CW Optical-Optical Double Resonance studies of the 23Πg, 33Πg, 43Πg+, and 13Δg Rydberg states of Na2

The 2³Π_g, 3³Π_g, 4³Σ_g⁺, and 1³Δ_g states of the Na₂ molecule are observed by sub-Doppler Perturbation Facilitated Optical-Optical Double Resonance (PFOODR) spectroscopy. Absolute vibrational assignments and molecular constants are obtained for two of these states (3³Π_g, v = 0–25 observed, and 4³Σ_g⁺, v = 3–5, 13, 14 observed). Tentative vibrational assignments and provisional molecular constants are obtained for the 2³Π_g (v = 43–89 observed) and 1³Δ_g (v = 31–35, 40, 46–51 observed) states. Spin-orbit, spin-spin, and hyperfine splittings are observed. The direct ³Λ_g⁺ → a³Σ_u, 2³Π_g ∼ 3³Π_g perturbation-induced, and collision-induced contributions of these four ³Λ_g states to the ubiquitous Na-vapor violet and ultraviolet emission bands are discussed.     

Transition probabilities of the X1Σ+, A1Π, B1Δ, C1Σ+, and D1Π states of the AlO+ cation

ABSTRACT

This study computes the potential energy curves of the X¹Σ⁺, A¹Π, B¹Δ, C¹Σ⁺, and D¹Π states of AlO⁺ cation and the transition dipole moments between them. The orders of the rotationless radiative lifetimes are 10–100?μs for the A¹Π state, 1–1000?ms for the B¹Δ state, 10?ns for the first well and 100?ns for the second well of the C¹Σ⁺ state, and 1?μs for the D¹Π state. Emissions of the B¹Δ–A¹Π and D¹Π–C¹Σ⁺ systems are so weak that they are hardly measured via spectroscopy, the emissions of the C¹Σ⁺–X¹Σ⁺, C¹Σ⁺–A¹Π, and D¹Π–X¹Σ⁺ systems are so strong that they can be detected readily, and emissions of the A¹Π–X¹Σ⁺ and D¹Π–A¹Π systems can be observed through spectroscopy only by a significant effort. There is a strong great similarity between spontaneous emissions of the A¹Π–X¹Σ⁺ system of the AlO⁺ cation and the A²Π–X²Σ⁺ system of the AlO radical. The emissions of the A²Π–X²Σ⁺ system of the AlO radical have been measured in outer space Therefore, it is highly possible that the emissions of the A¹Π–X¹Σ⁺ system of the AlO⁺ cation can be detected in the astrophysical media.     

High resolution Fourier spectroscopy of P2 infrared emission spectrum: Analysis of two new systems b3Πg → w3Δu and A1Πg → W1Δu

The investigation of the emission infrared spectrum of P₂ was performed with a high resolution Fourier spectrometer. Two new electronic systems were attributed to b³Π_g → w³Δ_u and A¹Π_g → W¹Δ_u transitions. The molecular parameters are obtained by a complete fitting procedure. The main equilibrium constants of the new states are (in cm^?1):

$\text{ω}{}^3\text{Δ}{}_{\mathrm{u}}\text{T}{}_{\mathrm{e}}\text{= 243228.07 ω}{}_{\mathrm{e}}\text{= 591.3 ω}{}_{\mathrm{e}}\text{X}{}_{\mathrm{e}}\text{= 2.5}$

$\text{B}{}_{\mathrm{e}}\text{= 0.256040 δ}{}_{\mathrm{e}}\text{= 0.001409 D}{}_{\mathrm{e}}\text{= 19.0 X 10}{}^{\mathrm{?8}}$

$\text{W}{}^1\text{Δ}{}_{\mathrm{u}}\text{T}{}_{\mathrm{e}}\text{= 31096.64 W}{}_{\mathrm{e}}\text{= 627.206 W}{}_{\mathrm{e}}\text{X}{}_{\mathrm{e}}\text{= 2.331}$

