Determination of A0 for the symmetric top molecules

A new method for the determination of the constant A₀ in symmetric top molecules is proposed. This method utilizes the data for the overtone bands of a doubly degenerate vibration of symmetry species E_1u. Transitions necessary for the determination of A₀ have been indicated for all symmetric top symmetry groups. The precision of A₀ values determined according to the method suggested is also discussed.     

Determination of A0 from the ν4 Raman band of CD3Br

The principles and methods of determining A₀ from the Raman spectra of degenerate fundamentals of C_3v molecules are outlined, and applied to the ν₄ band of CD₃Br to yield a value of A₀ = 2.6004 ± 0.0010 cm^?1.     

Determination of A0 of CH3Br from its Raman spectrum

A value of A₀ = 5.1800 ± 0.0010 cm^?1 for CH₃Br has been determined from an analysis of the ν₄ Raman band, based both on a direct fit of Q-branch frequencies and on ground state combination differences. The constants ν₄, (Aζ)₄, η₄₄, and A_e = 5.2442 ± 0.0015 cm^?1 were also determined. The equilibrium distance of the H atoms from the figure axis is calculated as 0.32077 ± 0.00005 Å. All the fundamental Raman bands of CH₃Br were observed, and experimental results for the ν₁, ν₂ and ν₅ bands are included.     

The propagator in the A0 = 0 gauge

We compute the Wilson loop in the A₀ = 0 gauge for abelian and non-abelian theories. We find to fourth order that only two choices for the longitudinal propagator are consistent with the results obtained in the Feynman and Coulomb gauges. In particular the principal value presciption does not work.     

Determination of A0 for CH335Cl and CH337Cl from the ν4 infrared and Raman bands

The ν₄ infrared and Raman bands of CH₃Cl were analyzed simultaneously. A direct fit yielded a complete set of constants for CH₃³⁵Cl, including A₀ = 5.20530 ± 0.00010 cm^?1 and D_K = (8.85 ± 0.13) × 10^?5cm^?1. For CH₃³⁷Cl an incomplete set of constants was obtained from the infrared band, and A₀ = 5.2182 ± 0.0010 cm^?1 was estimated by curve fitting of the Raman spectrum. The resulting equilibrium structure is $\text{r(}\text{CH) = 1.0854 ± 0.0005}\text{A}\text{?}$, $\text{r(}\text{CCl) = 1.7760 ± 0.0003}\text{A}\text{?}$, and <(HCH) = 110°.35 ± 0°.05.     

Analysis of the A1

We develop a unitary isobar model, and apply it to a study of partial wave analyses of the available three-pion and $\text{K}{}^1\text{K}$ data.     

A3-Weight multiplicity formula

We write down an explicite formula for the multiplicity of a weight in an arbitrary irreducible module of the classical algebra A₃. For this purpose we first derive a reccurrence relation between the multiplicities of the weights in A_a and A_s?1.     

High-resolution rotational analysis of HDS: 2ν3, ν2 + 2ν3, 3ν3, and ν2 + 3ν3 bands

High-resolution Fourier transform spectrum of the HD³²S molecule was studied in the region of 5000-9000 cm⁻¹. More than 1600 observed transitions yielded 239, 264, 131, and 116 upper state ro-vibrational energies of the states (002), (012), (003), and (013), respectively. With a Watson-type effective Hamiltonian model, the ro-vibrational parameters of these four upper states were determined by a least-square fitting which can reproduce the ro-vibrational energies close to the experimental accuracy. The relative linestrengths are also discussed.     

Lattice vibration analysis of cryolite A3B′X6 and elpasolite A3BB′X6 compounds. A force constant calculation of Sr2ZnTeO6

A normal coordinate treatment of crystals with general formula A₃B′X₆ and A₂BB′X₆ with cubic structure (space group F_m3m) is made with the G-F matrix method. A modified valence force field is assumed to give a set of ten force constants for calculating all fundamental vibrations in the k = 0 approximation.     

Resonant Raman scattering in GaP in the E0 − E0 + Δ0 region

Resonant enhancement of the cross section for Raman scattering by TO phonons in GaP at the E₀ and E₀ + Δ₀ gaps has been observed using a continuously tunable pulsed dye laser pumped by a nitrogen laser and a gated photon counting system. The resonance at the spin-orbit split E₀ + Δ₀ gap is much weaker than that at E₀ and has not been observed previously in first-order Raman scattering. The results are in good agreement with theoretical predictions.     

