Collisional Transition Probabilities Research Articles

Collisional excitation of thioformaldehyde and of Silylidene

For analysis of spectrum of a molecule in the interstellar medium, radiative and collisional transition probabilities for rotational transitions in the molecule are required. We have calculated collisional rate coefficients for rotational transitions in ortho and para thioformaldehyde (H2CS), and in ortho and para Silylidene (H2CSi) due to collisions with He atom for kinetic temperatures 10, 20, 30, 40 and 50K, following the procedure discussed in our earlier work. The accuracy of collisional rate coefficients may be within a factor of 2.

Quasiclassical predictions of final vibrational state distributions in reactive and nonreactive collisions

The validity of quasiclassical and semiclassical trajectory methods for predicting state-to-state vibrational transition probabilities in collisions of atoms with diatomic molecules is discussed with special emphasis on tests against accurate quantum calculations for He + H2, H + Cl2, and I + H2 collisions.

Kinetically Controlled Selective Ionization Study on the Efficient Collisional Energy Transfer in the Deactivation of Highly Vibrationally Excited trans-Stilbene

Direct measurements of the gas-phase collisional energy transfer parameters are reported for the deactivation of highly vibrationally excited trans-stilbene molecules, initially prepared with an average energy of about 40 000 cm(-1), in the bath gases argon, CO2, and n-heptane. The method of kinetically controlled selective ionization (KCSI) has been used. Complete experimental collisional transition probability density functions P(E',E) are determined, which are represented by a monoexponential form with a parametric exponent in the argument, P(E',E) proportional to exp[-{(E - E')/(C0 + C1E)}Y] (for downward collisions), well established from earlier KCSI studies. A comparison of the first moments of energy transfer rate constants, kE,1, or of resulting first moments of energy transfer, <DeltaE(E)>, for trans-stilbene with those for azulene and toluene clearly shows the considerably more efficient deactivation of trans-stilbene for all bath gases, presumably due to the much greater number of very low-frequency modes of trans-stilbene. However, on a relative scale this gain in deactivation rate of excited trans-stilbene is clearly collider dependent and decreases distinctly with the growing collision efficiency of the larger bath gas molecules.

Multiplex detection of collisional energy transfer using KCSFI

A new detection method for obtaining collisional transition probabilities P(E',E) of highly vibrationally excited molecules in the gas phase is presented. The technique employs energy-selective probing of the time-dependent vibrational population distribution by "kinetically controlled selective fluorescence (KCSF)". We present experimental results for a test system, the collisional deactivation of toluene by argon, where we use the well-known "kinetically controlled selective ionization (KCSI)" scheme as a reference for comparison. A newly designed setup is employed that allows simultaneous detection of fluorescence and ionization signals under identical experimental conditions ("kinetically controlled selective fluorescence and ionization = KCSFI"). For the system toluene + argon it is demonstrated that KCSF and KCSI yield identical results. A rate-equation model is presented to understand common features and differences of both approaches. The fluorescence detection scheme shows promise for future investigations on collisional energy transfer. The experimental setup is simpler, because it requires no additional ionization wavelength. This will hopefully give access to the P(E',E) of systems where, e.g., ionization schemes are difficult to implement due to short wavelengths required for the ionization step. A few examples will be outlined briefly.

Intensity Ratios between the 2s21S0–2s2p3P1and 2s2p1P1–2p21D2Transitions in Be‐like Ions as Electron Temperature Indicators for Solar Upper Atmosphere Plasmas

We investigate the relative intensities of the two moderately bright Be-like 2s2 1S0-2s2p 3P1 and 2s2p 1P1-2p2 1D2 lines as a function of electron temperature. We show that the intensity ratios of the lines in the beryllium isoelectronic sequence from C III to Ni XXV ions can serve as sensitive temperature indicators for a large variety of solar plasmas. While the C III-Ne VII lines can be used to diagnose unresolved fine structures in relatively cold solar atmosphere plasmas [(1-5) × 105 K], the Na VIII-Ar XV ions can be used to diagnose coronal plasmas [(0.8-3) × 106 K], and Ca XVII-Ni XXV lines are useful to measure the temperature in flaring plasmas [(5-16) × 107 K]. We investigate the effects on the temperature determination caused by varying the number of energy levels that are included in the atomic model for the considered ions. It is found that a model that includes the 2l2l' and 2l3l' configurations is sufficient for adequately describing the relevant level populations of the Be-like ions in coronal conditions. We compare theoretical ratios obtained using collisional cross section and transition probability values derived by different theoretical methods. The atomic data are obtained from the CHIANTI database, the Hebrew University Lawrence Livermore Atomic Code (HULLAC) suite of programs, and other available sources in the literature. Finally, we use spectra of an apparently isothermal coronal plasma observed by the Solar Ultraviolet Measurement of Emitted Radiation instrument on the Solar and Heliospheric Observatory to determine the electron temperature of streamer plasma using the HULLAC and CHIANTI atomic data sets. The result is compared with the temperature derived in an earlier study using different methods.

