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Helium is a prototype three-body system and has long been a model system for developing quantum mechanics theory and computational methods. The fine-structure splitting in the 23P state of helium is considered to be the most suitable for determining the fine-structure constant α in atoms. After more than 50 years of efforts by many theorists and experimentalists, we are now working toward a determination of α with an accuracy of a few parts per billion, which can be compared to the results obtained by entirely different methods to verify the self-consistency of quantum electrodynamics. Moreover, the precision spectroscopy of helium allows determination of the nuclear charge radius, and it is expected to help resolve the ‘proton radius puzzle’. In this review, we introduce the latest developments in the precision spectroscopy of the helium atom, especially the discrepancies among theoretical and experimental results, and give an outlook on future progress.

International audience; We investigate collisional line-shape effects that are present in highly accurate experimental spectra of the 3-0 S(1) and 2-0 Q(1) molecular hydrogen absorption lines perturbed by helium. We clearly distin-guish the influence of six different collisional effects (i.e.: collisional broadening and shift, their speed dependencies and the complex Dicke effect) on the shapes of H-2 lines. We demonstrate that only a very specific combination of these six contributions, determined from our ab initio calculations, gives unprece-dentedly good agreement with experimental spectra. If any of the six contributions is neglected, then the experiment-theory comparison deteriorates at least several times. We also analyze the influence of the centrifugal distortion on our ab initio calculations and we demonstrate that the inclusion of this effect slightly improves the agreement with the experimental spectra. (C) 2021 The Author(s). Published by Elsevier Ltd.

Ro-vibrational transitions of the 00°3–00°0 band around 1.52 µm with line intensities in the order of 10−24 to 10−23 cm−1/(molecule·cm−2) have been recorded using a comb-assisted laser-locked cavity ring-down spectrometer with high sensitivity as well as high precision. In total, 88 line positions were determined with a sub-MHz uncertainty (1-σ), better than previous experimental results by 1–2 order of magnitude. N2-induced line shape parameters of 20 isolated transitions were derived by using the Voigt profile and the quadratic Speed-Dependent Voigt profile with relative uncertainties of 1–2% (1-σ). Comparisons of the line parameters determined in this work with literature experimental values are given.

A bright beam of metastable helium atoms is useful in various studies. Laser spectroscopy of helium in an atomic beam can provide a determination of the fine-structure constant and the nuclear charge radius, towards a test of quantum electrodynamics (QED). In these measurements, it is necessary to control not only the internal quantum state but also the translation motion of the helium atom. Here we present a setup producing an intense and speed-adjustable continuous beam of helium atoms. By using a combination of laser cooling, focusing, and deflection, helium atoms are prepared at the single quantum state of ${2}^{\phantom{\rule{0.16em}{0ex}}3}{S}_{1}$ ($m=0$), with a very narrow distribution of the longitudinal speed ($\ensuremath{\delta}{v}_{z}l\ifmmode\pm\else\textpm\fi{}4.5$ m/s). At the same time, we obtain a flux of $1.8\ifmmode\times\else\texttimes\fi{}{10}^{13}$ (atoms/s)/sr with a fractional fluctuation below 0.02%. The atomic-beam quality was investigated by laser spectroscopy, indicating a considerable improvement over those used in previous helium precision-spectroscopy measurements.

H2 is the most abundant molecule in the universe. It is also the only neutral molecule whose energy levels can be precisely calculated based on quantum electrodynamics and fundamental physical constants without using any adjustable parameters. Precision spectroscopy of the hydrogen molecule is of great importance in astrophysical observation and in testing fundamental physics as well. Here we review the theoretical and experimental spectroscopy studies of the electronic ground state of the hydrogen molecule. The frequency of the R(1) transition in the V =2-0 band of HD is also determined with an accuracy of 5×10−10, which is the most precisely measured ro-vibrational transition of the hydrogen molecule to date. By comparing the calculated and experimental results, we present perspectives of the precision spectroscopy of the hydrogen molecule in the determination of fundamental physical constants such as the proton-electron mass ratio.

Transitions of the 6ν3 overtone band of 14N216O near 775 nm have been studied by continuous-wave cavity ring-down spectroscopy. Line positions and intensities were derived from a fit of the line shape using a hard-collisional profile. The line positions determined with absolute accuracy of 5×10−4 cm−1 allowed us to reveal finer ro-vibrational couplings taking place after J>14 except a strong anharmonic interaction identified by the effective Hamiltonian model. The absolute line intensities have also been retrieved with an estimated accuracy of 2% for a majority of the unblended lines. A new set of ro-vibrational and dipole moment parameters were derived from the experimental values. A comparison between the line positions and intensities of the 6ν3 band obtained in this work and those from previous studies is given.

