3Πg State Research Articles

Integral cross sections for the direct excitation of the A 3Σu+, B 3Πg, W 3Δu, B′ 3Σu−, a′ 1Σu−, a 1Πg, w 1Δu, and C 3Πu electronic states in N2 by electron impact

Integral cross sections for electron impact excitation out of the ground state (X 1Σg+) to the A 3Σu+, B 3Πg, W 3Δu, B′ 3Σu−, a′ 1Σu−, a 1Πg, w 1Δu, and C 3Πu states in N2 are reported at incident energies ranging between 10 and 100 eV. These data have been derived by integrating differential cross sections previously reported by this group. New differential cross section measurements for the a 1Πg state at 200 eV are also presented to extend the range of the reported integral cross sections for this state, which is responsible for the emissions of the Lyman‐Birge‐Hopfield band system (a 1Πg → X 1Σg+). The present results are compared and critically evaluated against existing cross sections. In general, the present cross sections are smaller than previous results at low impact energies from threshold through the excitation function peak regions. These lower cross sections have potentially significant implications on our understanding of UV emissions in the atmospheres of Earth and Titan.

Metastable helium cluster He 4 *

The existence of a metastable cluster He 4 * with total spin S = 2 is predicted. The cluster consists of two covalently bound excited spin-polarized triplet He 2 * molecules and is rectangular in shape. The electron wavefunctions, the dependence of the energy He 4 * system on the distance between the He 2 * triplet molecules, the atomic spacing, the frequency spectrum of natural oscillations of the cluster, and other characteristics are calculated from first principles. It is shown that the metastable state is formed if one of the excited He 2 * molecules is in the 3Σ u + state, while the other is in the 3Πg state. The radiation lifetime τ of the metastable cluster He 4 * is calculated; it is found to range from 100 to 200 s, which is much longer than the lifetime τ ≈ 20 s of the triplet molecule He 2 * (3Σ u + ). The height U ≈ 0.5 eV of the potential barrier preventing the departure from the local energy minimum is determined. The energy E acc ≈ 9 eV/atom accumulated in the He 4 * cluster is calculated; this energy considerably exceeds the energy of known chemical energy carriers. It is shown that the accumulated energy is released virtually completely during decomposition of the He 4 * cluster into individual helium atoms. This means that helium clusters are a promising material with a high accumulated energy density (HEDM).

Theoretical study of the K-photoabsorption cross section of carbon in the acetylene molecule

The magnitudes and the shape of the K-absorption spectrum of carbon in the C2H2 molecule are found by the one-center method. Within this method, one-electron wave functions of occupied and unoccupied states are calculated in the approximation of nonorthogonal orbitals. The processes of single and double excitation/ionization with additional excitation of an electron from the external 1πu shell to the 1πg state are taken into account. The mechanism of formation of a fine structure in the photoionization spectrum is refined. The calculated cross sections are compared with experimental and theoretical results obtained by other researchers. The results of calculation of the oscillator strengths of single photoexcitation are predictive.

Ab Initio calculations and vibrational energy level fits for the lower singlet potential-energy surfaces of C3

Ab initio multireference configuration interaction potential energy surfaces are computed for the eight lowest singlet surfaces of C(3). These reveal several important features, including several conical intersections in linear, nonlinear, and equilateral triangle geometries. These intersections are important because, particularly for the excited A (1)Pi(u) state, reasonable ab initio results could only be obtained by including nearby, near degenerate, (1)Sigma(u) (-) and (1)Delta(u) states that cross the A (1)Pi(u) state around 4500 cm(-1) above the equilibrium geometry, and a (1)Pi(g) state whose potential in turn crosses the other states about 2000 cm(-1) further up. These states are probably responsible for the complexity of the shorter wavelength UV absorption spectrum of C(3). The computed potential energy surface for the ground, X (1)Sigma(g) (+), state and for the lowest two excited singlet surfaces (which both correlate with the A (1)Pi(u) state in a collinear geometry) are fitted to analytic functional forms. Vibrational energy levels are calculated for both states, taking account of the Renner-Teller coupling in the excited A (1)Pi(u) state. The potential parameters for both states are then least-squares fitted to experimental data. The ground-state fit covers a range of approximately 8500 cm(-1) above the lowest level, and reproduces 100 observed vibrational levels with an average error of 2.8 cm(-1). The A (1)Pi(u) state surfaces cover a range of 3250 cm(-1) above the zero-point level, and reproduce the 44 observed levels in this range with an average error of 2.8 cm(-1).

Extremely narrow peaks in predissociation of sodium dimer due to rovibronic coupling.

