C1Πu States Research Articles

The C[formula omitted] state of potassium dimer revisited: An extensive study by polarisation labelling spectroscopy method

The polarisation labelling spectroscopy technique was applied to study the C1Πu← X1Σg+ band system in potassium dimer. About 1100 new rotationally resolved molecular lines were measured in the 22100–24100 cm−1 spectral range. Perturbations of the lowest vibrational levels of the C state were localised and their origin discussed. A set of Dunham coefficients was deduced to fit the unperturbed levels of the C1Πu state with 0≤v≤38 and 18≤J≤101 and the potential energy curve of the state was constructed.

Inferring gas temperature from N2 emission via rotational distribution of the N2 B3Πg and C3Πu states

Optical emission spectroscopy (OES) is frequently used to measure the rotational temperature of a plasma. The technique is relatively simple to implement and non-intrusive. However, in the visible and ultraviolet spectral regions, it relies on emission from excited vibronic states whose rotational and vibrational temperatures might not be equilibrated with the bulk temperature of the plasma. Oftentimes, rapid equilibration between the rotational and translational modes occurs so that these temperatures are equilibrated. However, many cases exist where these modes are not equilibrated. In this work, we have developed a simple model that can be used as an experimental tool when using OES. An updated criterion for ensuring rotational-translational equilibrium is proposed. In cases where nonequilibrium is expected, the model may be used to provide an estimate of the bulk gas temperature. An illustrative example is given where we use this model to analyze previous measurements made in a nonequilibrium discharge.

Impact of vibrationally and electronically excited H2 on the molecular assisted recombination rate in detached plasma regimes

The vibrational redistribution of H2 molecules via the B1Σu+ and C1Πu states are included in the determination of molecular assisted recombination (MAR) rates and are found to have negligible impact in detached plasma regimes. In high recycling and detached divertor plasma conditions, MAR occurs through the higher levels (v≥4) of vibrationally excited H2 which are primarily populated through direct electron impact excitation or the electronic excitation of H2 molecules and the subsequent radiative decay to another vibrational state. We use the collisional-radiative model CRUMPET to evaluate MAR rate coefficients with electronic transitions included, which are applied to detached plasma parameters found in the linear plasma device Magnum-PSI.

Ab initio study of the second positive system of N2 at high temperature

The potential energy-curves (PECs) and electronic transition dipole moment-curves (TDMCs) of the B3Пg and C3Πu states of N2 have been investigated by employing the multi-reference configuration interaction (MRCI) approach with the augmented correlation consistent polarized valence quintuple-zeta (aV5Z) set and active spaces 31103110. The calculated PEs of the two states (B3Πg, C3Πu) agree well with the Rydberg-Klein-Rees (RKR) potential energy, and the calculated TDMCs are more precise than those reported in previous literature studies. Calculation of the Einstein A coefficients, spectral parameters and wavelengths by using the exact potential energy and dipole moment are consistent with the recent experimental and literature values. For the first time, the intensities of eight bands of the second positive system (2PS) of N2 are obtained from the summation of their respective absorption spectral line intensities. The absorption spectral intensities of the 0–0, 0–1, 2–0, 2–1, 3–0, 3–1, and 4–0, 4–1 bands were computed in a wide temperature range, especially at high temperatures. For example, the 0–0 band intensities are 4.58 × 10−15 cm−1/(molecule cm−2), 2.50 × 10−15 cm−1/(molecule cm−2) and 9.47 × 10−16 cm−1/(molecule cm−2) at 300 K, 3000 K, and 6000 K, respectively. These results of spectral intensities can be utilized to predict spectral characteristics, and also definited as a theoretical reference value for high temperature astrophysics.

Dynamics of Radiation from Nanosecond Surface Sliding Discharge in Airflow with Shock Waves

Spatio-temporal distributions of radiation from pulsed sliding surface discharge of ~300-ns duration in quiescent air at pressures within 2–200 Torr and in the presence of shock waves in supersonic flow with Mach numbers M = 2.8–3.3 have been experimentally studied. The dynamics of radiation from discharge was analyzed based on processing of the streak images and nine-frame images of discharge glow intensity, emission spectra, and discharge current kinetics. It is established that variation of the radiation intensity from discharge interacting with shock waves is correlated with a model temporal dependence of the population of C3Πu states of nitrogen during shock compression of the discharge plasma region.