International audience; Fully quantum ab initio calculations of the collision-induced shapes of two rovibrational H-2 lines perturbed by He provide an unprecedented subpercent agreement with ultra-accurate cavity-enhanced measurements. This level of consistency between theory and experiment hinges on a highly accurate potential energy surface and a realistic treatment of the velocity changing and dephasing collisions. In addition to the fundamental importance, these results show that ab initio calculations can provide reference data for spectroscopic studies of planet atmospheres at the required accuracy level and can be used to populate spectroscopic line-by-line databases.

A laser-power-dependent shift has been observed in various atomic beam spectroscopy measurements, which was often treated by extrapolating the results to the zero-field limit. Here we present an experimental and theoretical study of this effect in the measurements of the $2{\phantom{\rule{0.16em}{0ex}}}^{3}S\ensuremath{-}2{\phantom{\rule{0.16em}{0ex}}}^{3}P$ transition frequency of $^{4}\mathrm{He}$. The light-force-induced shift was attributed as a result of modulated atomic trajectories induced by the standing-wave laser field and consequent distortions in the lineshape. Modulation of the beam spatial distributions was detected by imaging atoms at high laser power and was also simulated by the Monte Carlo wave-function approach. The nonlinear behavior of the light-force-shift was observed experimentally and reproduced by the simulations. The systematic shift in the extrapolated result at the zero-field limit was analyzed. As a consequence of this effect, a correction of +0.50(80) kHz was added to our previous result on the $2{\phantom{\rule{0.16em}{0ex}}}^{3}{S}_{1}\ensuremath{-}2{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}$ transition frequency [Phys. Rev. Lett. 119, 263002 (2017)], and the reevaluated value is 276 734 477 704.3(1.6) kHz.

Molecular transitions provide natural frequency standards for spectroscopy, telecommunication, and astrophysics. The frequency accuracy is also crucial in various tests of fundamental physics. A comb-locked cavity ring-down spectrometer measured lamb dips of sixty-one 12C16O transitions around 1.57 μm in the second overtone band. The positions were determined with an accuracy of a few kHz. A new set of rotational spectroscopic parameters was derived with 30 ground state combination difference for the ground vibrational state with a standard deviation of 4.5 kHz. It results in a refinement of the ro-vibrational spectroscopic constants for the v=3 vibrational state. These parameters allow the pure rotational line lists of the υ = 0 ← 0 and υ = 3 ← 3 in the 112 GHz – 3.89 THz regions.

Spectroscopy of molecules in the mid-infrared (MIR) region has important applications in various fields, such as astronomical observation, environmental detection, and fundamental physics. However, compared to that in the near-infrared, precision spectroscopy in the MIR is often limited by the light source and has not shown full potential in sensitivity. Here we report a cavity ring-down spectroscopy system using a tunable narrow-linewidth optical parametric oscillator, which fulfills the requirement of high sensitivity and high precision in the MIR region. The Lamb-dip spectrum of the N2O molecule at 2.7 μm was measured as a demonstration of spectroscopy in the MIR with kilohertz accuracy.

Precision spectroscopy of the hydrogen molecule is a test ground of quantum electrodynamics (QED), and may serve for determination of fundamental constants. Using a comb-locked cavity ring-down spectrometer, for the first time, we observed the Lamb-dip spectrum of the R(1) line in the overtone of HD. The line position was determined to be 217 105 182.79 $\pm0.03_{stat}\pm0.08_{syst}$ MHz ($\delta\nu/\nu=4\times 10^{-10}$), which is the most accurate transition ever measured for the hydrogen molecule. Moreover, from calculations including QED effects up to the order $m_e\alpha^6$, we obtained predictions for this R(1) line as well as for the HD dissociation energy, which are less accurate but signaling the importance of the complete treatment of nonadiabatic effects. Provided that the theoretical calculation reaches the same accuracy, the present measurement will lead to a determination of the proton-electron mass ratio with a precision of 1.3 parts per billion., Comment: 5 pages, 4 figures

The high-resolution absorption spectrum of acetylene is studied by Fourier-transform spectroscopy (FTS) in the 9280–10740 cm–1 region dominated by the 3ν3 band near 9640 cm−1. Line positions and intensities of 1899 12C2H2 and 151 12C13CH2 absorption lines are retrieved from a spectrum recorded at room temperature (298.5 K) with a pressure of 87.6 hPa and a path length of 105 m. The measured 12C2H2 lines belong to thirty-three bands, twelve of them being newly assigned. The lines of 12C13CH2 in normal abundance (2.2%) belong to seven bands. For comparison the HITRAN database in the same region includes 301 lines of four 12C2H2 bands. Spectroscopic parameters of the upper vibrational levels are derived from band-by-band fits of the line positions (typical rms values are on the order of 0.002 cm–1). The comparison to the HITRAN line list and to results obtained using the global effective operator approach reveals a number of significant deviations. The occurrence of local rovibrational perturbations affecting a number of the analyzed bands is illustrated by the case of the strong 3ν3 band.