In sodium dimer the 2 (3)Pi(g), 3 (3)Pi(g), and 4 (3)Sigma(g) (+) electronic states are coupled; the coupling of the two (3)Pi(g) states is due to vibrational motion while the nonadiabatic interaction between the (3)Sigma(g) (+) and the (3)Pi(g) states-in particular, the 3 (3)Pi(g) state-is mediated by rotational interaction. The resulting vibronic problem is studied in some detail. The bound vibrational states of the 3 (3)Pi(g) and 4 (3)Pi(g) (+) states lie in the dissociation continuum of the 2 (3)Pi(g) state and become resonances due to the prevailing nonadiabatic coupling. The resonances are calculated using the complex scaling method and the available ab initio adiabatic potential energy curves. It is demonstrated that the resonances associated with rotational nonadiabatic coupling are narrower by several orders of magnitude than those that emerge from the vibrational nonadiabatic coupling. The predissociation cross section is computed and compared with experiment.

Multipartitioning many-body perturbation theory calculations on temporary anions: applications to N−2 and CO−

The multipartitioning form of the second-order many-body perturbation theory for state-selective effective Hamiltonians is adapted to stabilization calculations of temporary molecular anionic states. We restrict our attention to the simplest case of a system composed of a closed-shell-like molecule and an electron. Pilot applications to the description of the 2Πg state of the nitrogen molecular anion and the 2Π state of CO− are reported.

Electronic Spectrum of the Gallium Dimer

A study of the electronic spectrum of the gallium dimer in the 33 600-36 800 cm - 1 spectral range is presented. The dimer was prepared in a pulsed, free-jet supersonic beam and detected by laser fluorescence excitation and depletion spectroscopy. All observed excited vibronic levels predissociate, and the transitions were detected by observation of Ga 5s → 4p atomic emission. Four excited-state progressions were observed, and it was possible to assign the excited-state vibrational quantum numbers on the basis of observed isotope shifts for two of the four progressions. Through comparison of the results with available quantum chemical calculations, these two progressions were assigned as electronic transitions to the 3 3 Πg and 2 1 Πg states from the ground X 3 Π u state. A Franck-Condon analysis was performed to determine the equilibrium internuclear separation of the 3 3 Π g state. An upper limit for the Ga 2 dissociation energy, D e < 8891 cm - 1 , was derived. This bound is consistent with previous experimental and computational estimates of the dissociation energy.

Semiempirical Characterization of Homonuclear Diatomic Ions: 6. Group VI and VII Anions

Sixteen Herschbach ionic Morse potential energy curves (HIMPEC) were classified using molecular ion formation M or dissociation D in a vertical transition. Two activation energies for thermal electron attachment to Cl2, Br2, and I2 are reported from a reanalysis of electron-capture detector data. The HIMPEC for the diatomic halogens and oxygen are optimized by including new experimental data. All of the halogen curves are defined by at least three data points. Two new curves for the 2Πg(1/2) states of Br2(−) and I2(−) are constructed using a lower experimental dissociation energy. New electron-capture detector data for O2 confirm multiple activation energies and electron affinities, Ea. The twelve M and twelve D curves for the 24 predicted anionic states of O2 are calculated using Ea, vertical electron affinities, activation energies, frequencies, and estimated dissociation energies. Two curves are calculated from experimental data for anions of S2, Se2, and Te2.

Time-resolved Fourier transform spectroscopy applied to collisional relaxation study of the B 3Πgv = 0 level of N2 in a pulsed electrical discharge

Time-resolved Fourier transform spectroscopy, with temporal and spectral resolutions respectively at best 1.6 μs and 0.014 cm−1 (Doppler-limited), is applied as a new diagnostic tool to the characterization of nitrogen plasma. A spectral range extending from 0.93 to 1.85 μm is recorded at once. The rotational lines of the B 3Πg→A 3Σu+, Δv = 0,−1,−2,−3 vibronic sequences are fully resolved. Thermodynamical plasma parameters are obtained from line intensity and width analysis. The relaxation of the B 3Πg state of N2 in a pulsed electrical discharge is observed under various pressures and pulse repetition rates. Evolutions of the low-lying vibrational levels B 3Πg,v = 0,1,2 during the early afterglow (post-discharge time period ⩽150 μs) are analysed. A simplified kinetic model based on the strong couplings between B 3Πg and A 3Σu+ states and between B 3Πg and W 3Δu states is adopted. It is found appropriate for the interpretation of the spectra within a restricted range (pressure 16–53 Pa (0.12–0.40 Torr), repetition rate 50–200 Hz) of the experimental conditions. Collisional rate constants coupling the B v = 0 level to the levels A v = 7 and W v = 0 are estimated to be kBW = 9×10−12 cm3 s−1 and kBA = 3×10−12 cm3 s−1, in accordance with existing results.

