Cross Sections For Fine-structure Transitions Research Articles

Fine-structure Transitions of Ne+, Ar+, Ne2+, and Ar2+ Induced by Collisions with Atomic Hydrogen

We calculate cross sections for fine-structure transitions of Ne+, Ar+, Ne2+, and Ar2+ in collisions with atomic hydrogen by using quantum-mechanical methods. Relaxation rate coefficients are calculated for temperatures up to 10,000 K. The temperature-dependent critical densities for the relaxation of Ne+, Ar+, Ne2+, and Ar2+ in collisions with H have been determined and compared to the critical densities for collisions with electrons. The present calculations will be useful for studies utilizing the infrared lines [Ne ii] 12.8, [Ne iii] 15.6, [Ne iii] 36.0, [Ar ii] 6.99, [Ar iii] 8.99, and [Ar iii] 21.8 μm as diagnostics of, for example, planetary nebulae and star formation.

Dynamics of spin–orbit recoupling in collisions of alkali atoms with noble-gas atoms using atomic core potentials

Spin–orbit recoupling in alkali-rare-gas atom colliding pairs is developed within a first principles description of the quantum dynamics introducing l-dependent pseudopotentials and including two and three-body polarization terms and the spin–orbit interatomic potential. The treatment combines an eikonal (or short wavelength) approximation for the nuclear motion and time-dependent molecular orbitals to provide interatomic potentials, their nonadiabatic couplings, and state populations during interactions. The time evolution of recoupling of angular momenta in alkali-rare-gas atom thermal collisions is described and computational aspects of spin–orbit coupling in terms of pseudopotentials are presented. Results for potentials arising from the spin–orbit splitting of the P2 states of Li and Na are presented along with cross sections for fine-structure transitions at 400 K and 450 K. The agreement with experiment and other theories is very good.

Determination of fine structure transition cross sections of Rb(7 2D) atoms induced by collisions with molecules of H2 or CO

The cross sections for fine-structure transition (FST) of Rb(72D) atoms induced by collision with molecules of H2 and CO have been experimentally determined by the method of selective stepwise excitation of Rb atoms and observation of the resulting fluorescence. The cross sections (in units of 10-14 cm2) for Rb(72D)-H2 are σfs*(72D5/2 → 7 2D3/2) = 0.16 ± 0.03, σfs*'(7 2D3/2 → 7 2D5/2) = 0.24 ± 0.05, for Rb(72D)-CO: σfs* = 0.10 ± 0.06 and σfs*' = 0.15 ± 0.09. The cross sections σtr* for transfer out of the 7 2D doublet were also determined.

Fine Structure Transition Cross Sections of Ar+and Ne+in Collisions with Rare Gases

With a high resolution ion energy-loss spectrometer, fine structure transition cross sections for the collision systems of Ar + and Ne + -rare gases have been measured in the incident ion energy range from 100 to 2000 eV. It appears that for each ion, the magnitude of the cross sections can be put in order with the absolute values of the ionization energy differences between the projectiles and targets; |Δ E |. If σ 0 is the fine structure transition cross section of the symmetric system, that of an asymmetric system becomes σ 0 exp (-|Δ E |/α).

Theoretical state-to-state inelastic cross sections for collisions of Ar+(2P3/2, 2P1/2) with N2

State-to-state cross sections for fine-structure transitions and vibrational excitation have been calculated for collisions of Ar+(2P3/2, 2P1/2) with N2 over the relative collision energy range 1–4000 eV. The computations were done by means of a vibronic semiclassical method, and the potential energy surfaces of Archirel and Levy were used. The cross sections are in good agreement with the limited amount of experimental data now available. The cross sections for fine-structure transitions are surprisingly large at all energies.

Absolute spin-orbit-state excitation cross sections for the reactions Ar +( 2 P [formula omitted]) + Ar( 1S 0) and Ar +( 2P [formula omitted]) + N 2 (X, v = 0)

A new triple-quadrupole and double-octopole photoionization apparatus has been developed for absolute state-to-state excitation and relaxation cross section measurements. Using this apparatus, we have measured absolute fine-structure transition cross sections for the reactions Ar +( 2P 3 2 ) + Ar and Ar +( 2P 3 2 )+ N 2(X, ν = 0) at laboratory collision energies of 25–200 eV.

Test of interatomic potentials and study of coupling mechanisms involved in fine-structure transitions for K(42P)+Ar collisions

Quantum mechanical cross section calculations have been performed in order to interpret the energy dependence of absolute total cross sections for fine-structure transitions in the 42P level of K, induced in collisions with Ar. The comparison between the experimental and theoretical data allows available interatomic potentials to be tested. The various adiabatic potential sets used in the calculations, along with a careful analysis of the polarisation in the 42P level of K, allow the coupling mechanisms responsible for the fine-structure transitions in K(42P)+Ar collisions to be analysed in some detail.