$\text{B}{}_{\mathrm{e}}\text{= 0.2628 δ}{}_{\mathrm{e}}\text{= 0.0014 D}{}_{\mathrm{e}}\text{= 23 X 10}{}^{\mathrm{?8}}$

     

Polarization spectroscopy of Na2 A1Σu+-b3Πu ← X1Σg+ intercombination bands

The A¹Σ_u⁺ ∼ b³Π_u perturbation of Na₂ in several high vibrational levels has been studied by polarization spectroscopy. Deperturbed molecular constants are given for the mutually interacting v_A = 26 ∼ v_b = 28 and v_A = 34 ∼ v_b = 34 vibrational levels.     

Calculation of molecular constants for the X 1Σ g + , A 1Σ u + , B 1Πu, and a 3Σ u + electronic states of 39K2

The molecular constants are calculated for the X ¹Σ _g ⁺ , A ¹Σ _u ⁺ , B ¹Π_u, and a ³Σ _u ⁺ and electronic states of a potassium dimer. The wave functions and vibrational energies necessary for calculating the molecular constants are determined by solving the radial wave equation with the use of potential energy curves constructed by the semiempirical method. The vibrational terms, the rotational constants, and the centrifugal distortion constants calculated from the potential curves are compared with those determined from the experimental data.     

Fourier spectroscopy of the Asundi system (a′3Σ+-a3Π) of 13C16O

The Asundi system (a′³Σ⁺-a³Π) of ¹³C¹⁶O has been studied between 3500 and 12 000 cm⁻¹ by high-resolution Fourier transform spectroscopy. The 10 bands, 0-0, 0−1, 1−0, 1−1, 1−2, 2−0, 2−1, 3−0, 4−0, and 4−2, were analyzed taking into account the strong perturbations appearing in the a′³Σ⁺ (v = 0,…,4) levels. Accurate perturbation parameters were obtained for all interacting states.     

Rotational and rovibrational transitions in the a 1Δ2 and b 1Σ+0+ states of sulfur monoxide radical

ABSTRACT

Sulfur monoxide radical has widely been detected in outer space using ground-state spectroscopy. The a ¹Δ₂ and b ¹Σ⁺₀₊ states of this radical have low excitation energies, and they possibly exist in outer space. In this work, the potential energy curves and dipole moment functions of the two states were evaluated using the complete active space self- consistent field method, followed by the valence internally contracted multireference configuration interaction approach. The transition line positions, oscillator strengths, band transition dipole matrix elements, Einstein A coefficients, and Franck–Condon factors of all transitions were calculated for lower vibrational levels at rotational angular momentum quantum number J up to 150. The transition line positions calculated in this study are in good agreement with the experimental results. The rovibrational transition became noticeably weak at Δυ > 5. Comparing the results of a ¹Δ₂ and b ¹Σ⁺₀₊ states reported in this paper with the previous values, we conclude that these results are the most accurate and complete to date.     

Molecule opacities of X~2Σ~+, A~2Π, and B~2Σ~+ states of CS~+

Carbon sulfide cation(CS~+) plays a dominant role in some astrophysical atmosphere environments. In this work, the rovibrational transition lines are computed for the lowest three electronic states, in which the internally contracted multireference configuration interaction approach(MRCI) with Davison size-extensivity correction(+Q) is employed to calculate the potential curves and dipole moments, and then the vibrational energies and spectroscopic constants are extracted. The Frank–Condon factors are calculated for the bands of X~2~+Σ~+–A~2Π and X~2Σ~+–B~2Σ~+systems, and the band of X~2Σ~+–A~2Π is in good agreement with the available experimental results. Transition dipole moments and the radiative lifetimes of the low-lying three states are evaluated. The opacities of the CS~+ molecule are computed at different temperatures under the pressure of 100 atms. It is found that as temperature increases, the band systems associated with different transitions for the three states become dim because of the increased population on the vibrational states and excited electronic states at high temperature.     