Bending vibrational wave numbers in the ã 3Πu and b̃ 3Πg states of C3

The spectrum of the 050 Σu−3–010 Σg−3 band of the b̃ 3Πg–ã 3Πu electronic transition of C3 is reported. The data, when considered with the previously observed 010 Σu−3–010 Σg−3 band, measure the absolute interval between the 050 Σu−3 and 010 Σu−3 levels of the b̃ 3Πg state. This interval, and the Renner parameters for ã 3Πu and b̃ 3Πg [D. W. Tokaryk and S. Civiš, J. Chem. Phys. 103, 3928 (1995)], allow us to greatly improve estimates of the bending vibrational wave numbers in these electronic states. The values (542.3 cm−1 for ã 3Πu, and 392.4 cm−1 for b̃ 3Πg) predict the origins of all previously reported bands of b̃ 3Πg –ã 3Πu involving bending to within 13 cm−1.

Lithium Hydrides and Lithium Dimers: Sub‐Doppler Spectroscopy and Dynamics

AbstractDeep insights into molecular structures and dynamics were obtained for lithium dimers and lithium hydrides by sub‐Doppler spectroscopy combining molecular beams and cw tunable laser beams. For 7Li7Li species, accurate spectroscopic studies of the B 1Πu‐X 1Σg+ system were carried out, with the measurement of hundreds of wave numbers and with the determination of dissociation rates due to tunneling through the potential barrier of the B 1πu state. They led to the full description of the B state potential, including its barrier. For 6Li7Li species, weak but non‐negligible dissociation rates in the B 1Πu state were observed, measured and interpreted assuming that an electronic coupling between the B 1Πu and 1 1Πg states takes place through an ungerade‐gerade symmetry breaking. For LiH species, the A 1Σ+‐X 1 Σ+ system was revisited for both isotopomers. For this molecule, dynamical effects are predicted in highly‐excited Rydberg states, that could be studied by use of similar sub‐Doppler techniques.

Hyperfine structure of the 13Δg, 2 3Πg, and 33Σg+ states of Li6Li7

The hyperfine splittings of the 1 3Δg, 2 3Πg, and 3 3Σg+ states of Li6Li7 have been resolved by sub-Doppler, continuous wave, perturbation facilitated optical–optical double resonance excitation spectroscopy through newly identified A 1Σu+ (vA′=5, J′=24)∼b 3Πu (vb′=12, N′=23, J′=24) mixed window levels. The 3 3Σg+ and 1 3Δg states follow the case bβS coupling scheme. The Fermi contact interaction between the Li7 nucleus and the electron spin is the dominant term for the observed hyperfine splittings. The Fermi contact constants for the Li7 nucleus in the Li6Li7 molecule have been determined to be 110 MHz for the 3 3Σg+ state and 107 MHz for the 1 3Δg state. The 2 3Πg state has doubly excited character and its hyperfine coupling is different from that of the 3 3Σg+ and 1 3Δg states. The Fermi contact constants of triplet Rydberg states of Li6Li7 versus Li27 are discussed, and insights into the physical basis for case bβS coupling are illustrated.

NON-FRANCK–CONDON EFFECTS IN THE PHOTOIONIZATION OF N2 TO THE ${\rm N}_2^+$ A 2Πu STATE AND OF O2 TO THE ${\rm O}_2^+$ X 2Πg STATE IN THE 19–34 eV PHOTON ENERGY REGION

Photoionization to the [Formula: see text] A 2Πu state and to the [Formula: see text] X 2Πg state is studied using photoelectron spectroscopy. The experimental vibrational branching ratios are obtained for the first time in the 19–34 eV region for the v′ = 0–3 levels, for both molecules. Ab initio many-body perturbation theory is used to calculate branching ratios for ionization to the [Formula: see text] A 2Πu state and branching ratios, vibrationally resolved partial cross sections and total cross section for ionization to the [Formula: see text] X 2Πg state. The Franck–Condon breakdown observed in the photoionization of the N 2 1πu electron is mainly explained by autoionization from Rydberg and valence states of N 2, whereas photoionization of the O 2πg electron is not fully explained either by channel coupling effects or by autoionization from known Rydberg series and valence states.

