Energy Transfer Cross Sections Research Articles

Evidence for quantum interference in collision-induced intramolecular energy transfer within CO singlet–triplet mixed states

The quantum interference effect associated with one type of radiationless transition, the collisional energy transfer between singlet–triplet mixed molecular states, is studied. The experiments are conducted on CO(A 1Π,e 3Σ−)–He(Ar) via the ultrasensitive optical–optical double resonance multiphoton ionization (OODR-MPI) technique which measures state-to-state cross sections to an accuracy of ±10%, irrespective of the lifetime of the excited state. Distinct evidence of a quantum interference effect on the transfer rate has been obtained for mixed state CO intramolecular energy transfer processes. A simple, explicit expression for the cross section for mixed state energy transfer, based on the first order Born approximation of time dependent perturbation theory, is derived. The use of a transition phase angle θST is incorporated in the expression to describe the phase angle difference between singlet and triplet channels. This greatly refines the existing theory of quantum interference for collisional processes in that it successfully calculates the energy transfer cross sections and interprets the observed quantum interference effect under various quantum transitions. Experimental values of θST obtained for the CO–He system are 66° for J=9 and 73° for J=13. These results indicate that the infinite-order-sudden approximation which calls for θST=0 cannot satisfactorily account for the quantum interference effect. In addition, measured θST values for CO–Ar system are consistent with our theoretical expectations.

Sodium 3P fine-structure excitation transfer induced by collisions with rubidium and caesium atoms

The cross sections for the excitation energy transfer in the collisional processes Na*(3P12/)+M(nS12/) to or from Na*(3p32/)+m(Ns32/), m being ground-state Rb (n=5) or Cs (n=6) atom, have been measured by laser fluorescence method. With either of the two sodium 3P fine-structure states optically excited, the intensity ratio of the sensitized to direct fluorescence was measured. The polarization effects due to partially polarized and anisotropic direct fluorescence were investigated. The measured cross sections (T=530 K) for the sodium 3P fine-structure excitation transfer induced by collisions with Rb are: sigma (1/2 to 3/2)=170 AA2, with an overall accuracy of 20%. The corresponding values in the Cs case are: sigma (1/2 to 3/2)=140 AA2, sigma (3/2 to 1/2)=83 AA2. The theoretical calculations reveal the decisive role of the dipole-quadrupole interaction. The obtained values are in satisfactory agreement with the experiment only if both the dipole-dipole and dipole-quadrupole interactions are taken into account, while the calculations involving the dipole-dipole term alone yield the cross section values which are as much as one order of magnitude lower than the experimentally observed ones.

The use of the energy sudden approximation in them-scaling of rotational cross-sections

We invoke energy sudden (ES) dynamics in the projection- or m-scaling of crossed-beam rotational energy transfer cross-sections. We identify the dynamical quantities which must be input to the scaling analysis and note their symmetry properties. Also we show that a partial m-summing of cross-sections is sufficient to effect significant simplifications of the scaling. Application of the scaling analysis is made to integral cross-sections in the scattering of He+CO. It is found that the ES scaling is very effective in describing the m-dependent transitions.

On the influence of collision mass and interaction potential to the energy transfer in small thermal gas phase clusters

We have studied the collisional energy transfer, and the sticking probability, between molybdenum clusters and the rare-gas atoms Ne, Ar, and Xe. We have chosen these systems as nontrivial models of the thermalization process of metal clusters in a background gas. The mean energy transfer cross sections and the energy transfer rate constants, and the sticking probability of molybdenum clusters (Mo4,9,14) with rare-gas atoms are computed as functions of relative collision energy (gas temperature) and reduced mass. The dynamics of gas phase molybdenum clusters are simulated by molecular dynamics trajectories whose initial conditions are sampled from a distribution appropriate to thermal collisions. The simulation shows that the energy transfer rate constants are dominated by the collision frequency. The mean energy transfer cross sections are coupled to the collision mass as well as to the actual interaction force. The coupling is nonlinear, and there is some evidence that in the energy transfer, for small clusters, complex collisions are involved. The sticking probability at equilibrium temperature is far below 1.

Quasi-resonant energy transfer in collisions: Na2(A1? u + )+K(4S)

Cross sections for electron energy transfer from the initial rotational stateJ′of the two lowest vibrational levelsv′=0 andv′=1 of excited dimers Na2(A) to potassium atoms as described by Na2(A1Σu+,v′J′)+K(4S)→Na2 (X1Σg+,v″J″)+K(4P)+ΔE have been examined by laser-induced fluorescence. A strong increase of the cross section by as much as an order of magnitude has been observed for those dimerv′J′-levels for which the dipole transitions are close to resonance of the 4S-4P transitions in the atom (ΔE<4 cm−1). The absolute cross sections for energy transfer have been calculated by the Rabitz approximation of first-order perturbation theory. In the case of closest energy resonance (ΔE=0.9 cm−1) the cross section is Q=7.8×10−13 cm2.