Three bands 4003i–00001 (i=2, 3, 4) of the Fermi pentad of 12C16O2 near 830 nm have been recorded with a continuous-wave cavity ring down spectrometer. A sensitivity at the 5×10–11 cm−1 level allowed us to obtain line positions and intensities of these very weak bands. The measured line intensities of these three bands together with those published for the 10051–00001 and 10052–00001 bands were used to obtain the effective dipole moment parameters of 12C16O2 for the ΔP=17 series of transitions, where P=2V1+V2+3V3 is a polyad number (Vi (i=1, 2, 3) are vibrational quantum numbers). Comparisons of the measured line positions and intensities of the 4003i–00001 (i=2, 3, 4) bands to those from the AMES and GEISA line lists are given.

A set of water transitions in the 782–840 nm region, including 38 H 2 16 O lines, 12 HD 16 O lines, and 30 D 2 16 O lines, were recorded with a cavity ring-down spectrometer calibrated using precise atomic lines. Absolute frequencies of the lines were determined with an accuracy of about 5 MHz. Systematic shifts were found in the line positions given in the HITRAN database and the upper energy levels given in recent MARVEL studies.

The $2\text{ }^{3}S--2\text{ }^{3}P$ transition of $^{4}\mathrm{He}$ was measured by comb-linked laser spectroscopy using a transverse-cooled atomic beam. The centroid frequency was determined to be 276 736 495 600.0(1.4) kHz, with a fractional uncertainty of $5.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$. This value is not only more accurate but also differs by as much as $\ensuremath{-}49.5\text{ }\text{ }\mathrm{kHz}$ ($20\ensuremath{\sigma}$) from the previous result given by [Cancio Pastor et al., Phys. Rev. Lett. 92, 023001 (2004); Cancio Pastor et al.Phys. Rev. Lett.97, 139903(E) (2006); Cancio Pastor et al.Phys. Rev. Lett.108, 143001 (2012)]. In combination with ongoing theoretical calculations, this work may allow the most accurate determination of the nuclear charge radius of helium.

Precision spectroscopy of the hydrogen molecule can be used to verify the quantum electrodynamics theory (QED) in a molecular system. The electric quadrupole transitions of the second overtone of H 2 have been recorded with a continuous-wave cavity ring-down spectrometer. In total, eight lines in the 784–852 nm range have been observed, including the extremely weak S 3 (5) line with a calculated intensity of 9.2 × 10 - 31 cm/molecule. The absolute line positions at the zero pressure limit have been determined with an accuracy of 3 × 10 - 4 cm - 1 , agreeing well with the high-level quantum chemical calculations including relativistic and QED corrections. The deviations between the experimental and theoretical frequencies are less than 5 × 10 - 4 cm - 1 , which is only 20% of the claimed theoretical uncertainty.

The fine-structure splitting in the $2^{3}{P}_{J}$ ($J=0$, 1, 2) levels of $^{4}\mathrm{He}$ is of great interest for tests of quantum electrodynamics and for the determination of the fine-structure constant $\ensuremath{\alpha}$. The $2^{3}{P}_{0}\text{\ensuremath{-}}2^{3}{P}_{2}$ and $2^{3}{P}_{1}\text{\ensuremath{-}}2^{3}{P}_{2}$ intervals are measured by laser spectroscopy of the $^{3}{P}_{J}\text{\ensuremath{-}}2^{3}{S}_{1}$ transitions at 1083 nm in an atomic beam, and are determined to be $31\text{ }908\text{ }130.98\ifmmode\pm\else\textpm\fi{}0.13\text{ }\text{ }\mathrm{kHz}$ and $2\text{ }291\text{ }177.56\ifmmode\pm\else\textpm\fi{}0.19\text{ }\text{ }\mathrm{kHz}$, respectively. Compared with calculations, which include terms up to ${\ensuremath{\alpha}}^{5}\mathrm{Ry}$, the deviation for the $\ensuremath{\alpha}$-sensitive interval $2^{3}{P}_{0}\text{\ensuremath{-}}2^{3}{P}_{2}$ is only 0.22 kHz. It opens the window for further improvement of theoretical predictions and an independent determination of the fine-structure constant $\ensuremath{\alpha}$ with a precision of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$.

High-resolution Fourier-transform spectra of water samples enriched by deuterium and oxygen-18 at room temperature are analyzed in the range 969–2148 cm−1. Line positions of about 2470 transitions up to Jmax = 22 and Ka max = 12 of the ν2 bands of the HD18O and D 2 18 O molecules are reported. This has allowed the determination of extended sets of rotational energies of the (0 0 0) and (0 1 0) vibrational states for both molecules. The generation function model of an effective rotational Hamiltonian was used in the data reduction to account for the strong centrifugal distortion of the rotational levels. Values of effective Hamiltonian parameters have been determined. The RMS standard deviations of the least-squares fits of the energy levels were 2.4 × 10−4 cm−1 for 293 energy levels of the ground state and 3.2 × 10−4 cm−1 for 281 energy levels of the (010) state of D 2 18 O , and 2.6 × 10−4 cm−1 for 227 energy levels of the ground state and 4.2 × 10−4 cm−1 for 246 energy levels of the (0 1 0) state of HD18O. Comparisons of obtained data with the theoretical predictions as well as with other observations are presented.