Spectroscopy and Predissociation of Acetylene in the np Gerade Rydberg States

The np gerade Rydberg states of acetylene were studied with various spectroscopic techniques to measure one-color resonant multiphoton ionization (REMPI) spectra, two-color REMPI mass spectra, fluorescence spectra, and fluorescence excitation spectra in the two-photon energy region of 72 000−92 000 cm-1. The rotational analysis was successfully performed for one of the upper levels, which was assigned to the 4p 1Δg Rydberg state. All of the gerade Rydberg states prepared under the two-photon resonance conditions were found to be predissociative, and the two-photon preparation was accompanied by the fluorescence of the C2 d 3Πg → a 3Πu Swan system. In the fluorescence excitation spectra measured by monitoring the C2 Swan system, higher members of the np 1 and 1Δg Rydberg series (n ≥ 4) were observed and assigned for the first time. The predissociative lifetimes of the np gerade Rydberg states are estimated from the spectral bandwidths. The mechanisms of the predissociation of acetylene in the Rydberg states and the formation of C2 in the d 3Πg state are discussed.

Reaction pathways in remote plasma nitridation of ultrathin SiO2 films

Low-temperature nitridation of 3 nm SiO2 films using He/N2 and N2 remote radio frequency (rf) plasmas was investigated. On-line Auger electron spectroscopy and angle-resolved x-ray photoelectron spectroscopy (ARXPS) were employed to determine the concentration, spatial distribution, and local chemical bonding of nitrogen in the resultant films. Experiments were performed using a substrate temperature of 300 °C and 30 W rf power. Nitridation using an upstream He/N2 remote plasma at 0.1 Torr incorporates nitrogen at the top surface of the SiO2 film. In contrast, a lower concentration of nitrogen distributed throughout the film is obtained when the process pressure is increased to 0.3 Torr. ARXPS indicates a N–Si3 local bonding configuration, irrespective of the spatial distribution of N atoms. Slightly more nitrogen is incorporated using a downstream He/N2 plasma at each process pressure. By comparison, nitridation of SiO2 films using a N2 remote plasma at 0.1 Torr is very slow. Optical emission spectroscopy indicates that He dilution enhances the generation of N2+(B 2Σu+) species by altering the plasma electron energy distribution and by providing an additional kinetic pathway (Penning ionization). Changing the He/N2 remote plasma configuration from upstream to downstream (at 0.1 and 0.3 Torr) also enhances N2+(B 2Σu+) generation. For upstream He/N2 remote plasmas, the intensity of N2 first positive emission from N2(B 3Πg) states increases with pressure, whereas the N2+ first negative emission from N2+(B 2Σu+) states decreases. We infer from these observations that N2+ species are primarily responsible for top surface nitridation at 0.1 Torr, and that neutral species [N2(A 3Σu+) metastables and N atoms] are associated with sub-surface nitrogen incorporation.

The 4pπ 3Πg–a 3Σu+ system in Ne220 and Ne222

Excitation spectra for the 4pπ 3Πg–a 3Σu+ system in Ne220 and Ne222 have been used to characterize the v=0 through v=3 levels in both electronic states. This is the first time levels with v&amp;gt;1 have been characterized experimentally in either dimer. Rotational analyses lead to Be- and αe-values of 0.5638 cm−1 and −0.9000×10−2 cm−1 and of 0.5113 cm−1 and −0.6651×10−2 cm−1 for the a 3Σu+ states in Ne220 and Ne222, respectively. The Be- and αe-values are, respectively, 0.5716 cm−1 and −0.6429×10−2 cm−1 (20Ne2) and 0.5201 cm−1 and −0.4172×10−2 cm−1 (22Ne2) for the 4pπ 3Πg state. The vibrational parameters ωe, xωe are found to be 556.2, 10.2 cm−1, and 593.2, 7.5 cm−1 for the a 3Σu+ state and 4pπ 3Πg state, respectively, in Ne220 with corresponding values of 529.5, 9.75 cm−1, and 567, 7.5 cm−1 in Ne222. The observed vibrational level differences [ΔG(v+1/2)-values] for the 4pπ 3Πg state are within 0.5% of analogous spacings for the ground electronic state (X 2Σu+) of Ne2+ reported by Kim et al. [Phys. Rev. Lett. 68, 1311 (1992)].