Lifetimes,population and deactivation mechanisms of theC 1 ∏ u , 23 ∏ g and 21∑ u + states of Na2

The UV and visible fluorescence of Na₂ molecules in a heat-pipe, excited by the frequency doubled radiation of a tunable mode-locked cavity-dumped cw dye laser was observed through a monochromator, using time-resolved single-photon counting. The effective lifetimes of the directly excitedC ¹ _u state and the collisionally populated 2³ _g and 2¹ _u ⁺ states have been measured as a function of sodium-vapor pressure and argon pressure which yields the radiative lifetimes, the population mechanisms and the collisional quenching cross sections of the three states.     

Rotational analysis of the a3Π-X1Σ+ bands of GaD

A new method of producing strong and clean emission spectra of the gallium hydride/deuteride molecule has been developed. Five bands belonging to the gallium deuteride molecule (GaD) have been photographed under high resolution. The rotational analyses of the bands lying at 5669.14 Å (0-0) and 5675.10 Å (1-1) in the a³Π₁-X¹Σ⁺ transition, 5761.0 Å (0-0) and 5766.20 Å (1-1) in the a³Π_0⁺-X¹Σ⁺ transition, and 5760.85 Å (0-0) in the a³Π_0⁻-X¹Σ⁺ transition have been performed. Accurate rotational constants (B, D) have been determined for the X¹Σ⁺, a³Π_0^± and a³Π_1^± states. The Λ doubling in the a³Π₀ (v = 0) and a³Π₁ (v = 0 and 1) states are obtained.     

Near-resonant electronic energy transfer induced by first- and second-order long-range potentials between the two states A1Σu+ and X1Σg+ of Li2 and Na2

Collision-induced rotational transitions between different electronic states are treated theoretically in the Born approximation for a second-order long-range interaction potential. It is shown that the experimentally observed cross sections for resonant channels in the A → X transfer of Li₂ are reproduced by this simple calculation taking the two terms' first-order dipole-dipole and second-order interaction potentials into consideration.     

Vibrational Analysis of the A3Π0−X1Σ+ and B3Π1−X1Σ+ Subsystems of the GaBr Molecule

Abstract

The emission band spectrum of gallium monobromide has been excited in a dc hollow cathode discharge. bands of the ³Π_0,1?X¹Σ⁺ system, lying in the range from 340 to 370 nm have been recorded at high resolution and measured. The previous vibrational analysis has been revised and corrected. New vibrational assignment has been proposed and improved vibrational constants of the upper and lower electronic states have been determined.     

Argon ion laser-induced BaS B1Σ+-A1Σ+, A′1Π, a3Π, and X1Σ+ fluorescence spectra: Analysis of A ∼ A′, A ∼ a,and A′ ∼ a perturbations

The 333.6-, 351.1-, and 363.8-nm lines of a cw argon ion laser are found to coincide with the BaS B¹Σ⁺-X¹Σ⁺ (12, 0) R(17), (6, 0) P(35), and (3, 0) R(125) transitions, respectively. Fluorescence transitions from the laser-prepared upper levels terminating in X¹Σ⁺v = 0–28, A¹Σ⁺v = 1–3, A′¹Π v = 1–13, and a³Π₁v = 3–12 are assigned. These results are combined with a previous analysis of the extensively perturbed BaS A¹Σ⁺-X¹Σ⁺ system [R. F. Barrow, W. G. Burton, and P. A. Jones, Trans. Farad. Soc.67, 902–906 (1971)]. Every observed perturbation of the BaS A¹Σ⁺ state is electronically and vibrationally assigned. The levels a³Π₀v = 10–13, a³Π₁v = 12–14, a³Π₂v = 15, and A′¹Π v = 10–13 are sampled via their perturbations of A¹Σ⁺v = 0–2. Although the mutual interactions of the a³Π, A′¹Π, and A¹Σ⁺ states approach Hund's case (c) limit, a complete deperturbation is performed from a case (a) starting point. Of the five lowest energy electronic states of BaS, only b³Σ⁺ remains uncharacterized. Principal deperturbed molecular constants are (in cm^?1, 1σ uncertainties in parentheses):

     

18.

