High-Resolution Fourier Transform Study of MgCl: The AΠ-XΣ Band System

The A²Π-X²Σ⁺ emission band system of the MgCl molecule has been studied by means of high-resolution Fourier transform spectroscopy. Excited MgCl molecules were produced by two different techniques: (i) at Orsay, they were created by mixing Mg vapor with a flow of He/Cl₂ and excited in a “heated” Schüller-type discharge tube, and (ii) at Waterloo, they were generated by using a copper hollow cathode lamp loaded with MgCl₂ powder. Rovibronic analysis of the (0, 0) and (0, 1) bands was performed. Molecular constants were derived in a weighted nonlinear least squares fit, including both the new line positions and the previously published microwave frequencies (M. Bogey, C. Demuynck, and J. L. Destombes, Chem. Phys. Lett.155, 265 (1989); Y. Ohshima and Y. Endo, Chem. Phys. Lett.213, 95 (1993)).     

Fourier transform spectral study of BΣ-XΣ system of AlO

The spectrum of B²Σ⁺-X²Σ⁺ system of AlO has been recorded on BOMEM DA8 Fourier transform spectrometer at an apodized resolution of 0.05 cm⁻¹. Nineteen bands of the Δv = 1, 0, −1, and −2 sequences of this band system have been analyzed for the rotational structure. Out of which seven bands, viz. 3-2, 4-3, 2-3, 3-4, 4-5, 5-6 and 6-7 have been analyzed for the first time. The rotational lines of these 19 bands along with 20 earlier analyzed bands, a total of 7200 lines, have been fitted in a simultaneous least squares fit. The study has resulted in determining more precise vibrational and rotational constants of the two states. Because of the high resolution employed it became necessary to invoke H₀ and H₁ coefficients, and a fifth order term to explain the anomalous spin-doubling observed in the v″ = 5, 6 and 7 levels of the X²Σ⁺ state.     

Fourier transform spectroscopy of chemiluminescence from the AΠ-XΣ system of SrO

The A^′1Π-X¹Σ⁺ near infrared system of strontium oxide (SrO) was observed at high spectral resolution by measuring the chemiluminescence from a Broida flow reactor using a Fourier transform spectrometer. In total, 32 bands from , , were measured within the spectral region at a resolution of . Vibrational levels of the upper state were observed up to v_A^′=4, and more than 5600 rotational lines were assigned. Incorporating previously published high resolution data for the A¹Σ⁺-X¹Σ⁺ system, a global fit to both data sets yields improved Dunham constants for the ground state and for the lower vibrational levels (v_A^′=0, 1, and 2) of the A^′1Π state. Because perturbations arising from interactions with the b³Σ⁺ and A¹Σ⁺ states affect the higher vibrational levels of the A^′1Π state more strongly, levels v_A^′=3 and 4 were represented by effective band constants in the fits. RKR potentials for the X¹Σ⁺,A^′1Π, and b³Σ⁺ states have been generated utilizing all the available data, Franck-Condon factors have been calculated for the A^′1Π-X¹Σ⁺ system, and A^′1Π∼b³Σ⁺ and A^′1Π∼A¹Σ⁺ perturbations are discussed.     

High-resolution Fourier transform emission spectroscopy of the AΠ-XΣ system of GeSe

Natural germanium and selenium consist of, respectively, five and six stable isotopes. Several of these isotopes have considerable abundances and one should expect to observe the bands of at least six isotopic variants of germanium monoselenide (GeSe). In this paper, for the first time, the results of the high-resolution electronic spectrum of the main transition A¹Π-X¹Σ⁺ of the specific isotopomer ⁷⁴Ge⁸⁰Se, excited in a microwave discharge and recorded in the 33 500-26 000 cm⁻¹ region using a Fourier transform spectrometer, is discussed. From the rotational analysis of 25 bands involving v″ = 0-12 and v′ = 0-7, accurate vibrational and rotational constants of the A¹Π state are determined. The present study has revealed perturbations in the v′ = 6 and 7 levels of the A¹Π state.     