The high-resolution Fourier-transform spectrum of the D216O molecule is recorded and analyzed in the region near 1.27 μ m (7360–8440 cm−1) where the bands of the V=3 (V=v1+v2/2+v3) polyad are located. A total of 2772 transitions have been assigned based on recent variational calculation of Shirin et al. [JQSRT 2008;109:549–58]. A set of 1094 energy levels (564 of which are new) is determined for nine vibrational states including those of newly reported (1 0 2) and (2 2 0) states. Calculations using an effective Hamiltonian are performed to establish reasonable ro-vibrational labeling of the observed energy levels. The latest variational calculation are found to agree well with the experiment for line positions (within 0.026 cm−1 on average); however, the calculated intensities for transitions to upper energy levels which are in close resonance with other states can be distorted.

This is the second of a series of articles reporting critically evaluated rotational-vibrational line positions, transition intensities, pressure dependences, and energy levels, with associated critically reviewed assignments and uncertainties, for all the main isotopologues of water. This article presents Preprint submitted to Journal of Quantitative Spectroscopy & Radiative Transfer10th June 2010 energy levels and line positions of the following singly deuterated isotopologues of water: HD16O, HD17O, and HD18O. The MARVEL (Measured Active Rotational-Vibrational Energy Levels) procedure is used to determine the levels, the lines, and their self-consistent uncertainties for the spectral regions 0–22 708, 0–1 674, and 0–12 105 cm−1 for HD16O, HD17O, and HD18O, respectively. For HD16O, 54 740 transitions were analyzed from 76 sources, the lines come from spectra recorded both at room temperature and from hot samples. These lines correspond to 36 690 distinct assignments and 8 818 energy levels. For HD17O, only 485 transitions could be analyzed from 3 sources; the lines correspond to 162 MARVEL energy levels. For HD18O, 8 729 transitions were analyzed from 11 sources and these lines correspond to 1 860 energy levels. The energy levels are checked against ones determined from accurate variational nuclear motion computations employing exact kinetic energy operators. This comparison shows that the measured transitions account for about 86 % of the anticipated absorbance of HD16O at 296 K and that the transitions predicted by the MARVEL energy levels account for essentially all the remaining absorbance. The extensive list of MARVEL lines and levels obtained are given in the Supplementary Material of this article, as well as in a distributed information system applied to water, W@DIS, where they can easily be retrieved. In addition, the transition and energy level information for H2 17O and H2 18O, given in the first paper of this series [J. Quant. Spectr. Rad. Transfer 110 (2009) 573-596], has been updated. Key words: Water vapor, transition wavenumbers, atmospheric physics, energy levels, MARVEL, information system, database, W@DIS, infrared spectra, microwave spectra, HD16O, HD17O, HD18O

An effective Hamiltonian built up to sixth order in the Amat–Nielsen ordering scheme describing all rovibrational energy levels in the ground electronic state and containing in explicit form all resonance interaction terms due to the approximate relations between harmonic frequencies ω1≈2ω2 and ω3≈4ω2 was applied to model the observed rovibrational line positions (collected from the literature) of 14N15N16O and 15N14N16O isotopologues of nitrous oxide. For 14N15N16O, 124 effective Hamiltonian parameters were fitted to near 28 000 observed line positions covering the 0.8–8860 cm−1 spectral range. The RMS of the weighted fit is 0.00126 cm−1 and dimensionless standard deviation is 1.48. For 15N14N16O, 121 effective Hamiltonian parameters were fitted to more than 31 000 observed line positions covering the same spectral interval. The RMS of the weighted fit is 0.00185 cm−1 and dimensionless standard deviation is 1.85. In both cases the models describe all available line positions with precision compatible to the measurement uncertainties. A number of local resonance perturbations was found and discussed. Among these perturbations there are interpolyad resonance Coriolis interactions. A comparison of HITRAN-2008 data with the calculations based on the fitted models is presented.

Persistent efforts in both theory and experiment have yielded increasingly precise understanding of the helium atom. Because of its simplicity, the helium atom has long been a testing ground for relativistic and quantum electrodynamic effects in few-body atomic systems theoretically and experimentally. Comparison between theory and experiment of the helium spectroscopy in 1s2p3PJ can potentially extract a very precise value of the fine structure constant a. The helium atom can also be used to explore exotic nuclear structures. In this paper, we provide a brief review of the recent advances in precision calculations and measurements of the helium atom.