Collisional energy transfer of highly vibrationally excited toluene and pyrazine: Transition probabilities and relaxation pathways from KCSI experiments and trajectory calculations

New experimental results for the collisional energy transfer of highly vibrationally excited toluene and pyrazine employing the method of “kinetically controlled selective ionization (KCSI)” are presented. By means of a master equation approach we determine complete and detailed collisional transition probabilities P(E′,E) for energies up to 50000 cm−1. The same monoexponential representation P(E′,E)∝exp[ − ((E − E′)/α1(E))Y] (for E′⩽E) with a parametric exponent Y in the argument and linearly energy dependent α1(E) = C0 + C1E successfully used in our earlier investigation [T. Lenzer, K. Luther, K. Reihs and A. C. Symonds, J. Chem. Phys., 2000, 112, 4090] can reproduce the toluene and pyrazine results for the whole range of bath gases studied. The parameters Y, C0 and C1 of P(E′,E) show a smooth increase with the size of the collider. An approximately linear energy dependence of the first moment of energy transfer 〈ΔE〉 is observed for all bath gases. Literature data from infrared fluorescence (IRF) experiments in general show significantly smaller − 〈ΔE〉 values outside the uncertainty limits of the KCSI results. It is shown that this can mainly be traced back to the critical dependence of the IRF data on small uncertainties in the calibration curve. Some of the trends with respect to the energy transfer efficiencies of different colliders observed in the KCSI experiments are easily rationalized on the basis of accompanying trajectory calculations on the deactivation of highly vibrationally excited pyrazine by n-propane and CO2. The negligible influence of the V–V relaxation channel in the pyrazine + CO2 system observed in earlier IR diode laser studies is confirmed.

Collisional dynamics of Bi2 A(0u+). I. Quantum-resolved vibrational energy transfer for v′=0–4

Vibrational-to-translational energy transfer between the lowest vibrational levels (v′=0–4) of the A(0u+) state of Bi2 has been investigated using spectrally resolved, laser-induced fluorescence techniques. The small vibrational spacing (ωe′≃132 cm−1) leads to highly nonadiabatic conditions, particularly for the Bi2(A)–He collision pair. However, the Δv=−1 transition probabilities for collisions with the rare gases range from 0.75% to 1.75% per collision, considerably lower than would be anticipated from standard vibrational energy transfer theory. Multiquantum (Δv′=±2) transfer rates are low, consistent with the low anharmonicity of the A(0u+) state. The rates for Δv′=±1 transitions scale linearly with vibrational quantum number as expected near the bottom of this nearly harmonic potential.

Quasiclassical trajectory simulations of collisional vibrationally excited HgBr(B 2Σ). II. Dependence on rotational excitation

The collisional deactivation of HgBr(B 2Σ) by different inert gases has been studied using quasiclassical trajectory calculations, with initial vibrational energy Evib=6452 cm−1, at different initial rotational energies in the range 0–6452 cm−1 and a temperature of 415 K for the translational energy. The effect of rotational energy on vibrational, rotational, and translational energy transfer was examined in terms of 〈ΔE〉 and 〈ΔE2〉1/2 for the inert gases (He, Ne, Ar, Kr, and Xe). The influence of mass of the collider and the interaction potential was analyzed computing trajectories using pseudo-isotopes of He and Xe. Collisional transition probabilities for vibrational, rotational, and translational degrees of freedom were obtained as a function on rotational energy. The computed transition probabilities became broader as the mass of collider and rotational energy increases and show a double exponential behavior for all gases.

Effect of the superposition of weak and strong collisions on unimolecular reaction rate

The effect of superimposed weak and strong collisions on unimolecular reaction rates is analyzed analytically. The reaction kinetics are described by a master equation with a two-scale collisional transition probability (CTP). Simple formulae for the low-pressure reaction rate are derived in terms of reaction rates for single-scale CTPs. The formulae accurately describe the crossover from the strong to the weak collision mechanism of reaction as the fraction of strong collisions decreases. Similar formulae are derived for a finite microcanonical reactivity.