The Fourier Transform Emission Spectrum of BΠ1-XΣ Band-System of InCl

The emission spectrum of the B³Π₁-X¹Σ⁺ band-system of the InCl molecule has been recorded on a Fourier transform spectrometer at an apodized resolution of 0.025 cm⁻¹. The rotational structure of 1-0, 2-1, 0-0, 0-1, 1-2, 0-2, and 1-3 bands belonging to the B³Π₁-X¹Σ⁺ transition of In³⁵Cl has been analyzed and accurate equilibrium rotational constants of the B³Π₁ state, have been obtained. Precise Λ-doubling constants of the B³Π₁ state (v=0, 1, and 2) are also reported for the first time.     

Fourier Transform Emission Spectroscopy of a New Φ-1Δ System of VO

High-resolution emission spectra of VO have been recorded in the region 3400-19 400 cm⁻¹ using a Fourier transform spectrometer. The molecules were observed from the reaction of VOCl₃ with active nitrogen. Two new bands, with origins near 5539.46 and 5551.69 cm⁻¹, are assigned as the 0-0 bands of the ²Φ_5/2-²Δ_3/2 and ²Φ_7/2-²Δ_5/2 spin-orbit components (respectively) of a ²Φ-1²Δ electronic transition of VO. A rotational analysis of both subbands has been carried out and spectroscopic constants have been extracted. The 1²Δ state is known from the previous analysis of the near infrared doublet transitions of VO and the new ²Φ excited state has rotational constants very similar to those of another ²Φ state observed previously [Merer et al., J. Mol. Spectrosc.125, 465 (1987)].     

Laser spectroscopy of VS: hyperfine and rotational structure of the CΣ-XΣ transition

The (0,0) and (0,1) bands of the C⁴Σ⁻-X⁴Σ⁻ electronic transition of VS (near 809 and 846 nm, respectively) have been recorded at high resolution by laser-induced fluorescence, following the reaction of laser-ablated vanadium atoms with CS₂ under supersonic free-jet conditions. A least squares fit to the resolved hyperfine components of the rotational lines gives the rotational constants and bond lengths as C⁴Σ⁻: , ; X⁴Σ⁻: , . The electron spin parameters for the two states show that there are some similarities between the states of VS and those of VO, but the hyperfine parameters show that the compositions of the partly filled molecular orbitals are by no means the same. The ground state Fermi contact parameter of VS, b(X⁴Σ⁻), is only 58% of that of the ground state of VO, which implies that the σ orbital of the ground σδ² electron configuration has less than 50% vanadium 4s character. Similarly, the excited state Fermi contact parameter, b(C⁴Σ⁻), is very much smaller than that of VO. No local rotational perturbations have been found in the C⁴Σ⁻ state of VS, though an internal hyperfine perturbation between the F₂ and F₃ electron components at low N confuses the hyperfine structure and induces some forbidden (ΔJ=±2) rotational branches.     

The Near-Infrared YΣ-XΠ Transition of CuSe

The near-infrared Y²Σ⁺-X²Π transition of the diatomic molecule CuSe was observed for the first time. A King-type carbon tube furnace was used to produce the gas phase of the CuSe molecules. The Fourier transform spectrometer associated with the National Solar Observatory, Kitt Peak, Arizona was used to record the molecular emission spectrum in the region 9850-12 400 cm⁻¹. A vibronic analysis and comparisons of the spin-orbit constant and the ²Σ⁺ transition energy to those for related isovalent molecules are presented.     

Rotationally Resolved LIF Spectra of the AΣ-XΠr Transition of Jet-Cooled GeCl

The A²Σ⁺-X²Π_r band system of ⁷⁴Ge³⁵Cl has been rotationally resolved for the first time using isotopically enriched ⁷⁴GeCl₄ as the precursor in a pulsed discharge jet experiment. The previous vibrational analysis of W. J. Balfour and K. S. Chandrasekhar (1986, J. Phys. B19, L187-L191) has been verified from the observed isotopic splittings of both the chlorine and germanium isotopomers. The ²Π_1/2 components of three vibronic bands have been rotationally analyzed leading to revised values for the ground state rotational constant B″₀=0.154165(35) cm⁻¹ and the lambda-doubling constant p″₀=6.560(97)×10⁻³ cm⁻¹. We have experimentally determined the value of B′_e=0.118710(24) cm⁻¹ for the A²Σ⁺ state leading to an excited state equilibrium bond length of 2.44581(25) Å.     

