Building transition probabilities per collision from transition rates per unit time for finding the mean observable quantities in the gas phase

A new method of finding transition probabilities per collision from a set of transition rates per unit time is proposed. The problem is solved by introducing a normalization function that is easily derived from a recursion equation. The solution of recursion equation is obtained in the analytical form for the case of separable kernels. The Morse oscillator in a thermal bath is considered as an example.     

Energy shifts in the relative coordinates treatment of the collinear collision between an atom and an oscillator. Exponential repulsive potential

The treatment of the kinetic term which may be taken as the perturbation when the collision between an atom and an oscillator is described with relative coordinates is shown to require the use of energy shifted basis functions in the calculation of the transition probabilities. For an exponential repulsive potential, a simple analytical formula is obtained for one quantum jumps in the first order Born approximation, which has a simple relationship with the first order Born distorted wave expression, and which lead to better results than the other available analytical formulas.     

Theoretical calculations of transition probabilities and oscillator strengths for Ti III and Ti IV

Due to the complicated electronic configuration of atoms and ions of the transition metal elements, the studies for properties such as transition probabilities and oscillator strengths for these atoms and ions are not systematic. Because of the existence in a variety of stellar objects and wide use in the field of astrophysics, titanium has long been of interest for many researchers. In this article within the Weakest Bound Electron Potential Model (WBEPM) theory, comprehensive set of calculations for transition probabilities and oscillator strengths for Ti III and Ti IV are performed. Many of our results had no previous experimental or theoretical values, so these predictive results could be of some value to the workers in this field. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Transition probabilities of a string oscillator subject to impulsive collisions with a heavy mass point

Impulsive linear collisions between a string oscillator (a one-dimensional particle in a box) and a mass point are studied quantum mechanically. In the limit of a very heavy mass point (which corresponds classically to many collisions during a single encounter) the transition probabilities are determined exactly. The result permits a discussion of the mixed quantum-classical regime where the collider becomes almost classical while the oscillator remains quantum mechanical. While the average transition probabilities P(m-->n) are well reproduced by the Ehrenfest mean-field approximation, the prediction for the superimposed high-frequency resonance structure is qualitatively wrong for a genuine quantum oscillator. Only if the oscillator is also almost classical and if (m-n)2 square root(mu) < m, where mu is the mass ratio collider/oscillator, this structure is correctly predicted by the Ehrenfest approximation.     

Solutions to the time-dependent,forced quantum oscillator equation in the coordinate representation

Time-dependent creation and annihilation operators are derived which are used to obtain exact solutions, in the coordinate representation, to the time-dependent, forced quantum oscillator equation. The solutions are used to obtain a general formula for the transition probabilities, valid for any time-dependent force.     

Stochastic theory of collisional energy transfer: nature of convergence of master equation transition probabilities and moments as a function of cumulant expansion order

Closed form expressions for collisional energy transfer transition probabilities and moments are determined for the forced oscillator model by solving cumulant expansion master equation in second, fourth, sixth and infinite order. This enables a study of convergence properties of the cumulant expansion.     

Allowed transitions in silicon isoelectronic ions

Dipole‐allowed transitions have been studied for the first few members of the Si isoelectronic sequence. Transition energies, oscillator strengths, transition probabilities and quantum defect values have been estimated for the low‐ and high‐lying excited states of s and d symmetries up to the principal quantum number n=7 for these 3p open shell ions from P⁺ to Cr¹⁰⁺. Time‐dependent coupled Hartree–Fock (TDCHF) theory has been utilized to calculate such transition properties. Most of the results for transition energies, oscillator strengths, and transition probabilities for higher excited states are new. The transition energies for low‐lying excited states agree well with experimental data wherever available. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