Population inversion of molecular nitrogen in an Ar: N2 mixture by selective resonance-enhanced multiphoton ionization

Resonance-enhanced multiphoton ionization (REMPI) is shown to offer an attractive strategy for population inversion of molecular nitrogen in an Ar: N2 gas mixture. We present a detailed analysis of the key processes leading to a population inversion of molecular nitrogen in a REMPI-pumped Ar: N2 gas mixture, including a (3 + 1) REMPI of argon atoms, conversion of the REMPI-generated atomic argon ions into molecular ions, and generation of long-lived metastable excited-state argon atoms through dissociative recombination, populating the C3πu states of molecular nitrogen. Population inversion achieved for the second-positive-band laser transitions of molecular nitrogen enables stimulated emission of ultraviolet radiation at 337 nm. A high selectivity of the REMPI process helps to radically reduce the depletion of the working medium through the ionization of N2, providing a pump mechanism that is ideally suited for the creation of a new type of a highly efficient nitrogen laser.

Kinetic processes initiated by a nanosecond high-current discharge in hot air

Results from numerical investigations of kinetic processes initiated by a pulsed nanosecond discharge in hot (T0 ≥ 1000 K) air at atmospheric pressure are presented. The calculated results on the dynamics of the electron density, the population of the N2(B3Πg) and N2(C3Πu) states, and the atomic oxygen density in the axial discharge region agree with experiment. The method for determining the gas temperature by measuring the rotational structure of the transitions N2(C3Πu, ν) → N2(B3Πg, ν′) of the 2+ nitrogen system is analyzed. It is shown that, in relatively weak reduced electric fields typical of secondary discharge pulses, the electron impact excitation of the N2(C3Πu) state from the ground state N2(X1Σg+) can be accompanied by its additional step population from the N2(B3Πg), N2(a′Σu−), and other electronic states. This effect substantially influences the rotational distribution of nitrogen molecules in the N2(C3Πu, ν) state; moreover, the temperature determined from this distribution can be substantially higher than the true gas temperature.

Spectrum of sprite halos

[1] Spectra of sprite halos in the spectral ranges 200–500 nm and 640–1065 nm are calculated for different spectral resolutions (between 2 nm and 10 nm), rotational temperatures (220 K and 1000 K) and observation altitudes corresponding to mountain (3 km and 4.3 km), airplane (14 km), balloon (35 km) and space observation platforms. We have calculated the non-equilibrium vibrational distribution functions (VDF) of different excited electronic states of molecular nitrogen (N2) associated to sprite halo optical emissions in the ultraviolet (UV), due to the N2 Lyman-Birge-Hopfield (LBH) and Vegard-Kaplan (VK) band systems, and near UV, visible and near infrared (NIR) due to the first (1PG) and second positive (2PG) bands of N2. Comparison of synthetic sprite halo spectra with the single sprite halo spectrum existing to date shows reasonable agreement after the observed sprite halo spectra was corrected for instrument sensitivity response. Calculated VDFs of the N2(B3Πg) and N2(C3Πu) states of sprite halos show that the blue and NIR emissions produced through strong N2-1PG (B3Πg → A3Σu+) and N2-2PG (C3Πu → B3Πg) transitions are generally similar to those of known sprite spectral emission patterns, but differences may be observable at some vibrational levels. The calculated sprite halo spectra can be used as a predictive tool for the expected spectral emissions of sprite halos in different possible scenarios.

Calculating the molecular constants for the B 1Π u , C 1Π u , (1)1Π g , and (2) Σ g + electronic states of the rubidium dimer

The vibrational, rotational, and centrifugal constants are calculated for the B1Πu, C1Πu, (1) 1Πg, and (2) electronic states of a 85Rb2 molecule. The calculations are based on the semi-empirical potential curves obtained in this work. The results from calculating the molecular constants are compared with experimental data. The Franck-Condon factors and Rv′v″ centroids are calculated for the electronic transitions B1Πu-X1Σg+, C1Πu-X1Σg+, C1Πu-(1) 1Πg, and C1Πu-(2) 1Σg+.

