes.

Line broadening in a strong radiation field: Application to electron–phonon systems

A theory is developed for the treatment of dephasing (line broadening) phenomena in strong radiation fields. The theory is valid for an arbitrary correlation time of the perturbing bath (relative to the broadening) and thus allows for non-Markovian effects (i.e. non-Lorentzian line shapes). Using this theory we are able to describe the behavior of a general line shape in strong radiation fields. In the Markovian limit of fast correlation time we recover the well known results of the Bloch equations. A specific application is made to electron–phonon systems where the necessary correlation functions may be explicitly calculated.

PMR spectroscopy of the tunneling ammonium ion: Generalized line shape theory and some experimental examples

The site symmetry of the NH4+ ion is low in many crystal structures of ammonium compounds. This renders inadequate the commonly considered theoretical models of the tunnel-split ground librational state of NH4+, which are based on a perfectly tetrahedral crystal field due to assumption of equivalent threefold, and neglect of twofold, axes of symmetry. A general treatment of the NMR line shape theory is therefore considered and Hamiltonian matrix elements for tunneling are explicitly calculated in terms of the seven overlap-integral parameters related to the four C3– and three C2–symmetry axes of a tetrahedron. The model allows us to discuss all possible ground torsional level structure of the tunneling ammonium ion. The proton NMR line shapes are calculated for all representative cases, and the results are used in comparison with experimental data to elucidate the ground torsional level structures of NH4VO3, (NH4)2ZrF6, (HN4)2TiF6, (NH4)2TeO4, and (NH4) IO4.

Photon-induced electron transfer transitions of the solvated electrons

The role of electron transfer transitions in the absorption spectrum of the solvated electron in liquid water is studied in terms of the generalized line shape function. When the density of trapping sites is greater than one third of the density of solvent molecules, the transition-dipole moment for photon-induced electron transfers was found to be greater than that of the single-site 1s→2p transition. The solvated electron is assumed to be coupled with low-frequency solvent modes and a high-frequency molecular mode. The latter mode is responsible for a small isotope shift in the peak energy. The spectrum consists of contributions from short-distance transfers (’’bound–bound’’) and long-distance (’’bound–free’’) transfers, the latter being the minor component of the total spectrum.

A method for the convolution of lineshapes which involve the Lorentz distribution

An expansion of the Lorentz distribution function in terms of the orthogonal Hermite-Gauss oscillator functions is developed for the purpose of examining the convolution of the Lorentz term with other general lineshapes.

Double quantum transitions in electric field deuterium magnetic resonance spectra

The appearance of double quantum transitions in the electric field 2H NMR spectrum of perdeuterobenzene in nitrobenzene is studied. Theoretical spectra have been calculated from the general lineshape formalism of Hoffman, as applied by Gestblom et al., and have been compared with experiment.

Approximate treatment of ion dynamics in stark broadening theory

A theory is proposed to cover cases of overlapping lines or partially overlapping lines whose components are not too well resolved. As a basic approximation, the neglect of time ordering in the low-frequency part of the time- evolution operator which enters the general line shape formula is introduced. This amounts to calculating the low-frequency average in the auto-correlation function for the line shape with a (time-dependent) distribution function of the time-averaged ionic microfield. (MOW)

The effect of channel correlation on the accuracy of photon counting digital autocorrelators (photon counting spectroscopy)

The estimation of spectral parameters of optical fields by digital autocorrelation of photon counting fluctuations is investigated, taking into account the correlations that exist between readings of the autocorrelator channels. A general expression for the covariance of the normalized intensity autocorrelation estimators is derived for a gaussian field with general lineshape. Two estimation schemes are outlined, the maximum likelihood and the least-squares. Dependence of the estimation accuracy on the channel correlations and the system parameters is discussed.