The absorption spectrum of 14 N 15 N 16 O-enriched sample of nitrous oxide has been recorded at Doppler limited resolution with a Fourier-transform spectrometer in the spectral range 3500–9000 cm −1 . More than 12 000 transitions of 14 N 15 N 16 O were observed and ro-vibrationally assigned on the basis of the global effective Hamiltonian model. The band-by-band analysis led to the determination of the ro-vibrational parameters of a total of 107 bands. Among the 107 bands, 80 are newly observed, for 27 others the rotational analysis is significantly extended and improved. The effective Hamiltonian parameters are determined from global fitting to the observed line positions presented in this paper and collected from the literature. As a result, a set of 117 obtained effective Hamiltonian parameters reproduces 16 134 observed line positions of 148 bands with RMS of 0.0014 cm −1 .

Recent advances in theoretical calculations of ${\mathrm{H}}_{2}$ dissociation energies and ultra-accurate measurements of ${\mathrm{H}}_{2}$ transition frequencies give possibilities not only for testing QED and relativistic effects, but also for searching for physics beyond the standard model. In this paper we show that at the level of ${10}^{\ensuremath{-}4}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ the uncertainty of the Doppler-limited ${\mathrm{H}}_{2}$ line position determination is dominated by collisional line-shape effects. We question the paradigm that the unperturbed transition energy can be determined from linear extrapolation of the line shift to zero pressure.

Laser spectroscopy has been performed on a beam of neutral $^{4}\mathrm{He}$ atoms. By using transverse laser cooling and focusing, we are able to prepare a bright beam of atoms in the metastable state $2\phantom{\rule{0.16em}{0ex}}{}^{3}{S}_{1}$ deflected from the original effusive atomic beam. The initial state preparation is completed with optical pumping on the $2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{1}\ensuremath{\leftarrow}2\phantom{\rule{0.16em}{0ex}}{}^{3}{S}_{1}$ transition at the wavelength of 1083 nm, followed by laser spectroscopy on the $2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{1,2}\ensuremath{\leftarrow}2\phantom{\rule{0.16em}{0ex}}{}^{3}{S}_{1}$ transitions. The $2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{1}\ensuremath{-}2\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{2}$ fine-structure splitting is determined to be $2\phantom{\rule{0.16em}{0ex}}291\phantom{\rule{0.16em}{0ex}}177.69\ifmmode\pm\else\textpm\fi{}0.36\phantom{\rule{0.16em}{0ex}}\mathrm{kHz}$. The quantum interference effect is included in data extraction. This is the most precise laser spectroscopy measurement of the interval. Our result is in agreement with both the latest QED-based calculation and the most precise measurement conducted with microwave spectroscopy.

High resolution Fourier transform spectra of the HDS molecule were recorded and analyzed for the first time in the region of the bands m1 +2 m2 (3938.6 cm � 1 ),m1 + m3 (4522.6 cm � 1 ), 2m2 + m3 (4638.8 cm � 1 ), 2m1 + m2 (4767.7 cm � 1 ),m1 + m2 + m3 (5525.2 cm � 1 ), 3m1 (5560.6 cm � 1 ), m1 +2 m3 (7047.2 cm � 1 ), and 2m2 +2 m3 (7123.9 cm � 1 ). The ro-vibrational energies of the upper vibrational states of these bands together with the ro-vibrational energies of 12 other bands already studied at high resolution were used as inputs in a Global Fit analysis firstly described in [O.N. Ulenikov, G.A. Onopenko, H. Lin, J.-H. Zhang, Z.-Y. Zhou, Q.-S. Zhu, R.N. Tolchenov, J. Mol. Spectrosc. 189 (1998) 29–39]. In this case, the resonance interactions between the states (v1 v2 v3) and (v1 ±2 v2 « 1 v3 « 1) were taken into account. The resulting set of 143 parameters reproduces all the experimental data (2984 vibration–rotation energies of 20 vibrational states which correspond to about 9700 ro-vibrational transitions with J max. = 23) with accuracies comparable with the experimental uncertainties.

High-resolution Fourier-transform spectra of the D 2 S molecule in the regions of polyads of interacting vibrational states v = 3/2, 2, 5/2, 3 and 7/2 ( v = v 1 + v 2 /2 + v 3 ) were recorded for the first time with a Bruker IFS 120 Fourier-transform interferometer and analysed. A global fit of all currently available rotation–vibration energies has been made for 22 vibrational states of the D 2 S molecule. The resulting set of 231 parameters reproduces all the initial experimental data (about 3670 vibration–rotation energies which correspond to more than 9700 ro-vibrational transitions with J max = 25) with accuracies close to the experimental uncertainties.