Spectroscopy of AlO: Combined analysis of the AΠi → XΣ and BΣ → XΣ transitions

A combined analysis of the A²Π_i → X²Σ⁺ and B²Σ⁺ → X²Σ⁺ band systems of AlO, involving 21,500 line assignments, has been performed. The analysis indicates that the previously reported γ values of the B²Σ⁺ state are questionable. The present analysis shows that γ(B²Σ⁺) ≈ 0.014 cm⁻¹, essentially independent of the vibrational level. The positive sign is consistent with second order interaction with the higher-lying C²Π_r and lower-lying A²Π_i states. It also appears that many of the previously reported γ and γ_D values of X²Σ⁺ (v > 0) are doubtful. In fact, γ(X²Σ⁺) is observed to become increasingly negative for v″ > 1, due to second order interaction with the low-lying A²Π_i state. The present results are based on models where the hyperfine structure of the ²Σ⁺ states has been taken into account explicitly. Intensity patterns of the branches of the B²Σ⁺ → X²Σ⁺ system have been shown to be influenced by the case bβ_S coupling in the ground state v = 0,1 levels. This gives rise to intensity differences of around 10 percent in the R₁/R₂ and P₁/P₂ doublet components. The synthesized intensity patterns are fully in accord with the F₁/F₂ assignments of the present work.     

Intracavity laser absorption spectroscopy of AuO: Identification of the BΣ-XΠ3/2 transition

The visible electronic spectrum of AuO has been recorded at rotational resolution using intracavity laser absorption spectroscopy. Six vibrational bandheads have been identified, and three of the bands have been analyzed and assigned as bands of a newly identified B²Σ⁻-X²Π_3/2 transition of AuO. The molecular parameters for the newly identified B²Σ⁻ state are presented.     

The Design of Lens Imaging System byMeans of Fractional Fourier Transform

The relation between the 2nd fractional Fourier transform and the imaging process of an optical system is discussed. By changing the coordinate scales of the input plane in respect to the magnification of the optical imaging system, the fractional Fourier transform can be a powerful tool in designing specific imaging system. The Gaussian imaging formula of single lens is obtained by using the tool. Finally the procedures are generalized for designing a double-lens imaging system through an example.     

Fourier Transform and Intracavity Laser Spectroscopy of NiCl System H: Identification of a [12.3] Σ State

The (0,0) vibronic band of NiCl system H near 12 259 cm⁻¹ was recorded at high resolution in absorption using intracavity laser spectroscopy (ILS) and in emission by Fourier transform (FT) spectroscopy. Though it was originally assigned in 1962 as the (1,1) vibronic band of ²Π_3/2-X²Δ_5/2, we have shown that this transition is the (0,0) vibronic band associated with a newly identified ²Σ⁺ excited state and the X²Π_3/2 ground state. The molecular constants for the new ²Σ⁺ electronic state were derived from the rotational analysis. For the ILS absorption spectra, the NiCl molecules were produced in a nickel hollow cathode, operated with a small amount of CCl₄. Line positions were referenced to iodine spectra observed from a heated extracavity cell using the intracavity laser as the light source. For the FT spectra, excited NiCl molecules were produced in a King-type carbon tube furnace.     

Pure Diffractive Multicolor Optical Fourier Transform System Design

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Intracavity Laser Absorption Spectroscopy and Fourier Transform Spectrum of the 3ν1 band region of cyanoacetylene

The second CH stretching overtone of cyanoacetylene, HC₃N, near 9700 cm⁻¹ has been recorded by Fourier Transform Spectroscopy (FTS) and by Intracavity Laser Absorption Spectroscopy (ICLAS) with a Vertical External Cavity Surface Emitting Laser (VECSEL). In total thirteen bands have been identified in the highly congested spectra and rotationally assigned. Their rovibrational spectroscopic parameters have been obtained from a fit of the line centers.     