High-resolution infrared Fourier transform spectroscopy of SO in the X3Σ− and a1Δ electronic states     

《Journal of Molecular Spectroscopy》1987,124(2):379-392

The v = 1 ← 0 vibration-rotation absorption bands of ³²S¹⁶O, ³⁴S¹⁶O, and ³²S¹⁸O in the ground electronic state, X³Σ⁻, and the v = 1 ← 0 vibration-rotation band of ³²S¹⁶O in the first excited electronic state, a¹Δ, were measured at 0.004 cm⁻¹ unapodized resolution with a high-resolution Fourier transform spectrometer coupled to a long path absorption cell. The v = 2 ← 0 vibration-rotation band of ³²S¹⁶O in the X³Σ⁻ state was also observed. Line positions for P- and R-branch transitions up to N = 44 for ³²S¹⁶O have been measured and analyzed yielding improved molecular parameters. The present measurements are compared with previous infrared and microwave measurements.     

19.

Improved adiabatic corrections for the a3Σg+ state of the hydrogen molecule     

《Journal of Molecular Spectroscopy》1987,125(1):159-166

Adiabatic corrections have been calculated for a wide range of internuclear distances for the lowest bound triplet state of molecular hydrogen. It is shown that the existing small discrepancy between theoretical and experimental D₀ values can be removed if an additional correction to the Born-Oppenheimer energy on the order of 0.4 cm⁻¹ is taken into account.     

20.

Calculation of the interaction potential energy curve and vibrational levels for the a3Σu+ state of Li27 molecule     

Jian-Yi Liu  Guang-Dong Zhang  Chun-Sheng Jia 《Physics letters. A》2013,377(21-22):1444-1447

     

	$\text{T}{}_{\mathrm{e}}$	$\text{ω}{}_{\mathrm{e}}$	$\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}$	$\text{B}{}_{\mathrm{e}}\text{× 10}{}^2$	$\text{α}{}_{\mathrm{e}}\text{× 10}{}^4$	$\text{R}{}_{\mathrm{e}}\text{(}\text{A}\text{?}\text{)}$
$\text{A}{}^1\text{Σ}{}^{\mathrm{+}}$	14 498.6(1)	287.7(1)	1.15(5)	9.365(5)	5.0(10)	2.633
$\text{A′}{}^1\text{Π}$	12 095(6)	258.9(5)	0.7	8.21(5)	3.6(5)	2.813
$\text{a}{}^3\text{Π}{}_{\mathrm{i}}$	11 835(6)	259.6(5)	0.7	8.21	3.6	2.813
$\text{X}{}^1\text{Σ}{}^{\mathrm{+}}$	0	379.50(4)	0.91(1)	10.334(1)	3.4(2)	2.507

High-resolution infrared Fourier transform spectroscopy of SO in the X3Σ− and a1Δ electronic states

The v = 1 ← 0 vibration-rotation absorption bands of ³²S¹⁶O, ³⁴S¹⁶O, and ³²S¹⁸O in the ground electronic state, X³Σ⁻, and the v = 1 ← 0 vibration-rotation band of ³²S¹⁶O in the first excited electronic state, a¹Δ, were measured at 0.004 cm⁻¹ unapodized resolution with a high-resolution Fourier transform spectrometer coupled to a long path absorption cell. The v = 2 ← 0 vibration-rotation band of ³²S¹⁶O in the X³Σ⁻ state was also observed. Line positions for P- and R-branch transitions up to N = 44 for ³²S¹⁶O have been measured and analyzed yielding improved molecular parameters. The present measurements are compared with previous infrared and microwave measurements.     

Improved adiabatic corrections for the a3Σg+ state of the hydrogen molecule

Adiabatic corrections have been calculated for a wide range of internuclear distances for the lowest bound triplet state of molecular hydrogen. It is shown that the existing small discrepancy between theoretical and experimental D₀ values can be removed if an additional correction to the Born-Oppenheimer energy on the order of 0.4 cm⁻¹ is taken into account.