The lowest order relativistic corrections for the hydrogen molecule

AbstractWe have calculated the lowest order relativistic corrections for the X 1Σ, B1Σ, a3Σ, b3Σ, I1Πg, C1Πu, i3Πg, c3Πu, J1Δg, and j3Δg states of the hydrogen molecule using variational Monte Carlo methods and compact, explicitly correlated trial wavefunctions. Our values are in good agreement with earlier calculations on the X1Σ and B1Σ states. For the other states, our work provides the first estimate of these properties. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Sigma, pi, and delta wavefunction forms for the hydrogen molecule

Using variational Monte Carlo methods, we examine simple, explicitly-correlated trial wavefunction forms for the X1Σ, B1Σ, a3Σ, b3Σ, I1Πg, C1Πu, i3Πg, c3Πu, J1Δg, and j3Δg states of the hydrogen molecule. The energies produced by our best wavefunctions are slightly above the best values in the literature. When we combine our trial wavefunction forms with the generalized Feynman-Kac path integral method, our results are in excellent agreement with the best nonrelativistic values for these systems except for the I1Πg state. Our best energy for this state, −0.65951554(6), is lower by several microhartrees than that obtained by Wolniewicz [J Mol Spectrosc 1995, 169, 329]. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Quantum non-adiabatic study of the quasi-molecular satellites of the Lyman α line perturbed by H

In the so-called one-perturber approach, free–bound and free–free transitions contribute to absorption in the wings of atomic lines perturbed by collisions. Perturbation theory for the interaction of light with a binary collisional complex is applied to the calculation of the absorption coefficient. The initial and final wavefunctions of the binary complex are quite general, taking into account non-adiabatic effects between the adiabatic electronic states. Application to the calculation of the Lyman α quasi-molecular satellite due to H–H collisions is presented. We compare the results that include rotational coupling between the upper B1Σ+u and C1Πu states with the results obtained in an adiabatic approach. It is shown that no significant difference between these results is obtained so that the total absorption coefficient may be calculated by summing up the contributions of the different electronic transitions calculated in the Born–Oppenheimer approximation. As expected, discrepancies between quantal and semi-classical results appear at low temperatures, which are slowly reduced as the temperature increases.

Transition Moments between w3Πg State and the First Three 3Σu and 3Πu States of the Hydrogen Molecule

An explicitly correlated variational electronic wave function is obtained for the w3Πg state of the hydrogen molecule and the Born−Oppenheimer potential energy curve as well as adiabatic corrections are given for internuclear distances 1 ≤ R ≤ 50 au. The electronic dipole transition moments between w3Πg and b3Σu, e3Σu, f3Σu, c3Πu, d3Πu, and k3Πu states for 0.6 ≤ R ≤ 20 au are computed. These are the first accurate ab initio results for the above transitions. Also, the adiabatic vibrational levels are presented for N = 1.

Electronic excitation of the a3 ∑ g+ and c3Πu states of H 2 by electron impact using the method of continued fractions

In the present work we use a multichannel extension of the method of continued fractions (MCF) to study the low-energy electron-impact excitation in linear molecules at the two-state close-coupling level. In particular we have calculated the excitation cross sections for the X 1 ∑ g + → a 3 ∑ g + and X 1 ∑ g + → c 3 Π u transitions in H 2 for incident energies from near threshold to 30 eV. In our work, in contrast with the early two-state studies of Chung and Lin, no orthogonality constraint between the bound and continuum orbitals is imposed and the one-electron exchange terms are explicitly considered. In general our calculated cross sections are in good agreement with the results of the two-state Schwinger multichannel method. Our results for the a 3 ∑ g + are also in quite good agreement with the available experimental data. However, the cross sections for excitation of the c 3 Π u state differ significantly from the measured values at 20 and 30 eV, where they are available. The disagreement is attributed to the multichannel effects, not accounted for in this study.

Sub-Doppler laser spectroscopy of H2 and D2 in the range 91–98 nm

The absorption spectra of hydrogen and deuterium have been measured in the range 91–98 nm. A narrowband extreme ultraviolet laser source is employed in combination with a molecular beam, allowing for sub-Doppler resolution and yielding linewidths of 0.23 cm−1. Transition frequencies of 291 lines of the Lyman and Werner bands are determined with an average absolute accuracy of 0.03 cm−1. The data are analyzed in a semi-empirical perturbation model, involving heterogeneous couplings between nearby lying levels of B1Σu+ and C1Πu states. This model is found to be accurate on the level of accuracy of the data obtained.