A Monte Carlo wave function study of the effect of collisions on the coherent multiphoton excitation of SF6

Collisional interruption of coherent excitation of SF6 in the lower discrete region of its laser absorbing mode (ν3) have been studied using the recently developed quantum Monte Carlo wave function (QMCWF) method. The usual pure pump mode description up to 3ν3 and complete mixing of all modes (QC) above it have been assumed. The rotational and anharmonic splitting of the vibrational states upto 3ν3 are taken into account but splitting due to tensor interaction terms are neglected. Excitation to QC is represented by irreversible leakage from the coherent ladder modeled by an imaginary term in the Hamiltonian of the coherently excited vibrational rotational levels. QMCWF study has been carried out at the laser frequency 942.8 cm−1 for which the local time average populations in the intermediate excited vibrational states are found to be negligible. Large leakage occurs only from narrow band of ground rotational states due to 3 photon resonances but their number increases with increasing intensity. Two different collisional energy transfer models, one obeying symmetry imposed restrictions and propensity rule, and the other free from such restrictions except the fact that collisions restore the thermal distribution, have been used. Results show different pressure effects at different temperature and for different intensities. However, the two different models used for collisional rotational transition probabilities give similar enhancement of leakage at high intensities.

Screening effects for transition probabilities in collisions of charged particles with an atom or stripped ion.

Screening effects for transition probabilities in collisions of charged particles with an atom or stripped ion are investigated using the modified hyperbolic-orbit path in the semiclassical approximation. Effective nuclear charges for bound electrons in many-electron atoms are determined by new screening constants [Y.-D. Jung and R. J. Gould, Phys. Rev. A 44, 111 (1991)]. Applications were made to O, ${\mathrm{O}}^{4+}$, and ${\mathrm{O}}^{7+}$. For these targets, the transition probabilities are calculated for 1s\ensuremath{\rightarrow}2p transitions. The results show that the maximum point of the transition probability is shifted to the nucleus with an increase of the screening effect. Moreover, the maximum amplitude of the transition probability is appreciably reduced as the screening effect increases.

Dependence of the collisional relaxation of highly vibrationally excited polyatomic molecules on the population distribution function

The influence of the population distribution function on the collisional relaxation of highly vibrationally excited polyatomic molecules is analyzed in a non-reactive system. Unimodal and bimodal energy distributions are considered. Calculations made with unimodal energy distributions showed that the energy decay is almost independent of its initial shape and also of the collisional transition probability models, provided they have the same dependence on energy. When the initial distribution is bimodal, the rate of energy decay, for constant average energy transferred, depends on the fraction of molecules excited, but if the decay is exponential, the energy loss profile is almost independent of the fraction q of molecules excited. These results are discussed in relation to the use of IR multiphoton absorption as an experimental technique for the study of energy transfer processes.

Transition probabilities in collisions between an atom and an anharmonic oscillator

Transition probabilities between vibrational states of an anharmonic diatomic molecule are studied as a function of the total collision energy and as a function of the strength of the anharmonicity. The molecule is modeled by an anharmonic oscillator with cubic and quartic terms while the interaction between the atom and the molecule is a repulsive exponential which is expanded in a Taylor series and up to quartic terms are kept. The transition probabilities are obtained with the use of algebraic methods. Numerical results are presented for the systems H2 + He, H2 + H and are compared with exact quantum mechanical results of Clark and Dickinson. We also present numerical results in two approximations for the very anharmonic system ClH + He where no exact results were found.

Quantum study of electronically non-adiabatic collinear reactions. III. Influence of vibrational and electronic excitations on the Cs + HH → CsH + H reaction

A new hyperspherical close-coupling method, involving non-orthogonal diabatic electronic bases adapted to each arrangement, is developed to compute collisional transition probabilities for the collinear Cs + HH system, close to the threshold of the reactions Cs *(7p) + HH(υ = 0) → CsH(υ = 0) + H. A simple model, taking into account the overall rotation of the linear CsHH complex, provides estimates of inelastic and reactive cross sections. A hyperspherical adiabatic analysis, based on adiabatic electronic potential energy surfaces, points out two prominent features in the dynamics of the CsHH system namely: (i) Approximate electrovibrational adiabaticity, which gives rise to large cross sections (≈ 5 Å 2), for both the vibrationally adiabatic process Cs *(7p) + HH(υ = 0) → CsH(υ = 0) + H and the vibrational-into-electronic energy conversion Cs(6s) + HH(υ = 6) → CsH(υ = 0) + H. (ii) Sharp resonances, which yield rapid oscillations on total cross sections, related to the rotational structure of an intermediate linear long-lived complex.