强激光场中NO分子多光子选择激发──含时薛定鄂方程的代数解法

报道了在半经典偶极近似下应用二次型非谐振子李代数模型研究强激光场中NO分子的多光子选择激发，并计算了NO分子的跃迁几率．     

Effect of dense plasma on the spectral properties of hydrogenic ions

The effect of strongly coupled plasma on the energy levels, dynamic polarizabilities, oscillator strengths, and transition probabilities of a number of hydrogenic ions is estimated, using the ion‐sphere (IS) model. The transition properties are calculated using time‐dependent variation perturbation theory. The variation of the atomic properties under different plasma densities are analyzed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Tests of semiclassical treatments of vibrational-translational energy transfer collinear collisions of helium with hydrogen molecules

Three kinds of semiclassical theory are tested against quantum mechanical results for vibrational transition probabilities and average vibrational energy transfers in collinear collisions of atoms with harmonic and Morse vibrators for the He-H₂ mass combination. The interaction potential is assumed to be a repulsive exponential function with an exponential parameter which is realistic for He-H₂ collisions. The energy range studied is total energies of 2–8 in units of ?ω_e. The uniform semiclassical approximations of classical S matrix theory are tested only for classically allowed transitions, i.e., for transition probabilities greater than about 0.2. They are accurate quantitatively for both harmonic and Morse vibrators. The integral expressions of classical S matrix theory are found to be quantitatively accurate for classically allowed and weakly classically forbidden transitions, i.e., for transition probabilities greater than about 0.01–0.05, and to be unreliable for strongly classically forbidden transitions. Quasiclassical trajectory methods yield qualitatively accurate results only for classically allowed transitions but the phase-averaged energy transfer in quasiclassical collisions may be accurate even when classically forbidden transition probabilities are important for the calculation of the average energy transfer. Forced quantum oscillator methods using a classical path whose initial velocity is the average of the initial and final velocities corresponding to the transition of interest are accurate for transition probabilities as small as 4 × 10^?8 for harmonic vibrators but do not seem to accurately account for the effect of anharmonicity.     

A quantum-mechanical investigation of collinear models for collision-induced dissociation

Accurate quantum-mechanical wavepacket results are reported for two collinear A + BC → A + B + C dissociation models. Both systems are of the MO EXP (Morse oscillator, exponentially repulsive interaction) type and thus do not allow for the possibility of reaction. One of these models has been previously subjected to a semiclassical study by Rusinek and Roberts. In the present paper, dissociation probabilities from vibrational states υ = 0, 1 and 3 of the diatomic are reported in a wide energy range for both systems. Numerous state-to-state transition probabilities are also given and the results are compared to those of related studies.     

Generating functions and recurrence relations for harmonic oscillator matrix elements

A simple and straightforward way of obtaining generating functions and recurrence relations for harmonic oscillator integrals is presented. The method, which is based on the properties of unnormalized coherent states and canonical transformations, allows a unified treatment of several different physical problems. Matrix elements of Gaussian and exponential functions, Franck-Condon overlaps, and transition probabilities for time-dependent quadratic Hamiltonians are discussed as illustrative examples.     

Dynamical Lie algebraic treatment for the A+BC scattering

We report the study of translational‐vibrational energy transfer in the A+BC scattering using the dynamical Lie algebraic approach combined with the intermediate picture. The rotational sudden approximation is applied to treat the rotational motion of the BC molecule, which is regarded as an anharmonic oscillator. The calculated results show that the transition probabilities increase with increasing rotational quantum number. Comparison with those obtained in the collinear collision of system A+BC manifests that the transition probabilities here increase indeed. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 214–221, 2001     

Rotational-vibrational rainbows in impulsive electron — diatomic molecule collisions: I. state-to-state transitions

Collisional induced combined rotational-vibrational excitation of diatomic molecules is discussed in a simple quantum mechanical spectator model with applications to electron-molecule collisions at intermediate collision energies (≈ 10² eV) within the rigid rotor/harmonic oscillator approximation. Quantum mechanical transition probabilities of the rotational-vibrational excitation, which show typical vibrational and rotational rainbow patterns, are calculated and compared with the structure of classical rainbow singularities.     