Radiative processes of the solvated electron in polar fluids

In this paper we present a theoretical study of the physical properties of solvated electrons in ammonia based on the Copeland-Kestner-Jortner model, which incorporates short-range interactions uia a first solvation layer and long-range interactions via polaron modes. We have studied bound-bound and bound-continuum optical transition emphasizing the problem of line shapes in absorption and emission. The total energy of the ground and excited states and its dependence on nuclear configuratiens was handled by three successive approximate calculations: (a) a temperature dependent potential including short -range radial displacements; (b) a temperature independent potential incorporating both radial and angular short-range displacements; (c) a multidimensional potential surface including both short-range and long-range (polaron) nuclear displacements. The calculated line shapes in absorption for a single solvent configuration include major contributions from short-range radial displacements and from the polaronl modes. The energy and line shape for the 2p -* ls emission band is predicted. A general formula is presented for photoionization cross section including the contribution of all medium modes and in this caise the role of the polaron modes is crucial. In our previous paper,2 we advanced a model for the solvated electron in polar fluids which took into account the strong short-range interactions of the electron and the first coordination layer solvent molecules as well as the long-range interactions with the bulk medium. This model was capable of yielding quantitative information on the properties of solvated electrons in ammonia as well as providing qualitative data on excess electrons in other polar solvents. In the latter cases we did not attempt a detailed study. Rmxntly, Fueki, Kevan and Christoffersen, in particular, have applied a similar model to study solvated electrons in water and al~ohols.3~,~ Although many questions remain concerning the trends observed in wideby differing solvents4 and solvent mixtures,4-' these are predicted well enough by our model to allow us to consider an entirety different set of problems, namely the details of radiative processes in which the state of the electrlon changes. In this paper we will use metal-ammonia solutions as a representative system for the study of these processes. We expect the same general behavior in other polar fluids except that the relative rates of the various processes could change in different solvent systems. We will begin with a display of the latest calculations on our model2 as well as an improved version. These new results provide a better insight into the physical properties of the solvated electron. We shall focus attention on the radiative processes of the solvated electmn and, in particular, the observed absorption line shapes for bound-bound and for boundcontinuum transitions as well as the yet unobserved emission line shape and the photoionization profile. The study of optical line shapes provides a starting point for the understanding of nonradiative processes of the solvated electron, such as electron capture from the conduction band to form the localized ground state, or the reverse process of thermal ionization of the ground state and of excited states. In general, the nonradiative transition probability can be expressed in terms of a generalized line shape function in the limit of zero frequency. However, in view of the special nature of the problem, where the localized excess electron wave function is strongly dependent on the (short-range and polaron type long-range) nuclear coordinates, the theory of the optical line shapes presented herein requires a gross modification before it can be applied for the elucidation of the nonradiative decay processes of the solvated electron. 11. Calculations

Quantum-Mechanical Transport Equation for Atomic Systems. II. Inelastic Collisions and General Line-Shape Considerations

Inelastic-collisional effects are incorporated into a quantum-mechanical transport equation (QMTE) that was developed in an earlier paper. The QMTE enables one to follow the quantum-state evolution of moving atoms which are interacting with some external fields while undergoing collisions with perturber atoms. The collisional processes are treated quantum mechanically and then reinterpreted in terms of classical variables so that the QMTE becomes an integrodifferential equation for atomic density-matrix elements containing both well-defined quantum-mechanical collision parameters (i.e., scattering amplitudes) and densitymatrix elements which are functions of classical position and velocity variables. Solutions of the QMTE enable one to derive line-shape formulas, and a discussion will be given of the general features to be expected for spectral profiles, Hanle-effect line shapes, and laser output curves, as well as the manner in which these features differ from those predicted by theories that neglect some quantum-mechanical aspects of the collision events. The inclusion of inelastic-collisional effects does not cover cases in which the frequency spacing of the atomic levels under consideration is comparable to the inverse duration time of a collision; nevertheless, the QMTE to be derived will be applicable to the analysis of a large number of atomic systems.

Fast computation of exchange-broadened isotropic E.S.R. spectra

A general line shape equation for intramolecular exchange among many sites has been derived by means of the Liouville density matrix theory and adapted to fast computer calculations. Applications of the computer programme ESREXN, which is based on the formalism of the present paper, are shown by examples.

Some extensions and applications of the new random model for molecular band transmission

AbstractThe general line shape transmission is derived for the new random model described by Malkmus (1967) for the representation of molecular band transmission. The model is applied to two absorbing paths in series, where an expression is found which is simpler than the corresponding expression for the Goody random model. The new model is also used to give an empirical fit to the ozone transmission measurements of Walshaw (1957).

Interpretation of experimental Mössbauer spectrum areas

The method of Shirley et al. 1) for interpreting Mössbauer spectrum areas is reformulated and extended to more general line shapes. The treatment is independent of source line shape and may be applied to multiple line absorbers, provided that the contribution to the spectrum of a given absorber line is distinct.