Classical Simulation of Near-Resonance Rotational Energy Transfer between Two Dipole Rotors

A classical simulation of near-resonance energy transfer in collisions between two dipole linear rotors with slightly different moments of inertia is carried out. It is shown that, for initially unpolarized partners, the sudden approximation (i.e., the conservation of rotational polarization of colliding partners during a collision) provides a satisfactory approach to the calculation of the cross section as a function of the energy mismatch. Cross sections for energy transfer in collision of rotors, one of which is initially polarized, are also presented. The method is applied to the interpretation of near-resonance rotation-to-rotation energy transfer between HCl molecules in jet expansion experiments

Response to ‘‘Comment on ‘14N spin relaxation studies of N2 in buffer gases. Cross sections for molecular reorientation and rotational energy transfer’ ’’ [J. Chem. Phys. 100, 1775 (1994)

The origin of the factor 1/4 in the equation describing the quadrupolar relaxation times for linear molecules in the dilute gas phase is clarified. The quadrupolar relaxation cross-sections for nitrogen molecule are around 30 Å2 as reported by us and not around 120 as claimed in the comment.

Estimation of cross sections for energy transfer in bimolecular collisions

The proper definition of a cross section for energy transfer in bimolecular collisions is considered. Three models transforming smooth impact parameter dependence into hit or miss cross section form are discussed. The property dependence of the concept of a collision cross section is investigated. Translational energy cross sections (viscosity, diffusion, deflection energy) are found to be smaller than internal energy cross sections (thermal conductivity, thermal activation). An effective potential analysis of the concept of cross section shows that both radial and rotational collisions must be considered. Properly defined theoretical (effective potential, MD simulation) and experimental cross sections for Br 2-Br 2 show satisfactory agreement.

The effects of collision mass and potential on the energy transfer in thermal collisions of gas phase clusters

We have studied the collisional energy transfer between molybdenum clusters and the rare-gas atoms Ne, Ar, and Xe. We have chosen these systems as nontrivial models of the thermalization process of metal clusters in a background gas. The mean energy transfer cross sections and energy transfer rate constants for collisions of molybdenum clusters (Mo5) with rare gas atoms are computed as functions of relative collision energy (gas temperature) and mass. The dynamics of gas phase molybdenum clusters are simulated by classical trajectories whose initial conditions are sampled from a distribution appropriate to thermal collisions. For the interaction of the molybdenum cluster atoms with the background gas, a Buckingham-type potential for unlike atoms was fitted to energies obtained using standard quantum chemistry techniques. The molybdenum cluster atoms interact among themselves by a Lennard-Jones potential. The simulation shows that the energy transfer rate constants are dominated by the characteristic collision velocity, i.e., within the domain of internal cluster temperature and background gas temperature investigated here, the mass and the interaction force do not change the energy transfer rate constants very much. The mean energy transfer cross sections, however, are coupled to the collision mass as well as to the actual interaction force. The coupling is nonlinear, and there is some evidence that in the energy transfer, for small clusters, complex collisions with more than one cluster atom are involved.

Vibrational-state-to-state collision-induced intramolecular energy transfer N2(A 3Σu+, v″→B 3Πg, v′)

Absolute cross sections for collision-induced intramolecular energy transfer from the metastable A 3Σu+ state into the radiating B 3Πg state of N2 have been measured for the first time under single-collision conditions, using a thermal energy molecular beam of N2(A). The collision partners studied were the five rare gases, H2, N2, NO, and O2. The product vibrational levels (B, v′=4–10) were separated using spectrally resolved detection by means of filters as in our earlier related work [R. Bachmann, X. Li, Ch. Ottinger, and A. F. Vilesov, J. Chem. Phys. 96, 5151 (1992)]. In addition, in the present study the contributing reactant state vibrational levels (A,v″) were labeled, using optical pumping by a specially developed broad-band (∼1 nm) pulsed tunable dye laser. A depletion of up to 30% of a given v″ level could be achieved, about one-half of the theoretical maximum, at a pump pulse energy of 4 mJ. This quantity was also measured directly using a second synchronized probe laser. Pumping on a particular A,v″ level reduces the emission from the collisionally coupled B,v′ level by an amount which is a measure of the state-to-state cross section. Quasiresonant energy transfer was found to be strongly preferred, the cross section decreasing exponentially with an increasing energy gap. Absolute cross sections were obtained from a simultaneous measurement of the intensity of the fluorescence induced by the laser pumping of the selected A,v″ level, with corrections for predissociation of the excited upper state. Cross sections on the order of 0.1 Å2 for He to 15 Å2 for Xe were found for closely resonant (ΔE≊100 cm−1) processes. These results as well as our earlier, absolute measurements of the analogous intramolecular N2(W→B) transfer, are discussed in terms of interaction potential models.