Rotational-vibrational rainbows in impulsive electron-diatomic molecule collisions

Rotational and vibrational rainbow effects in electron-diatomic molecule scattering at intermediate impact energies (≈10² eV) are discussed in a simple quantum mechanical spectator model within the rigid rotor/harmonic oscillator approximation. The total vibrational (summed over all final rotational quantum numbers) and rotational (vibrationally summed) transition probabilities show vibrational or rotational rainbow patterns, characteristic steps, and rainbow singularities, which are analyzed and interpreted in terms of classical cross sections.     

Photostability of complexes based on fluorescent CdSe/ZnS nanoparticles and polyelectrolytes

By means of fluorescence spectroscopy, it has been found that the oscillator strength of the electronic transition in CdSe/ZnS nanoparticles increases when the hydrophilic fluorescent CdSe/ZnS nanoparticles form complexes with cationic and anionic polyelectrolytes. However, an increase in the relative quantum yield and photostability is possible only in the complexes of the anionic shell-covered CdSe/ZnS nanoparticles with polycations. The mechanisms of the effect of ionic interactions on the probabilities and channels of electronic transitions in the nanoparticles are discussed.     

On the definition of a Monte Carlo model for binary crystal growth

We show that consistency of the transition probabilities in a lattice Monte Carlo (MC) model for binary crystal growth with the thermodynamic properties of a system does not guarantee the MC simulations near equilibrium to be in agreement with the thermodynamic equilibrium phase diagram for that system. The deviations remain small for systems with small bond energies, but they can increase significantly for systems with large melting entropy, typical for molecular systems. These deviations are attributed to the surface kinetics, which is responsible for a metastable zone below the liquidus line where no growth occurs, even in the absence of a 2D nucleation barrier. Here we propose an extension of the MC model that introduces a freedom of choice in the transition probabilities while staying within the thermodynamic constraints. This freedom can be used to eliminate the discrepancy between the MC simulations and the thermodynamic equilibrium phase diagram. Agreement is achieved for that choice of the transition probabilities yielding the fastest decrease of the free energy (i.e., largest growth rate) of the system at a temperature slightly below the equilibrium temperature. An analytical model is developed, which reproduces quite well the MC results, enabling a straightforward determination of the optimal set of transition probabilities. Application of both the MC and analytical model to conditions well away from equilibrium, giving rise to kinetic phase diagrams, shows that the effect of kinetics on segregation is even stronger than that predicted by previous models.     

Application of dynamical Lie algebraic method to atom–diatomic molecule scattering

The dynamical Lie algebraic approach developed by Alhassid and Levine combined with intermediate picture is applied to the study of translational–vibrational energy transfer in the collinear collision between an atom and an anharmonic oscillator. We find that the presence of the anharmonic terms indeed has an effect on the vibrational probabilities of the oscillator. The computed probabilities are in good agreement with those obtained using exact quantum method. It is shown that the approach of dynamical Lie algebra combining with intermediate picture is reasonable in the treating of atom–anharmonic oscillator scattering.     

I+HI'(v)→IH(v')+I'反应几率振荡行为的量子散射理论研究

本文基于振动绝热性分析, 用量子散射理论研究I+HI'(v)→IH(v')+I'反应几率的振荡行为, 其中双原子间相互作用势的振动本征态是Morse振子的严格解。在计算反应几率时采用分布高斯基(Distributed Gaussian Basis Sets; DGBS)展于方法, 既保持了反应几率的解析表达式, 又有效地简化了计算。计算结果明显地揭示了反应几率在低碰能区域的振荡行为。对反应机理也作了探讨。     

On the evolution equations for reduced density operators in quantum open systems

Evolution equations for transition probabilities of reduced density operators in quantum open systems are derived. Information contained in such equations is obtained from spectral resolutions and the role of memory kernels is elucidated within the scenario of many body theory as a function of the self-energy fields. As an analytical example of this formulation relaxation times for dissipative systems are evaluated in terms of the interaction between subsystems.