A study of the K = 3nA1 - A2 centrifugal splitting in the 3ν2 and 4ν2 states of PH3 using a difference-frequency laser system

A frequency tunable infrared source has been constructed by using the (Ar-laser) - (dyelaser) difference frequency method developed by Pine and applied to the observation of the overtone bands of PH₃ 3ν₂ ← 0 and 4ν₂ ← ν₂ in the 3.4 μm region and 4ν₂ ← 0 in the 1.6-μm region. A Stark modulation method was used to increase the sensitivity of detection. For transitions which were well modulated, the minimum detectable absorption coefficient was estimated to be ～3 × 10^?7 cm^?1 using a 3-m cell. Emphasis was placed on the observation of the A₁-A₂ splitting for K = 3n rotational levels. For the 3ν₂ state splittings were observed for K = 3, 6, and 9 because PH₃ is a very nearly spherical top in this state. The magnitude and the J dependence of the observed K = 3n splittings have been analyzed by using a normal symmetric rotor Hamiltonian and a centrifugal distortion term of the form $\text{τ}{}_{\mathrm{xxxz}}\text{[(J}{}_{\mathrm{+}}{}^3\text{+ J}{}_{\mathrm{?}}{}^3\text{)J}{}_{\mathrm{z}}\text{+ J}{}_{\mathrm{z}}\text{(J}{}_{\mathrm{+}}{}^3\text{+ J}{}_{\mathrm{?}}{}^3\text{)]}\text{4}$.     

The high-resolution infrared spectrum of ethane-1,1,1-D3 rovibration analyses of the pseudoperpendicular A1A2ν9 + ν10 band and the parallel ν3 + ν4 and ν5 bands

A complete vibration-rotation analysis was made of the A₁A₂ combination band ν₉ + ν₁₀ of CH₃CD₃ at 2582 cm^?1. This band exhibits pseudoperpendicular structure due to the large effective Coriolis interaction constant (ζ ≈ 0.7), which couples the almost degenerate A₁ and A₂ vibrational components for all nonzero values of the rotational quantum number K, and gives a subband Q-branch spacing of 2.5 cm^?1. The location of the band center is assisted through an interruption of the perpendicular-like structure, since both K = 0 Q branches are forbidden by the vibrational and rotational selection rules. The conventional A₁ parallel bands ν₃ + ν₄ at 2507 cm^?1 and ν₅ (CC stretch) at 905 cm^?1 were also analyzed. For ν₅, a combination of numerical analysis and band contour simulation was used to determine a set of upper-state rotation parameters. Combination of the present results with previous data for ν₉ and 2ν₃ permits rotational parameters to be derived for the ν₄ and ν₁₀ fundamentals of CH₃CD₃. Neither of these fundamentals are amenable to straightforward analysis, both being very weak in the infrared and overlaid by the intense ν₁₁ fundamental.     

The ν1 + 3ν2 + 3ν3 and 4ν1 + ν2 + ν3 bands of ozone by CW-cavity ring down spectroscopy between 5900 and 5960 cm

The absorption spectrum of ozone, ¹⁶O₃, has been recorded in the 5903-5960 cm⁻¹ region by high sensitivity CW-cavity ring down spectroscopy (α_min ∼ 5 × 10⁻¹⁰ cm⁻¹). The ν₁ + 3ν₂ + 3ν₃ and 4ν₁ + ν₂ + ν₃ A-type bands centred at 5919.15 and 5947.07 cm⁻¹ were newly observed. A set of 173 and 168 energy levels could be experimentally determined for the (1 3 3) and (4 1 1) states, respectively. Except for a few K_a = 5 levels of the (4 1 1) state, the rotational structure of the two states was found mostly unperturbed. The spectroscopic parameters were determined from a fit of the corresponding line positions by considering the (1 3 3) and (4 1 1) states as isolated. The determined effective Hamiltonian and transition moment operators were used to generate a list of 785 transitions given as Supplementary Material.     

Determination of the B0 constant of C6H6

The ν₁₁ infrared band of gaseous benzene C₆H₆ is recorded at a resolution of 0.010 cm^?1. The analysis yields a number of constants, primarily B₀ = 0.1897543 ± 0.0000061 cm^?1 (standard error). This number is in perfect agreement with a value determined from a recent analysis of the ν₁ Raman band.     

Analysis of the ν3, A-type band of C2H3D

The ν₃, A-type band of C₂H₃D centered at 1288.780 cm^?1 has been analyzed up to J = 33 and K_a = 15. The spectral range from 1351 to 1235 cm^?1 was recorded with a grill-spectrometer “type Girard” and with a resolution of 0.06 cm^?1, and a wavenumber precision of about 2 × 10^?3 cm^?1. From 787 identified transitions it was possible to calculate the rotational energies in the ν₃ excited state, and to refine the corresponding set of parameters.     

Measurement of the spin correlation parameter A00nn and the polarization A00n0 in elastic p-p scattering between 400 and 600 MeV

We have measured the spin correlation parameter A_00nn and the polarization A_00n0 for p-p elastic scattering in the c.m. angular range between 30° and 90° at seven energies between 400 and 600 MeV. The experiment was performed at SIN using a polarized beam and target and a fast on-line event reconstruction method. The results are compared with phase-shift predictions.     