The 1-v″ bands progression of the BΣ → XΣ system of CO

The B²Σ⁺ → X²Σ⁺ (0-1, 2, 3, 4 progression) electronic transition of ¹²C¹⁷O⁺ was first observed and analyzed by Szajna and Ke¸pa [Spectrochim. Acta A 65 (2006) 1014-1020]. We have now extended our previous studies. The use of high resolution conventional spectroscopic techniques has allowed first rotational analysis of the 1-2, 1-3, 1-4 and 1-5 bands of the first negative system in the 37,000-43,000 cm⁻¹ spectral region. Approximately 500 transition wavenumbers were measured with an estimated accuracy of 0.005 cm⁻¹. The present data were combined with the previous measurements to yield an improved set of molecular constants for the B²Σ⁺(v′ = 0, 1) and X²Σ⁺(v″ = 1, 2, 3, 4, 5). The v′ = 1 and v″ = 5 vibrational levels were observed for the first time and the main molecular constants are (in cm⁻¹, one standard deviation in parentheses)

B2Σ+		X2Σ+
B1 = 1.710792(20)		B5 = 1.825694(23)
D1 = 7.799(15) × 10−6		D5 = 6.085(21) × 10−6
γ1 = 1.9491(37) × 10−2		γ5 = [8.381] × 10−3

Full-size table

     

Fractional Fourier Transform of Cantor Sets

A new kind of multifractal is constructed by fractional Fourier transform of Cantor sets. The wavelet transform modulus maxima method is applied to calculate the singularity spectrum under an operational definition of multifractal. In particular, an analysing procedure to determine the spectrum is suggested for practice. Nonanalyticities of singularity spectra or phase transitions are discovered, which are interpreted as some indications on the range of Boltzmann temperature q, on which the scaling relation of partition function holds.     

Rotational analysis of the (3, 6) band in the comet-tail (AΠi -XΣ) system of CO

The direct observation and rotational analysis of the (3, 6) band in the comet-tail (A²Π_i-X²Σ⁺) system of CO⁺ are carried out for the first time employing optical heterodyne and magnetic rotation enhanced velocity modulation spectroscopy. That 193 lines are assigned to this band ranging from 12 100 to 12 370 cm⁻¹ results in most accurate molecular constants by nonlinear least-squares fitting procedure employing the effective Hamiltonians.     

The emission spectrum of the CΣ–XΣ system of AlH

The ultraviolet spectrum of AlH has been investigated at high resolution between 42 000 and 45 000 cm⁻¹ using a conventional spectroscopic technique. The AlH molecules were formed and excited in an aluminium hollow-cathode lamp with two anodes, filled with a mixture of Ne carried gas and a trace of NH₃. The emission from the discharge was observed with a plane grating spectrograph and recorded by a photomultiplier tube. The 0–0, 1–1 and 1–2 bands of the C¹Σ⁺–X¹Σ⁺ transition have been identified and rotationally analyzed. The new data were elaborated with help of recent X¹Σ⁺ state parameters reported by White et al. [J. Chem. Phys. 99 (1993) 8371–8378] and by Szajna and Zachwieja [Eur. Phys. J. D. 55 (2009) 549–555]. Determined constants of the excited C¹Σ⁺ state include: T_e = 44 675.3711(57) cm⁻¹, ω_e = 1575.3357(42) cm⁻¹, ω_ex_e = [125.5] cm⁻¹, B_e = 6.66804(32) cm⁻¹, α_e = 0.55839(56) cm⁻¹, D_e = 2.23(13) × 10⁻⁴ cm⁻¹, β_e = 6.13(25) × 10⁻⁴ cm⁻¹ and r_e = 1.613132(39) Å. The C¹Σ⁺ state is found to be extensively perturbed in the v = 0 and 1 vibrational level at J = 20, 22 − 27 and J = 5 − 9, respectively. This was probably caused by the interaction with the vibrational levels of the outer minimum.