The Fourier-transform absorption spectrum of H218O was recorded in the 6000–7940 cm−1 region and assigned on the base of the very accurate ab initio calculations by Partridge and Schwenke (PS) [J. Chem. Phys. 106 (1997) 4618–4639; J. Chem. Phys. 113 (2000) 6592–6597]. A set of 821 accurate rovibrational energy levels was obtained for six interacting states of the first hexad: (101), (120), (021), (200), (002), and (040). 290 of them are reported for the first time. The experimental line intensities are also estimated and compared with the PS calculations and the available literature data in the considered spectral range.

High-resolution Fourier transform infrared spectrum of H 2 32 S was recorded and analyzed in the region of the second hexade v = v 1 + 1 2 v 2 + v 3 = 2.5 . More than 1700 transitions were assigned to the 2ν1 + ν2, ν1 + ν2 + ν3, ν1 + 3ν2, 3ν2 + ν3, 5ν2, and ν2 + 2ν3 bands with the maximum value of quantum number J equal to 18, 18, 13, 11, 13, and 9, respectively. The theoretical analysis was fulfilled with a Hamiltonian model which takes into account numerous resonance interactions between all the vibrational states in this polyad. By a least-square fitting, finally 505 upper energy levels were reproduced by 80 parameters with an rms deviation of 0.0019 cm−1.

The absolute line intensities of 13 C 16 O2 were retrieved from Fourier-transform spectra recorded in the region 4200–8500 cm � 1 . The accuracy of the line intensity determination is estimated to be 5% or better for most lines and about 10% for weak ones. The vibrational transition dipole moments squared and Herman–Wallis coefficients have been determined. The global fittings of the observed line intensities within the framework of the effective operators approach have been performed. As the result of the fittings, most line intensities are reproduced within the experimental accuracy. The comparison between the new measured data and the HITRAN database are also carried out.

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.

The high-resolution absorption spectrum of the HDO molecule was recorded with a Fourier-transform interferometer in the region of 8900–9600 cm −1 , where the strongly interacted bands 2 ν 1 + ν 3 , 3 ν 1 + ν 2 , ν 1 + 2 ν 2 + ν 3 , 2 ν 1 + 3 ν 2 , 4 ν 2 + ν 3 , ν 1 + 5 ν 2 , and 7 ν 2 are located. About 1000 transitions were assigned to these seven bands based on the ab initio predictions [J. Chem. Phys. 106 (1997) 4618]. Altogether, 375 upper energy levels were determined, including 24 energy levels of the highly excited bending (070) state. On that basis, the necessity of the “Effective Hamiltonian” concept in the spectroscopic analysis is discussed.

High-resolution Fourier transform infrared spectrum of H2S was recorded and analyzed in the region of the v = v 1 + 1 2 v 2 + v 3 = 3.5 polyad. More than 450 transitions were assigned to the 3ν1 + ν2 and 2ν1 + ν2 + ν3 bands with the maximum values of quantum numbers J and Ka equal to 14, 7, and 14, 9 for these two bands, respectively. The theoretical analysis was fulfilled with the Hamiltonian which takes into account strong resonance interactions among the studied vibrational states (3 1 0), (2 1 1), and also “dark” states (0 3 2) and (2 3 0). The rms deviation is 0.0019 cm−1. The intensity borrowing effect in the doublets in the P-branch transitions of the 3ν1 + ν2 and 2ν1 + ν2 + ν3 bands is observed and discussed.

High-resolution Fourier transform infrared spectrum of H 2 S was recorded and analyzed in the region of the v = v 1 + v 2 /2+ v 3 =3 poliad. Experimental transitions were assigned to the 3 ν 1 , 2 ν 1 + ν 3 , ν 1 +2 ν 3 , 3 ν 3 , 2 ν 1 +2 ν 2 , and ν 1 +2 ν 2 + ν 3 bands with the maximum value of quantum number J equal to 11, 14, 10, 11, 8, and 11, respectively. The theoretical analysis was fulfilled with the Hamiltonian model which takes into account numerous resonance interactions between all the mentioned vibrational states. The rms deviation of the reproduction of 510 upper energy levels (derived from more than 1550 transitions) with 75 parameters was 0.0022 cm −1 .

The high-resolution (0.005 cm −1 ) Fourier transform infrared spectrum of PH3 is recorded in the region between 3280 and 3580 cm −1 where the following bands are located: ν 1 +ν 4 (E), ν 3 +ν 4 (E), ν 3 +ν 4 (A 1 ) , forbidden on symmetry band ν3+ν4(A2), and very weak bands ν 1 +ν 2 (A 1 ), ν 2 +ν 3 (E) . Transitions are assigned to the first four ones. Vibrational analysis of known experimental data is made.

The absorption spectrum of a 13 C enriched carbon dioxide sample has been recorded with a Fourier-transform spectrometer in the spectral range 4000–9500 cm −1 . In addition to six bands observed from the spectrum of the atmosphere of Venus in this region, eight new 16 O 13 C 18 O bands were measured. The new observations together with the data collected from the literature have been used to fit parameters of an effective Hamiltonian for the 16 O 13 C 18 O. More than 4000 line positions in 38 bands have been used to derive 48 parameters of effective Hamiltonian. The RMS (root-mean-square of residuals) of the fit is 0.00106 cm −1 .