Spectroscopy study and modelling of an afterglow created bya low-pressure pulsed discharge in N2-CH4

Time-resolved emission spectroscopy is used to investigate therelaxation of N2(B 3Πg), N2(C 3Πu) and CN(B 2Σ)states in the time afterglow of a low-pressure N2-CH4 pulsed discharge,with time duration of 1 ms and in the range [CH4]/[N2] = 0-2%. Thedecays in the relative measured concentrations in the afterglow areinterpreted by modelling the relaxation of a set of time-varying kineticmaster equations for the various species produced in the discharge, withconditions at the beginning of the afterglow calculated from a time-dependentkinetic model for the pulsed discharge. It is observed that theN2(B 3Πg) state is populated in the afterglow mainly via thereaction N2(A 3Σu+) + N2(X 1Σg+, 5⩽v⩽14)→N2(B 3Πg) + N2(X 1Σg+, v = 0), sincethe pulse duration is large enough to populate theN2(X 1Σg+, v) levels at its end and, to a smaller extent, alsoby pooling of N2(A 3Σu+). The N2(C 3Πu) state ispopulated by pooling of N2(A 3Σu+) only, whereas theCN(B 2Σ) state is created through reactions involving eitherN2(A 3Σu+) states or N2(X 1Σg+, v) levels incollisions with CN(X 2Σ+) molecules. The agreement between measuredand calculated concentrations of N2(B 3Πg) and N2(C 3Πu)states is very good in pure N2 and it may be considered satisfactory in thecase of N2-CH4 mixtures, and for the CN(B 2Σ) state theagreement between theory and experiment is also reasonably good.

In situ determination of absolute number densities of nitrogen molecule triplet states in an rf-plasma sheath

A laser induced fluorescence technique (LIF) in combination with optical emission spectroscopy (OES) and Rayleigh scattering (RS) was applied to investigate absolute number densities of the population of the three nitrogen triplet states C 3Πu, B 3Πg, and the metastable A 3Σu+ in an asymmetric low pressure rf discharge. Primary targets of this investigation were the three lowest vibrational levels (v=0,1,2) of each triplet state and additionally v=8 of A 3Σu+ which can be populated very efficiently in the plasma sheath. Calibration of LIF intensities to absolute densities of A 3Σu+ and B 3Πg has been realized by comparison with the signal of the RS experiment done in pure nitrogen gas. Calibration of C 3Πu which we could not detect by LIF but rather only by OES was achieved after comparing OES and LIF signals of the B 3Πg state. Excitation energies of the analyzed states range from 6 up to 11.5 eV and the measured number densities differ by about seven orders of magnitude from as much as 1012 cm−3 down to almost 105 cm−3. In addition to the interpretation of the results this article describes the used calibration methods which are partly based on a suggestion made by P. Bogen (Proceedings of the XVI International Conference on Phenomena in Ionized Gases, Invited Papers, edited by W. Bötticher, H. Wenk, and E. Schultz-Gulde, Düsseldorf, 1983, pp. 164–173).

Tuning the scattering length on the ground triplet state of Cs2

Two schemes for tuning the scattering length on the ground triplet state of Cs2 are developed. The absolute value of the triplet scattering length of 133Cs2 is determined from the experimental data [A. Fioretti, D. Comparat, C. Drag, C. Amiot, O. Dulieu, F. Masnou-Seeuws, and P. Pillet, Eur. Phys. J. D 5, 389 (1999)], we demonstrate that the large scattering length can be made small and positive by coupling the 3Σu+(6S+6S) potential to the 3Πg state by strong off-resonant radiation. A weaker laser field coupling the 3Σu+(6S+6S) continuum to the lowest bound level of the excited 3Σg+(6S+6P) state also leads to a small positive scattering length. The scattering length of the 135Cs isotope is found to be positive. The method used solves the Schrödinger equation for two electronic states coupled by an electromagnetic field with no approximations employed. The scattering length is determined from the calculated continuum wave functions at low energies.

Multichannel quantum defect theory treatment of triplet gerade and ungerade &lt;i&gt;d&lt;/i&gt;-symmetry levelsof H&lt;sub&gt;2&lt;/sub&gt; and its isotopomers

This work presents a systematic multichannel quantum defect theory (MQDT) analysis of the triplet d-symmetry levels of the hydrogen molecule. First, a new compilation of the best available experimental term values for these levels was prepared. Second, R-dependent quantum defect matrices for the 3Πu, 3Πg, and 3Δg states of H2 were obtained from ab initio potential-energy curves and used in an ab initio MQDT calculation of all known triplet d-symmetry rovibronic levels of H2, HD, and D2. For a few of these levels previous ab initio calculations have been reported. The agreement currently obtained is generally significantly better than that in previous work. Finally, the quantum defect matrices are used to calculate the electronic transition moments 3Πu 3Πg, 3Δg as functions of energy and internuclear distance, R, for application in a companion article. PACS Nos: 31.15Ar, 33.20Wr, 34.10+x, 34.80Kw