Comparison of semiempirical and ab initio absolute probabilities of rovibronic transitions for the I 1Π g − , J 1Δ g − →C 1Π u ± system of bands of the H2 molecule

The absolute values of probabilities of the I ¹Π _g ^? , v′, J′; J ¹ Δ _g ^? , v′, J′→C ¹Π _u ^± , v″, J″ spontaneous transitions in the H₂ molecule (for the vibrational and rotational quantum numbers v′=v″=0–3, J′=1–6, and J″=J′, J′ ±1) are calculated by using ab initio and semiempirical data on the dipole moments of the 3dπ ¹Π_g, 3dδ¹Δ_g→2pπ¹Π_u electronic transitions. In both cases, the calculations are performed both in the adiabatic approximation and with an allowance for the nonadiabatic effect of electronic-rotational interaction. The coefficients of expansion of the wave functions of perturbed rovibronic states in the Born-Oppenheimer basis functions used in the calculations were obtained in the approximation of pure precession from experimental values of the terms. It was found that the values of transition probabilities based on the ab initio calculations systematically exceed the corresponding semiempirical data by a factor of 1.2–1.9 for the I ¹Π_g→C ¹Π _u ^± transition and by a factor of 1.4–1.6 for the J ¹Δ _g ^? →C ¹Π _u ^± transition. It was established that the difference between the ab initio and semiempirical values of electronic transition moments virtually has no effect on the dependence of the transition probabilities on the vibrational quantum numbers. The discrepancies between the results of adiabatic and nonadiabatic calculations are significant and reach two orders of magnitude, which is indicative of the important role of perturbations in the probabilities of the transitions considered.     

Probabilities of rovibronic transitions in the I 1Π g − , J 1Δ g − →C 1Π ± u systems of bands of the deuterium molecule

Probabilities of spontaneous rovibronic transitions I ¹Π _g ^? , v′ J′, J ¹Δ _g ^? , v′, J′→C ¹Π _u ^± , v″, J″ of the D₂ molecule (for vibrational and rotational quantum numbers v′=v″=0–3 and J′=1–9, J″=J′±1) have been obtained for the first time. They were determined using (1) the previously proposed nonadiabatic model, which takes into account the electron-rotational interaction of the upper levels; (2) the coefficients of expansion of wave functions of perturbed states in the Born-Oppenheimer basis, which were found from the experimental data on rovibronic terms; and (3) semiempirical b initio data on electronic transition dipole moments of the 3dπ¹Π_g→2pπ¹Π_u and 3dπδ¹Δ_g→2pπ¹Π_u transitions. The dependences of the transition probabilities on J′ for the same bands of both hydrogen isotopomers H₂ and D₂ were found to be identical. They represent monotone functions for R and P branches and functions with a maximum (minimum) for Q branches. The ratios of transition probabilities of different isotopomers for different branches of the same systems of bands and for the same branches of different systems of bands were found to be correlated. The semiempirical values obtained in the paper agree with the experimental values within the limits of the errors of their determination. The nonempirical values of transition probabilities agree with the experiment considerably worse.     

Electronic branching ratios of spontaneous emission for transitions between states of the 3d and 2p singlet complexes of terms of H2

The ratios of probabilities (the electronic branching ratios) for the rovibronic spontaneous transitions are for the first time measured for transitions from the rotational levels with J′≤6 of the I ¹Π _g ^? , v′=0–2 and J ¹Δ _g ^? , v′=0 states to the vibrational-rotational levels of different low-lying electronic states B ¹Σ _u ⁺ , v″, J′ and C ¹Π _u ^? , v?, J′?1 of the H₂ molecule (for the vibrational quantum numbers v″≤4 and v?≤2). Values of these quantities provide a new channel of information on the internal structure of the hydrogen molecule thus far unused and should be particularly sensitive to the adiabatic values of the electronic transition dipole moments. In studying the entire set of rovibronic radiative transitions, they may significantly add to the experimental data on rovibronic terms, radiative lifetimes, and vibrational and rotational branching ratios used before. The experimental data obtained are compared to the corresponding values derived from the results of an earlier semiempirical determination and ab initio calculation of the absolute transition probabilities. Our experimental data are in remarkable agreement with the semiempirical results and significantly differ from the ab initio results. This fact directly suggests the necessity of performing more accurate ab initio calculations of the rovibronic transition probabilities for the given systems of bands.     