Non‐adiabatic effects on resonance‐enhanced Raman scattering in H2

AbstractResonance‐enhanced Raman scattering (RERS) from the ground X1Σg+(νg = 0, Jg) state of H2 via the excited intermediate C1Πu(ν = 0/1/2/3, Ji) state coupled non‐adiabatically with the B1Σu+(νiB = 8/10/12/14, Ji) state was studied theoretically, applying second‐order perturbation theory. The excitation and Raman spectra for the pure rotational, fundamental and higher overtones are presented. Effects of non‐adiabatic coupling on the excitation profiles, scattered intensities and depolarization ratios were investigated. The intensities of excitation spectra and Raman lines for O‐, Q‐ and S‐branches were calculated using thermal Boltzmann factors for vibrational–rotational distribution at room temperature (300 K). The RERS cross‐sections with adiabatic and non‐adiabatic corrections are reported together with Born–Oppenheimer (BO) results where available, for comparison. The calculated RERS cross‐sections including non‐adiabatic effects were found to vary significantly from adiabatic or BO results.

Experimental observation of the (3)Σ1u+ state of Na_2 by deperturbation of the CΠ1_u−XΣ1g+ system

Doppler-free UV-excitation spectra, obtained by modulated population spectroscopy, reveal perturbations of a few hundred e levels of the C1Πu state in Na2. We ascribe the perturbations to the (3)Σ1u+ state. After deperturbation, information about 15 vibrational levels of the (3)Σ1u+ state was extracted. This information was used to deduce a set of Dunham coefficients and the Rydberg–Klein–Rees potential for the state. The experimental results show that the potential of the (3)Σ1u+ state is one with a double minimum or an inflection. In addition, it has a flattened bottom with Te = 31 247.82 cm−1. As a consequence, the vibrational spacing at first increases and then decreases as a function of υ. Comparison of the experimental results and theoretical calculations yielded fairly good agreement.

Doppler-free ultraviolet excitation spectra of C ^1II_u–X^1Σ^ + _g in Na_2 by modulated population spectroscopy

The C1Πu state of Na2 has been studied in detail by cw UV Doppler-free excitation spectra from its ground state, simplified by modulated population spectroscopy. 270 levels of e parity and 180 levels of f parity with 11 ≤ υ ≤ 35 and 8 ≤ J ≤ 70 were measured with high resolution. The observations reveal that many of the e levels with 15 ≤ υ ≤ 24 are perturbed. A likely candidate for the perturbing state is the (3)Σ1u+ state. A set of Dunham coefficients was deduced to fit the spectroscopic data after deperturbation and used to construct the Rydberg–Klein–Rees potential for the C1Πu state. In addition, Λ-type doubling of the state was observed directly.

Preferential population of magnetic sublevels of photodissociated atoms. Photodissociation of alkali-metal dimers and the effect of magnetic field

By applying an external magnetic field, we have determined the population of the magnetic sublevels of photodissociated atoms from the intensities of atomic fluorescence lines split by the Zeeman effect. A preferential population of the magnetic sublevels of the atomic fragment Na(3 2P3/2), which arises from the direct photodissociation through the D1Π(continuum) state of the NaK molecule, has been observed. The results are explained by assuming the separability of electronic and nuclear motion during the dissociation. The observed results could be rationalized by the sum of the photodissociation amplitudes caused by excitation of the P, Q and R branches. The population of the magnetic sublevels of Rb(5 2P3/2) atoms produced by predissociation of the C1Πu state of the Rb2 molecule by the repulsive molecular state c3Σ+u has been determined from the Zeeman spectra of the emission Rb(5 2P3/2→ 5 2Sm′1/2). The observed results are interpreted by including the spin-orbit coupling between an excited level of the C1Πu state and levels of the c3Σ+u state and the effect of the external magnetic field.

The I1Πg state of hydrogen: adiabatic corrections, energy levels, L uncoupling, and electronic transition moments

Employing Kołos and Rychlewski's ab initio wave functions for the electronic I1Πg. state of molecular hydrogen (Dieke's 3dπ 3E) we calculated the diagonal corrections for nuclear motion to the electronic energies over the internuelear-distance range R = 1 – 12 au. The vibration–rotation energy levels calculated in the adiabatic approximation are compared with spectroscopic results in H2, HD, and D2 and it is concluded that the convergence error of the electronic energy in the inner well [Formula: see text] of the double-minimum potential curve is 1.0 ± 0.5 cm−1. The electronic matrix elements of angular-momentum coupling with the [Formula: see text] state and of the dipole transition moments to the (B, B′) [Formula: see text] and C1Πu states are also presented.