The collision cross sections for excitation energy transfer in Rb*(5P 3/2) + K(4S 1/2) ? Rb(5S 1/2) + K*(4P J ) processes

The collisional excitation transfer for the processes Rb*(5P3/2)+K(4S1/2) → Rb(5S1/2)+K*(4P J ),J=1/2, 3/2, was investigated using two-photon laser excitation technique with a thermionic heat-pipe diode as a detector. The population densities of the K 4P J levels induced by collisions with excited Rb atoms as well as those produced by direct laser excitation of the potassium atoms were probed through the measurement of the thermionic signals generated due to the ionization of the potassium atoms emerging from the K(4P J ) → K(7S1/2) excitation channel. The measurements of the thermionic signals in addition to the spectroscopic determination of the potassium number density yield the following values for the excitation transfer cross sections: σ1(Rb 5P3/2 → K 4P1/2)=8 A2 and σ2(Rb 5P3/2 → K 4P3/2)=11 A2. The accuracy of the presented results is ∓15%. The obtained results are compared to those for the opposite processes K*(4P J )+Rb(5S1/2) → K(4S1/2)+Rb*(5P3/2).

Semiclassical calculations for energy transfer reactions in collisions between polarized sodium atoms

A semiclassical theory is applied to describe collisions between sodium atoms which are independently excited to a specific magnetic sublevel of the 3p state. Cross sections for energy transfer are calculated for different combinations of the initial magnetic quantum numbers (ma,mb) of the atoms, and as a function of the thermal collision velocity. The motion of the cores is described either by curved trajectories, based on non-averaged adiabatic potential curves, or by straight trajectories. The largest basis set used for the electronic wavefunction contains the 4p, 5s, 4d and 4f exit channels. The electronic interaction Hamiltonian is approximated by a multipole expansion, for which all non-vanishing contributions are evaluated.

High-resolution study of collision-induced transitions from N 2(A 3Σ +u, ν=10) to N 2(B 3Π g, ν=2)

The collision-induced intramolecular energy transfer N 2(A 3Σ + u)+M→N 2(B 3Π g)+M was studied under molecular beam conditions using Xe and N 2 as the collision partners. Specifically, the near-resonant transfer between the levels A, ν″=10→B, ν′=2 was investigated by means of the product emission, isolated by an interference filter. The rotational and fine structure levels of the A, ν″=10 reactant state were labeled by selective narrow-band laser pumping. The laser was scanned over the whole B, 12←A, 10 band and the subsequent decrease in the collision-induced emission B, 2→A, 0 was recorded. Repeating the scan, the laser-induced fluorescence intensity was recorded. These spectra are similar, showing that there is no significant dependence of the cross section for collision-induced energy transfer on the rotational or fine structure state of the reactant N 2(A, ν″=10) molecules.

Dynamics and Kinetics of Metal Atoms in the Gas Phase

AbstractThe review is divided into four sections. We first consider the varied behavior of K n2S and n2D states in their chemical reactivity and physical characterization. We review the effect of orbital alignment of an electronically excited metal atom on the cross section of energy transfer or chemical reaction, and report the technique of a single supersonic jet employed to measure this effect on the Ca spin‐changing collision. We discuss the effects of temperature and isotopic mass on the distribution of rotational quantum number of the product MgH to identify the reaction mechanism of Mg(1P1) + H2. The final concerns are the quantum yield, fine‐structure branching ratio and rate of collisional mixing for the K 2PJ doublets following photodissociation of KI at 193 nm.

Fine structure excitation transfer between the lithiumD-lines by collisions with cesium atoms

Applying resonant Doppler-free 2-photon laser spectroscopy with thermionic diode detection, the cross sections for the excitation energy transfer of the collisional process7Li*(2P 1/2+Cs(6S 1/2)→7Li*(2P 3/2)+Cs(6S 1/2) have been measured. The experimental cross sections, σLi-Cs (1/2→3/2)=890 A2 and σLi-Cs (3/2→1/2)=430 A2, are compared with theoretical data obtained by a sudden impact approximation approach taking into account the long-range interaction potentials only. The calculated cross sections show an excitation mixing process at large internuclear distances where Li-Cs dipole-dipole and dipole-quadrupole interaction forces are predominant.