Quantum mechanical calculation of rotational constants and Franck-Condon factors of diatomic molecules

In this paper, the question of reliability of the Morse potential as a potential curve for a diatomic molecule is investigated on the basis of calculating the rotational constant. It is shown that the Morse potential describes well potential curves of X¹Σ _q ⁺ and B¹Π_u electronic states of a Na₂ molecule. Calculations of Franck-Condon factors for X¹Σ _q ⁺ ? B¹Π_u band of a Na₂ molecule using wave functions of the Morse potential confirm the known correlation between the values of Franck-Condon factors and rotational constants of combined electronic states.     

Optische Messung der Elektronenstoß-Anregung von Xenon und molekularem Stickstoff im Schwellenbereich mit hoher Energieauflösung

Relative optical excitation functions of Xe and N₂ have been measured in the threshold region. The inciting electron beam had a FWHM of 50 meV. The threshold behaviour of the excitation functions ofp-levels of Xenon is strongly influenced by resonances. The onset is step-like, in some cases resonance structure is to be seen just above threshold. In some excitation functions resonance structure is found immediatly above the ionization limit. This is believed to be caused by two compound states the parent states of which could be the 6d′ and the 8s′ autoionizing state of Xenon. In nitrogen, the excitation functions of two bands of the second positive group have been measured (3371 and 3755 Å), the upper levels of which are thev=0 and thev=1 levels of theC ³Π _u state. The excitation raises linear from threshold. In the 3371 Å excitation function a resonance maximum at 11.50 eV is observed, where the cross section is increased due to resonance population by about 100%, as measured with a FWHM of 50meV of the electron beam. The broad absolute maximums of the excitation functions are found to lie at 14.0±0.1 eV in the case of the 3371 Å- and at 14.3±0.1 eV in the 3755 Å-band.     

A comment on Hönl-London factors

The literature on the Hönl-London factors of diatomic molecules, the factors in intensity formulas dependent on the rotational quantum numbers, is somewhat confused for the case of perpendicular transitions. We derive a formula, Eq. (23), for allowed singlet-singlet transitions between levels of definite parity, and show that it is consistent with standard sum rules. As an illustration, the formula is applied to the calculation of lifetimes in the B¹Π_u state of Na₂, showing that the corrected formula gives results in good agreement with experimental measurements.     

Molekularstrahlmessungen von Stoßquerschnitten für Übergänge zwischen definierten Rotationszuständen zwei-atomiger Moleküle

Inelastic collision cross sections for transitions between specified rotational states designated by (J, M) have been measured in a molecular beam apparatus. With an electrostatic four pole field molecules in a specified rotational state are separated out of a molecular beam and focussed into a gas filled scattering chamber. Molecules which have been scattered by less than 1/2° are then collected in a second four pole field, located directly behind the scattering chamber, and are analyzed for their rotational state. From a comparison of the measured pressure dependence with calculated curves a determination of inelastic collision cross sections for specified quantum jumps is possible. Measured inelastic scattering cross sections for the transitions (2,0→3,0) are reported for the gases He, Ne, Ar, Kr, CH₄, SF₆, H₂, O₂, Air, N₂O, H₂O, CF₂Cl₂. The values range between about 5 and 100 Ų in the order indicated. The scattering gases NH₃ und ND₃ yielded larger cross sections of about 600 Ų and, in addition, the transitions (3,0)→(2,0),(1,0)→(2,0), (2,0)→(1,0) and (3,0)→(1,0) were observed. Total cross sections for the same gases were also measured with the apparatus.     