Vibrational spectra and force constants of symmetric tops: Rovibrational analysis of 2ν6 and 2ν6 − ν6 of H3Si35Cl and H3Si37Cl,and a new method for the determination of A0 and DK0

The gas-phase ir spectra of monoisotopic H₃Si³⁵Cl [35] and H₃Si³⁷Cl [37] in the 2ν₆ region near 1300 cm^?1 have been studied with a resolution of 0.05 cm^?1. A total of 467 and 1206 lines have been assigned for [35] and [37], respectively, and analyzed by a least-squares procedure, σ(J, K) ～ 6 × 10^?3cm^?1, to yield three parameters for the 2ν₆⁰ and six for the 2ν₆^±2 states for both isotopomers. In the ν₆ region $\text{32}\text{47}$ and $\text{127}\text{150}$ lines have been assigned to the hot bands 2ν₆⁰ ? ν₆^±1 and 2ν₆^±2 ? ν₆^±1 of [35] and [37], respectively. While a hot band 2ν_t⁰ ? ν_t^±1 does not provide any information above that available from ν_t^±1 and 2ν_t⁰, a hot band 2ν_t^±2 ? ν_t^±1 may supply extra data concerning the ground state. A new method for the evaluation of A₀ and D_K⁰ from combination differences of ν_t^±1, 2ν_t^±2, and 2ν_t^±2 ? ν_t^±1 of a symmetric top with C_3v symmetry is presented. Application to [35] and [37] yielded A₀ of 2.8447(5) and 2.8437(3) cm^?1, and D_K⁰ of 2.12(20) and 2.38(9) × 10^?5 cm^?1, respectively.     

High-resolution study of the ν1 + ν2 and ν2 + ν3 strongly interacting bands of D2Se

A high-resolution Fourier transform spectrum of the D₂^MSe species (M = 82, 80, 78, 77, and 76) in the region 2300-2500 cm⁻¹ was recorded for the first time and assigned. On the basis of these experimental data, rotation-vibration energies of the (1 1 0) and (0 1 1) vibrational states were fitted, and band centers, and rotational, centrifugal distortion, and resonance interaction parameters were determined for the main D₂⁸⁰Se species. The obtained set of 32 fitted parameters reproduces the 647 rotation-vibration energies with a rms deviation of 0.00024 cm⁻¹. The ν₁ + ν₂ and ν₂ + ν₃ bands of the other four isotopic species are analyzed as well.     

The ν2, 2ν2, 3ν2, ν4, and ν2 + ν4 bands of 15NH3

The ir absorption of gaseous ¹⁵NH₃ between 510 and 3040 cm^?1 was recorded with a resolution of 0.06 cm^?1. The ν₂, 2ν₂, 3ν₂, ν₄, and ν₂ + ν₄ bands were measured and analyzed on the basis of the vibration-rotation Hamiltonian developed by V. ?pirko, J. M. R. Stone, and D. Papou?ek (J. Mol. Spectrosc.60, 159–178 (1976)). A set of effective molecular parameters for the ν₂ = 1, 2, 3 states was derived, which reproduced the transition frequencies within the accuracy of the experimental measurements. For ν₄ and ν₂ + ν₄ bands the standard deviation of the calculated spectrum is about four times larger than the measurements accuracy: a similar result was found for ν₄ in ¹⁴NH₃ by ?. Urban et al. (J. Mol. Spectrosc.79, 455–495 (1980)). This result suggests that the present treatment takes into account only the most significant part of the rovibration interaction in the doubly degenerate vibrational states of ammonia.     

Microwave and sub-mmwave study of CH3SiH3 including the perturbation-allowed torsion-vibration difference band (ν12=0,ν6=3)↔(ν12=1,ν6=0)

The vibration-torsion-rotation Hamiltonian in CH₃SiH₃ has been investigated using Fourier transform microwave methods and tunable sideband far-infrared spectroscopy. Four different studies have been carried out. First, the Q-branch of the torsion-vibration difference band (ν₁₂=0,ν₆=3)↔(ν₁₂=1,ν₆=0) has been measured between 17.8 and 26.6 GHz. When three quanta of the torsional mode ν₆ are excited in the ground vibrational state (gs) for (σ=−1) torsional sublevels with K=6, these transitions become allowed through resonant Coriolis-like coupling to the lowest lying degenerate mode ν₁₂ with no quanta of ν₆ excited. Second, direct l-doubling transitions in the state (v₁₂=1, v₆=0) have been observed between 8.3 and 17.5 GHz for both torsional sublevels σ=0 and σ=±1. In the limit that the intervibrational interactions vanish, the σ-splitting between lines of the same J would be difficult to resolve, but frequency differences of more than 1 GHz due to these interactions have been determined. Third, the (J=1←0) spectrum just below 22 GHz has been re-measured with higher resolution for 0?v₆?4 in the gs and for (v₆=0) in ν₁₂. Finally, the (J=45←44) spectrum near 1 THz has been obtained for 0?v₆?2 in the gs. A global data set of 3423 frequencies has been formed by merging the present 123 measurements with the data set used recently in the simultaneous analysis of the ν₁₂ and ν₅ bands by Schroderus et al. [J. Chem Phys. 115 (2001) 1392]. By refining the (gs/ν₁₂/ν₅) Hamiltonian developed in this earlier work in which the torsional motion is grouped with the vibrational degrees of freedom, a good fit to within experimental error has been obtained by varying 45 parameters. A fit of comparable quality has also been obtained using a similar analysis in which the torsional motion is grouped with the rotational degrees of freedom. The values of the molecular constants determined in the two models are compared.