Deexcitation of He(2 1P) in collisions with diatomic molecules

Deexcitation cross sections of He(2 1P) by N2 and O2 have been measured using a pulse radiolysis method in a region of the mean collisional energy between 18 and 38 meV. Fairly large deexcitation cross sections (≂100 Å2) by N2 and the negative slope of the curve of cross section vs energy are interpreted in terms of the energy transfer cross section based on a dipole–dipole interaction. Validity of theoretical formula based on a semiclassical approach with rectilinear trajectories, i.e., the Watanabe–Katsuura formula, is discussed. The deexcitation cross section of He(2 1P) by O2 and its collisional energy dependence are not very different from that by N2. Optical model calculation of the deexcitation cross section has been also presented for collisions between He(2 1P) and M (M=H2 or N2) with an isotropically averaged complex potential optimized through a fitting procedure to the experimental cross sections. It has been found by the model calculation that an electron exchange interaction is not negligible in the deexcitation process.

Fine structure excitation transfer between the potassium 42P states induced by collisions with caesium atoms

Applying diode-laser resonant fluorescence method, the cross sections for the excitation energy transfer of the collisional process K*(42P1/2)+Cs(62S1/2)↔K*(42P3/2)+Cs(62S1/2) have been measured. The values we have obtained are σ(1/2→3/2)=77 A2 and σ(3/2→1/2)=48 A2. These results complete the sequence of data for the fine-structure mixing of the first-resonance states of alkali atoms colliding with the ground-state caesium atoms.

Calculations on laser-induced collisional energy transfer.

We examine theoretically the behavior of cross sections for laser-induced collisional energy transfer (LICET) over a wide range of detunings and laser intensities for the two-atom pairs Li-Sr and Eu-Sr which have been previously studied experimentally. These two cases are complementary in that the laser and collisional interactions enter in opposite orders, and their level structures are such as to give weak-field line shapes of opposite asymmetry and intensity shift. A three-state model is used and the Bambini-Berman formula for the weak-field quasistatic wing is verified. At high intensities the peak cross section is found to go through a maximum and the LICET profile is found to become symmetric about a shifted center with notable departures from a uniform falloff in the far quasistatic wing, apparently arising from radiative collisional interference effects.

Rate coefficient for the reaction H+O2→OH+O: Results at high temperatures, 2000 to 5300 K

The tunable-laser flash-absorption technique has been used to study the high-temperature behavior of the reaction H+O2→OH+O by monitoring the absorption of the hydroxyl radical. Sensitivity analysis of a detailed reaction mechanism shows that for fuel rich mixtures only two reactions are sensitive when hydroxyl is monitored: H2+M→2H+M and H+O2→OH+O. Rate coefficients for these reactions have been determined by least-squares analysis of measured absorption profiles. For the rate of dissociation of H2 in krypton we obtain k1(T)=(8.86±0.88)×10−10 exp[−48321/T(K)] cm3 s−1 from 3450 to 5300 K. For the H+O2 reaction we combined our results with previous low temperature measurements and recommend k2(T)=(1.62±0.12)×10−10 exp[−(7474±122)/T(K)] cm3 s−1 from 960 to 5300 K. The uncertainties are at the 95% confidence level. Measured cross sections for rotational and vibrational energy transfer in O2 and OH have been used to show that relaxation effects do not influence the results. We compare our results to recent trajectory calculations. In addition, we calculate the rate of the reverse reaction, OH+O→H+O2, and compare it to trajectory and statistical adiabatic channel calculations. Finally, we point out that the first excited surface of the hydroperoxyl radical, 2A′, which correlates with H(2S)+O2(1Δg), may be needed to explain very high temperature results.

1 4N spin relaxation studies of N2 in buffer gases. Cross sections for molecular reorientation and rotational energy transfer

Nuclear spin–lattice relaxation times (T1) have been measured as functions of temperature for 14N in N2 gas and in N2–Ar, Kr, Xe, CO, CO2, HCl, CH4, CF4, and SF6 mixtures. The relaxation is dominated by the quadrupolar mechanism so that empirical values of the collision cross sections for molecular reorientation (σθ,2) could be obtained as functions of temperature. The values of σθ,2/Å2 at 300 K are 29.6±0.9 (N2–N2), 33±1 (N2–Ar), 41±2 (N2–Kr), 44±2 (N2–Xe), 32±1 (N2–CO), 59±3 (N2–CO2), 46±1 (N2–HCl), 31±1 (N2–CH4), 59±2 (N2–CF4), and 73±2 (N2–SF6). For all 14N2 –buffer pairs, the temperature dependence of the cross section deviates from T−1, which is not very different from that of the collision cross section (σJ) for changes in the rotational angular momentum vector. This is the first molecule for which the collision cross sections σθ,2 and σJ have both been measured for a series of collision partners. The ratio (σθ,2/σJ) is found to be nearly constant, 2.1±0.2 for the N2 molecule with the ten collision partners. Based on Kouri’s IOS factorization scheme, (σθ,2/σJ)&amp;gt;1 may be true in general. The data for N2 are compared with the theoretical reduced correlation times based on existing mathematical models for molecular reorientation in fluids.