Analytic solutions to two-state collision problems for the case of exponential coupling

Analytic solutions to two-state collision problems are obtained for systems in which the interaction matrix element of the Hamiltonian displays an exponential variation with time. When the difference in the diagonal matrix elements is either constant or governed by the same exponential function, exact analytic solutions can be found. When it is in the form of a constant plus an exponential term, the case of practical importance, an approximate solution is obtained based upon these exact solutions. The solution is used to calculate cross sections for fine-structure transitions in atomic collisions (Na-He, F-Xe, F-H/sup +/).

Fine-structure transitions in Rb(5P) induced by H2and N2molecules

The energy dependence and the absolute value of the cross section for the P1/2 to P3/2 fine-structure transition (FST) in Rb(5P) induced by H2 or N2 molecules and He atoms has been measured for the first time in a crossed-beam apparatus. The results for He, in excellent agreement with previous experimental data, are used for comparing atomic and molecular target behaviour with regard to FST processes in heavy alkalis. One observes much larger cross sections for H2 and N2 at low energies with a much weaker energy dependence. Theoretical work suggests two seemingly competing mechanisms for including large FST cross sections for molecular targets. One, involving an intermediate ionic complex, accounts for the general trend (absolute value and energy dependence) of the experimental data for N2 while the other, recently suggested by Hickman seems to play the major role when H2 is the target.

Fine-structure transitions in K(4P) induced by rare gases and diatomic molecules

The energy dependence and the absolute value of the cross section for the P1/2 to P3/2 fine-structure transition (FST) of K(4P) induced by H2 molecules has been measured in a crossed-beam experiment. For K(4P)-rare-gas pairs, the beam data and the theoretical results for the energy dependence of the FST cross sections are in good agreement. The discrepancy between 'bulk' experimental results and theoretical data is shown to be associated with errors in the experimental data. For the K(4P)-H2,-N2 pairs, under beam conditions, the mechanism responsible for the FST process is similar to that involved when the target is a rare gas. Under the conditions of a 'bulk' experiment, when the rotational temperature of the N2 molecules is higher, another mechanism seems to play a role. The nature of this additional mechanism is discussed.

Lithium [Li*(2 2P J)] fine structure transitions and quenching induced by collisions with molecular hydrogen [H2, D2

Dye laser excitation and interferometric fluorescence analysis techniques were used to measure collision induced quenching and fine structure transition rate coefficients in the 7Li*(2 2PJ)+H2,D2 systems at a temperature of 564 K. The quenching and fine structure transition energy transfer processes all occur at ’’gas kinetic’’ rates, but the magnitudes of cross sections for each process are determined by different electronically nonadiabatic interactions at different ranges of internuclear separation. Fine structure transition cross sections are determined by the forms of long range interaction potentials, which are undoubtedly very similar to those of the isoelectronic Li*(2 2PJ)+He system. Quenching cross sections are determined by short-to-intermediate range interaction potentials, some of which may effectively be coupled by fine structure transitions. Simple dynamical models provide limited insight into these rate processes, suggesting that ab initio potential hypersurface calculations plus refined quantal and/or semiclassical dynamical computations using these hypersurfaces are required for proper treatment of the Li*(2 2PJ)+ H2,D2 systems.

Franck–Condon factors in studies of dynamics of chemical reactions. IV. Nonadiabatic collisions

We investigate the application of the Franck–Condon approach to nonadiabatic molecular scattering processes. Computationally simple, analytic formulas are developed to describe the energy dependence of quenching of electronically excited atoms by atoms and molecules. These formulas include the dependence of the Franck–Condon factors on the translational wavefunctions as well as the wavefunctions for the internal degrees of freedom. We use these formulas to evaluate the translational energy dependence of the fine structure transition cross sections for F(2P3/2)+X→F(2P1/2)+X, where X= Xe, H+, and H2. The cross sections generally increase as the initial translational energy increases. Our results agree semiquantiatively (or better) with those obtained from other theoretical techniques. In the case of F+H+ we find that the absolute cross section is sensitive to the analytic form used for the nonadiabatic coupling but our model gives the correct energy dependence. At the energies of our calculations we find only a small amount of vibrational excitation of H2. Finally, we use our expressions to interpret some trends of available experimental results on the quenching of Hg (3P2→3P1) by several molecules. We find that collisional excitation of the internal modes of the molecule becomes more important as the initial translational energy increases. However, these modes do not contribute to the quenching cross section in a statistical fashion.