Identification of New Low-Lying Electronic States of the FeF Radical

Dispersed fluorescence studies on the ⁶Π-X⁶Δ and ⁶Φ−X⁶Δ systems of the FeF radical have resulted in the observation of vibrational progressions for transitions to the X⁶Δ state as well as at least two previously unobserved electronic states about 5000 cm⁻¹ above the ground state. The states are assigned as the A⁶Π and B⁶Σ⁺ electronic states. The spin components of both electronic states were found to be heavily perturbed resulting in uneven splittings between them. A third, weak series was also observed but could not be assigned. The (0,0) band of the ⁶Π_7/2−B⁶Σ⁺_5/2 transition at 398 nm was observed in absorption by laser induced fluorescence and its rotational structure was assigned. The spectra obtained were weak because of a poor population of the B⁶Σ⁺ state by the reaction used to form FeF. The levels were found to be markedly perturbed at high J values. Attempts were made to fit the data on the ⁶Π_7/2-B⁶Σ_5/2⁺ system to an effective Hamiltonian, but the presence of perturbations meant that the system is not well described by such a model.     

用能量自洽法研究碱金属双原子分子的势能曲线

用能量自洽法(ECM)研究了碱金属双原子分子一些电子激发态的势能曲线：Na₂ 分子的2¹Π_g,4³Π_g和b³Π< sub>u电子激发态,K₂分子的a³Σ^＋_{u,2¹Πg,B¹Πu和A^{关键词： 能量自洽 双原子分子 势能 碱金属}}     

Excitation transfer between excited electronic states of the H2 molecule due to interaction with a CO2 Laser beam

A spectroscopic study of the band systemsG ¹ Σ _g →B ¹ Σ _u andI ¹ Π _g →B ¹ Σ _u of H₂ emitted by a glow discharge in H₂ gas showed that the populations of theG ¹ Σ _g (v, J) states decrease for the benefit of theI ¹ Π _u (v′, J′) states when the discharge is irradiated by a powerful CO₂ Laser beam (power density 70 kW/cm²). The effect is interpreted as an absorption process in which two Laser photons intervene according to the transition scheme:G ¹ Σ _g →B″¹ Σ _u →I ¹ Π _g. A change of the populations of excited electronic states should lead to a change of the populations of excited atomic states as well.     

Rotational analysis of the B-X band system of the SbO molecule

Rotational analyses of the two 0-0 bands of theB ²ΣX ²Π_reg system of SbO were carried out for the first time from spectrograms taken in the second order of a 21 ft. concave grating spectrograph having a dispersion of 1·25 Å/mm. The rotational constants of the ν=0 vibrational levels of the upper and lower states, and of the coupling constant A₀ of the lower²Π_reg state were deduced. These values are summarised below. v₀₀=25 334·93 cm^?1 B′₀=0·3190 cm^?1 B″₀=0·3490 cm^?1 A ₀=2276 cm^?1 r′₀=1·933 Å r″₀=1·848 Å.     

Rotational analysis of 4730 Å band of MgCl

Magnesium chloride was excited in a high frequency discharge source and the 4730 Å band was photographed at an inverse dispersion of 0.48 Å mm^?1 in a two meter plane grating spectrograph. The rotational analysis of the band has been carried out and the molecular constants of the upperB ²Σ⁺ state are reported for the first time. Observation of rotational isotopic shifts due to Cl³⁷ supports the rotational analysis. The electronic transition involved is identified to beB ²Σ⁺ →A ²Π_1/2(a) (inverted).     

Observation of the 5pΠu Rydberg state of Li2

Some weak, collisionally induced transitions in ⁷Li₂ have been recorded by Fourier transform spectrometry in the near infrared, following excitation of the 5d¹Π_g state by optical-optical double resonance. They have been assigned as transitions to the 1 ¹Δ_g state from levels v=0 and 1 of a new ungerade Rydberg state, 5p¹Π_u. Quantum defect considerations indicate that the principal quantum number for this new state is 5, and that the assignment to 5p is compatible with a Rydberg series of which the lowest members would be the B¹Π_u and C¹Π_u states.     