Collisional energy transfer in non-reactive systems

If the internal energy of target molecules highly dispersed in a heat bath is monitored as a function of time, their one-photon laser excitation and subsequent bulk collisional relaxation yields information only about energy transfer in the bulk system (a macroscopic time-dependent property). This paper discusses three special cases when [Formula: see text], the average energy transferred in a collision (a microscopic property) can be deduced from bulk relaxation data without knowledge of the collisional transition probability: (i) initial excitation is a δ function; (ii) relaxation of bulk average energy follows simple exponential law; or (iii) it is linear in time. The implications of exponential relaxation is that [Formula: see text], which is the first moment of the collisional transition probability, is a linear function of internal energy. These conclusions are illustrated using available laser relaxation data on azulene, benzene, and hexafluorobenzene, and are compared with similar data on toluene and two cycloheptatrienes. Some inconsistencies are noted, the probable origin of which is discussed.

XeF ground state kinetics analysis

A physical model of the temporal aspects of the ground electronic state of XeF in an e-beam pumped environment has been developed in terms of the most recent kinetic and thermochemical information available. Surprisal theory was used to interrelate the individual collision transition probabilities, including those describing promotion of molecules to the dissociation continuum. Molecular dissociation was assumed to occur solely from the continuum, the rate for which was obtained from the constraints of equilibrium. The model includes thermochemical aspects which account for the possibility of dissociation arising from thermally derived rotational excitation. The model, as developed, considerably impacts our interpretation of the phenomenon of improved laser performance at elevated temperatures. Considerable light is also shed on the physics of energy distribution among the principal operating frequencies of the laser.

Collisions of NO(X 2II) with a Ag(111) surface: Validity of the energy sudden approximation

Energy sudden calculations of the rotationally inelastic scattering of ground-state (NO(X 2 II) from an uncorrugated, rigid Ag(111) surface have been carried out. In this approximation, the inelastic transition probabilities are obtained by solution of a fixed-orientation, single-channel Schrodinger equation, which must be solved for each of the two adiabatic potential energy surfaces which arise when a molecule in a 2 II electronic state interacts with a surface. These two potential surfaces were based on a description of the NO−Ag(111) potential used by Muhlhausen, Williams and Tully [J. Chem. Phys. 83 (1985) 2594]. Comparison of the calculated transition probabilities with the results of our previous close-coupling calculations at a collision energy of 6700 cm −1 shows that for this potential, which possesses a deep, strongly anisotropic, and fairly long-ranged attractive region, the sudden approximation predicts significant flux into high rotational levels which are neither energetically nor dynamically accessible. The dependence of the collisional transition probabilities on the symmetry of the electronic wavefunction of the NO A -doublet state, with respect to reflection in the plane of rotation of the molecule, is described reasonably well within the sudden approximation. The sudden results also adequately predict the relative flux into rotational levels associated with the two ( Ω =1/2 and Ω =3/2) spin-orbit manifolds of NO.

Average collisional vibrational energy transfer quantities. The exponential model

Abstract : The important collisional energy transfer ratio, gamma = delta Esub all/delta E sub d was examined by using a fitted classical approximation for the density of internal energy eigenstates. The exponential form of the collisional energy transfer probability function was applied to four model unimolecular reaction systems. Two parameters, the inversion temperature TI and the effective temperature Te (defined previously in I), were employed to develop a form for the parametric dependence of gamma on delta E sub d, energy level E and temperature T; these quantities are related to a reduced average energy transfer quantity E' sub e. Comparison was made with previous literature expressions for the inter-relationship between delta Esub all and delta Esub d for both exponential and stepladder models of the collisional transition probabilities.

Calculation of collisional and radiative transition probabilities between excited argon levels

Average radiative transition probabilities for argon atoms have been calculated for transitions between 24 levels in two groups characterized by the atomic core terms 2 P 1/2 and 2 P 3/2 by using the method of Bates and Damgaard. The results are compared with data in the NBS tables (Wiese et al.) and with those of Katsonis and Drawin. We find satisfactory agreement for the order of magnitude, even for transitions between lower lying levels. Parameters, which appear in Drawin's semiempirical cross-section expressions for electronic excitation of optically allowed and parity-forbidden transitions, are determined with the multipole expansion method proposed by Sobel'man for transitions between the specified levels. Most of these are easily obtained, but the method must be improved for transitions between levels having the same azimuthal quantum number because the summation over the constituent terms does not converge.

Study of vibrational energy transfer at a surface by a time-of-flight method

A single collision, time-of-flight extension of the VEM method for the study of molecule-surface vibrational energy transfer is introduced. The technique helps election between possible alternative trial analytic forms of the collisional transition probability function. A Gaussian form is preferred over a Boltzmann-exponential form for cyclobutene isomerization to 1.3-butadiene energized by collisions at a silica surface at 800 K.