Collision models of intramultiplet transitions at thermal energies

An analysis is presented of the range of validity of the approximations currently used to calculate cross sections for fine-structure transitions at thermal energies. The particular example considered is the 2P1/2-2P3/2 transition in C+-H collisions. For a given set of interaction potentials of CH+, the full quantum-mechanical close-coupling method is used to provide a reference for comparison with a number of approximate dynamical models-semiclassical sudden approximation, quantal elastic and Omega -conserving methods. All of the dynamical models examined proved to be very satisfactory. On the other hand, the calculated cross sections are sensitive to the interaction potentials, especially for intermediate and long internuclear distances where the presently available data are not sufficiently reliable; errors in the calculated cross sections may attain 40%.

A b i n i t i o calculations for the X 2Σ, A 2Π, and B 2Σ states of NaAr: Emission spectra and cross sections for fine-structure transitions in Na–Ar collisions

Configuration interaction (CI) calculations were performed for the X 2Σ, A 2Π, and B 2Σ states of NaAr. The A 2Π state is calculated to have a well depth of 492 cm−1 at an internuclear separation of 3.04 Å. Small wells of 55 and 32 cm−1 were found for the X 2Σ and B 2Σ states located at 5.01 and 6.80 Å, respectively. The spectra for A 2Π–X 2Σ emission in the limits of zero and infinite Ar pressure were calculated and compared with the experiment of York, Scheps, and Gallagher and the predictions using the pseudopotential curves of Pascale and Vandeplanque. The potentials from this work give spectra in much better agreement with experiment than the pseudopotential predictions. Total and differential cross sections for fine-structure changing transitions Na(2P1/2) +Ar→Na(2P3/2)+Ar−17.2 cm−1 were calculated by a quantum mechanical technique. The total cross sections are in excellent agreement with experimental results. The excited state differential cross sections exhibit prominent rainbow structure centered at τR=EΘR=5.5–6.0 eV deg.

Semiclassical calculations of cross sections for fine-structure transitions in Rb (62P) and Cs (82P) colliding with rare gas atoms

Calculations of cross sections for fine-structure transitions in the second and third excited 2P state of rubidium and cesium, respectively, have been carried out using a semiclassical theory for collisions with ground state He, Ar, and Xe atoms. The primary difference from previous theories for the first 2P state of an alkali is the full formulation of the semiclassical theory in terms of molecular states of the alkali–rare gas atom complex. The molecular states are consistent with the interaction potential and both radial and rotational coupling are explicitly included in the calculations. In the collision energy range investigated (from threshold to 0.3 eV) the cross sections are found to have an undulatory structure, especially prominent for the Rb–Ar system. Except for the Cs–He system, the thermally averaged cross sections agree with experiment within a factor of 1.4–2.8. For cesium, these results reduce considerably the large discrepancy between previous calculations of Nikitin and Reznikov (1971) and experiment.

Total cross sections for Na(3 2P1/2→3 2P3/2) + rare gas collisions

Quantum-mechanical calculations that use the recent pseudopotentials of Pascale and Vandeplanque were employed to obtain the 3 2P1/2→ 3 2P3/2 fine structure transition cross sections for Na+He, Ne, Ar, Kr, and Xe collisions. The collision energy range investigated was from threshold (0.00213 eV) to 0.5 eV. The cross sections are found to rise rapidly from threshold to a plateau, with the Na+Ar, Kr, Xe systems also exhibiting a large secondary maximum at approximately 0.1 eV. Regular undulatory structure was observed superimposed on all the cross sections except for the Na+Ne system, while resonances caused by quasibound states were found to be most prominent on the Na+Ar system. Thermally averaged cross sections were calculated from 100 to 1000 °K and are found to be in reasonable accord with experiment.

Fine structure transition cross sections for several alkali + rare gas systems

The energy dependence, E c.m. </ 0.2 eV, of the inelastic total cross sections for the 2P 1 2 → 2P 3 2 fine structure transition of the lowest excited states of the alkali atoms are calculated for the following systems: Na, K, Rb + He, Ne, Ar and Cs + He. Encouraging agreement between theory and experiment is obtained.

Broadening of theDLines and the Relaxation of the Resonance Levels of Sodium Due to Collisions with Helium

Calculated potentials for the NaHe molecule are used to obtain collision-induced widths and shifts for the sodium D lines together with cross sections for fine-structure transitions and the relaxation of the multipole polarizations of the resonance levels. The atomic collision is treated in an adiabatic approximation in which the colliding atoms form a molecular system which rotates during the collision. We find the resonance lines to be broadened equally and to be approximately 70% wider, and with associated shifts of an order of magnitude smaller, than expected on the basis of van der Waals forces. The dependence of the cross sections for relaxation of the multipole polarizations of the resonance levels on the molecular-coupling conditions and the rotation of the system during collision is discussed and indicates a limitation of the sum rule for these cross sections.