The weak overtone transitions of nitrous oxide, N 2 O, have been investigated around 1.05 μm by Fourier Transform spectroscopy and intracavity laser absorption spectroscopy (ICLAS) using different vertical external cavity surface emitting lasers (VECSELs). Nine bands were rotationally analyzed revealing the occurrence of some local rotational perturbations. The interaction mechanisms and the perturbers are univocally assigned on the basis of the effective Hamiltonian model. In two cases, interpolyad couplings were evidenced indicating that the polyad version of the effective Hamiltonian has to be extended to include Coriolis and interpolyad anharmonic interactions.

An Intracavity Laser Absorption Spectrometer (ICLAS) based on a Vertical External Cavity Surface Emitting Laser (VECSEL) has been used to record the absorption spectrum of H2S between 9540 and 10 000 cm −1 with pressures up to 122 Torr (160.5 hPa) and equivalent absorption path lengths up to 45 km. More than 1600 absorption lines were attributed to the transitions reaching the highly excited (40±,0), (30±,2), and (11+,4) states (local mode notation). The existing information relative to the (40±,0) local mode bright pair at 9911.02 cm −1 was considerably enlarged, while the other states are reported for the first time. Eight hundred and ninety two precise energy levels were derived, including 181 and 28 levels for the H 2 34 S and H 2 33 S minor isotopomers, respectively. These energy levels were fitted using a Watson-type rotational Hamiltonian and the spectroscopic parameters were obtained, yielding an rms deviation of 0.006 cm −1 for the H 2 32 S species—close to the experimental accuracy. The dark states—(20+,4) and (11+,4)—at 9647.77 and 9744.88 cm −1 , respectively, were found to perturb the observed energy levels and were then included into the final energy levels modeling. The (40±,0) states are very close to the local mode limit, i.e., with a mostly identical rotational structure. The (30±,2) states are separated by 0.077 cm −1 and this separation holds for most of the rotational sublevels. The resonance interactions between the three local mode pairs—(40±,0), (30±,2), and (20±,4)—and the (11+,4) state affect in some cases specifically one of the component of the pair and then the energy separation of the corresponding near degenerate rotational levels. Line intensities were obtained on the basis of the relative intensities measured by ICLAS and from absolute values of the stronger lines measured separately by Fourier Transform Spectroscopy associated with a multipass cell. The transition intensities could be successfully modeled and the integrated band intensities are given and discussed.

This paper is the fourth of a series of papers reporting critically evaluated rotational–vibrational line positions, transition intensities, pressure dependences, and energy levels, with associated critically reviewed assignments and uncertainties, for all the main isotopologues of water. This paper presents energy level and transition data for the following doubly and triply substituted isotopologues of water: D216O, D217O, and D218O. The MARVEL (Measured Active Rotational–Vibrational Energy Levels) procedure is used to determine the levels, the lines, and their self-consistent uncertainties for the spectral regions 0–14 016, 0–7969, and 0–9108 cm−1 for D216O, D217O, and D218O, respectively. For D216O, D217O, and D218O, 53 534, 600, and 12 167 lines are considered, respectively, from spectra recorded in absorption at room temperature and in emission at elevated temperatures. The number of validated energy levels is 12 269, 338, and 3351 for D216O, D217O, and D218O, respectively. The energy levels have been checked against the ones determined, with an average accuracy of about 0.03 cm−1, from variational rovibrational computations employing exact kinetic energy operators and an accurate potential energy surface. Furthermore, the rovibrational labels of the energy levels have been validated by an analysis of the computed wavefunctions using the rigid-rotor decomposition (RRD) scheme. The extensive list of MARVEL lines and levels obtained is deposited in the Supplementary Material of this paper, in a distributed information system applied to water, W@DIS, and on the official MARVEL website, where they can easily be retrieved.

The high-resolution Fourier transform spectrum of the D 2 O molecule were recorded and analyzed in the region near 0.97 μm (10 200–10 440 cm −1 ) where the bands of the v =4 ( v = v 1 + v 2 /2+ v 3 ) polyad are located. Transitions belonging to the strongest band of the polyad, 3ν 1 +ν 3 , are assigned up to the value of the rotational angular momentum quantum number J =13. The presence of strong local resonance interactions allowed us to assign some transitions to the very weak band 4ν 1 . Upper states energies obtained on that basis were fitted with a Hamiltonian model which took into account resonance interactions between the states of the v =4 polyad. The derived spectroscopic parameters reproduce the overwhelming majority of assigned transitions within experimental accuracy.