Λ-Doubling investigation of the 5Πg Rydberg state of Na2 using optical-optical double resonance spectroscopy

The splitting of Λ-doubling in the 5¹Π_g Rydberg state of Na₂, which dissociates to Na(3s) + Na(4d), has been measured using the high-resolution cw optical-optical double resonance technique. The observed data are in the range of 0 ? v ? 22 and 11 ? J ? 83 with Λ-doubling revealed. A set of Dunham coefficients with Λ-doubling constants has been obtained from the experimental results. The splitting of Λ-doubling increases quadratically with the rotational quantum number J and weakly depends on the vibrational quantum number v. These splitting constants are much larger than those in the Na₂B¹Π_u state, which dissociates to Na(3s) + Na(3p). This indicates that the splitting of Λ-doubling in the 5¹Π_g state is affected by both the perturbations by adjacent Σ states and the L-uncoupling.     

Quenching cross sections of the B3Π+(Ou+) v′ = 14 level of I2 by H2, CO,and CH4

In this work the deexcitation of the B³Π⁺(O_u⁺), v′ = 14 level of I₂ after pulsed laser excitation has been studied. The quenching cross sections by collisions with I₂, H₂, CO, and CH₄ have been measured. The experimental results are 190 ± 14, 2.5 ± 0.3, 15.1 ± 0.4, and 18.0 ± 0.6 Ų, respectively. These values are compatible (within 30%) with the semiempirical scaling law of proportionality with the product of polarizability and the square root of reduced mass.     

Laser transitions among the C1Πu, 31Σg+, A1Σu+, and X1Σg+ states of Na2

Intense infrared stimulated lines at wavelengths around 2.5 μm have been observed upon excitation of Na₂ by uv radiation from a frequency-doubled narrow-band dye laser. Frequencies of these IR lines have been measured when the pump laser was tuned to C¹Π_u ← X¹Σ_g⁺ assigned transitions in the wavelength range 331–334 nm. High-resolution spectroscopy measurements of the involved rovibrational levels of both C¹Π_u and 3¹Σ_g⁺ electronic states allow the unambiguous assignment of these IR laser lines to C¹Π_u → 3¹Σ_g⁺ transitions.     

Spectroscopic study of an rf discharge in nitrogen

The absolute populations of the vibrational levels of the B³Πg and C³Π_u states in an rf nitrogen discharge are calculated from the quantum yields of the 1⁺ and 2⁺ systems in the discharge, and the “excitation temperature” of these states is measured. Emission spectroscopic methods are used to determine the vibrational and rotational temperatures of the C³Π_u state, as well as the vibrational temperature of the B³Π_g state. These data are used to estimate the vibrational temperature of the X′∑ _g ⁺ state and the stored energy in the activated nitrogen, and to examine the mechanism by which translational-vibrational degrees of freedom are excited in nitrogen molecules in the discharge.     

High-resolution Fourier spectrometry of 14N2 infrared emission spectrum: Extensive analysis of the B3Πg-A3Σu+ system

The B³Π_g-A³Σ_u⁺ system of N₂ excited in a microwave discharge was recorded between 3 000 and 18 000 cm^?1 with a high-resolution Fourier spectrometer. There are no observed irregularities in the levels of the A³Σ_u⁺ and B³Π_g states at least for the values of v and J considered here, except the predissociation in the B³Π_g state for v = 12 and J higher than 33. This predissociation will be checked with more complete data in another article. Thirty three bands of the first positive system with 0 ≤ v′ ≤ 12 and 0 ≤ v″ ≤ 8 are analyzed. The molecular parameters of the B³Π_g and A³Σ_u⁺ are obtained by a complete fitting procedure. Derived values of equilibrium constants are deduced; RKR potential energy curves for the two states are constructed, and the Franck-Condon factors calculated for the A-B system.     

High resolution Fourier transform spectrum of GaCl

The electronic emission spectrum of the A³Π₀-X¹Σ⁺ and B³Π₁-X¹Σ⁺ transitions of Gallium monochloride molecule (⁶⁹GaCl) has been recorded on BOMEM DA8 Fourier transform spectrometer at an apodized resolution of 0.035 cm⁻¹. The rotational structure of the 0-0, 1-0, 2-1, and 3-2, bands belonging to A-X and 0-0, 0-1, 1-2, and 0-2 bands belonging to B-X transitions has been analyzed and equilibrium rotational constants for the X¹Σ⁺ and A³Π₀ states have been obtained. For the first time we are able to determine the Λ-doubling constants in the v = 0 and 1 levels of the B³Π₁ state.