The high-resolution Fourier transform spectrum of the DO 35 Cl molecule was recorded and analyzed in the region of the two lowest D–O overtone bands, 2ν 1 and 3ν 1 . Because of the presence of strong resonance interactions, the influence of the (130) state on the (200) state, and also that of the (221), (230) states on the (300) sate, was taken into account. Transitions belonging to the 2ν 1 and 3ν 1 bands were assigned up to J max. =35 in both cases. The sets of spectroscopic parameters and resonance coefficients obtained from the fit reproduce the “experimental” rovibrational energies of the (200) and (300) vibrational states with accuracies close to experimental uncertainties.

The high-resolution Fourier transform spectrum of the HDO molecule was recorded and analyzed in the region 6140–7040 cm −1 where the bands ν 1 +ν 3 , 2ν 2 +ν 3 , and 2ν 1 +ν 2 are located. The presence of strong local resonance interactions allowed us to assign some tens of transitions to the weak bands 5ν 2 and ν 1 +3ν 2 as well. Spectroscopic parameters of the analyzed bands were estimated. They reproduce initial upper energies with the accuracy close to experimental uncertainties.

Analysis of the high-resolution Fourier transform spectra of the D(2)O first decade was carried out in the framework of the Hamiltonian model which took into account resonance interactions between the seven states, (300), (201), (102), (003), (220), (121), and (022). Assigned from the experimentally recorded spectrum transitions belonged to the four bands, 2nu(1) + nu(3), 3nu(3), nu(1) + 2nu(2) + nu(3), and 3nu(1), gave the possibility both of obtaining rotational, centrifugal distortion, and resonance interaction parameters of "appeared" states, (201), (003), (121), and (300), and of estimating from the fit band centers, rotational, and resonance interaction parameters of the three "dark" states, (220), (022), and (102). Copyright 2000 Academic Press.

Wepresentafully ab initiomodelandcalculationsofthespectralshapesofabsorptionlinesinapuremolecular gas under conditions where the influences of collisions and of the Doppler effect are significant. Predictions of the time dependence of dipole autocorrelation functions (DACFs) are made for pure CO2 at room temperature using requantized classical molecular dynamics simulations. These are carried, free of any adjusted parameter, on the basis of an accurate anisotropic intermolecular potential. The Fourier-Laplace transforms of these DACFs then yield calculated spectra which are analyzed, as some measured ones, through fits using Voigt line profiles. Comparisonsbetweentheoryandvariousexperimentsnotonlyshowthatthemainline-shapeparameters(Lorentz pressure-broadening coefficients) are accurately predicted, but that subtle observed non-Voigt features are also quantitatively reproduced by the model. These successes open renewed perspectives for the understanding of the mechanisms involved (translational-velocity and rotational-state changes and their dependences on the molecular speed) and the quantification of their respective contributions. The proposed model should also be of great help for the test of widely used empirical line-shape models and, if needed, the construction of more physically based ones.

International audience; The very weak S(0)-S(3) electric quadrupole transitions of the second overtone band of molecular hydrogen have been recorded in the laboratory by continuous-wave cavity ring-down spectroscopy near 0.8 μm. The ultrahigh sensitivity of the spectrometer (αmin ~ 1 × 10-10 cm-1) allows us to detect the considered transitions at a relatively low sample pressure (50-750 torr). The line positions, intensity, and pressure-shift coefficients are derived from a fit of the line shape using a Galatry profile. Compared with literature values, the relative differences between the experimental and theoretical transition intensities are reduced by one order of magnitude, reaching a value of about 2% mainly dependent of the line-shape function adopted for the profile fitting. The thermal equilibrium relative intensity of the S(1) to S(0) line is determined with an accuracy of 0.4%, which can be used to probe the ortho- to para-H2 concentration ratio. Our measurements confirm the quality of the high-level ab initio calculations, including the relativistic and quantum electrodynamics corrections.

Atom trap trace analysis, a laser-based atom counting method, has been applied to analyze atmospheric $^{39}\mathrm{Ar}$ ($\mathrm{\text{half-life}}=269\text{ }\text{ }\mathrm{yr}$), a cosmogenic isotope with an isotopic abundance of $8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$. In addition to the superior selectivity demonstrated in this work, the counting rate and efficiency of atom trap trace analysis have been improved by 2 orders of magnitude over prior results. The significant applications of this new analytical capability lie in radioisotope dating of ice and water samples and in the development of dark matter detectors.

The Boltzmann constant kB is a fundamental physical constant in thermodynamics. The present CODATA recommended value of kB is 1.3806488(13) × 10–23 J/K (relative uncertainty 0.91 ppm), which is mainly determined by acoustic methods. Doppler broadening thermometry (DBT) is an optical method which determines kB T by measuring the Doppler width of an atomic or molecular transition. The methodology and problems in DBT are reviewed, and DBT measurement using the sensitive cavity ring-down spectroscopy (CRDS) is proposed. Preliminary measurements indicate that CRDS-based DBT measurement can potentially reach an accuracy at the 1 ppm level.