Quantum electrodynamic effects have been systematically tested in the progression of rotational quantum states in the X 1Σ(g)(+), v=0 vibronic ground state of molecular hydrogen. High-precision Doppler-free spectroscopy of the EF 1Σ(g)(+)-X 1Σ(g)(+) (0,0) band was performed with 0.005  cm(-1) accuracy on rotationally hot H2 (with rotational quantum states J up to 16). QED and relativistic contributions to rotational level energies as high as 0.13  cm(-1) are extracted, and are in perfect agreement with recent calculations of QED and high-order relativistic effects for the H2 ground state.

The strong electronic absorption systems of the B 1 u ÿ X 1 g Lyman and the C 1 u ÿ X 1 g Werner bands can be used to probe possible mass-variation effects on a cosmological time scale from spectra observed at high redshift, not only in H 2 but also in the second most abundant hydrogen isotopomer HD. High resolution laboratory determination of the most prominent HD lines at extreme ultraviolet wavelengths is performed at an accuracy of = 5 10 ÿ8 , forming a database for comparison with astrophysical data. Sensitivity coefficients K i d ln i =d ln are determined for HD from quantum ab initio calculations as a function of the proton-electron mass ratio . Strategies to deduce possible effects beyond first-order baryon/lepton mass ratio deviations are discussed. DOI: 10.1103/PhysRevLett.100.093007 PACS numbers: 33.20.ÿt, 06.20.Jr, 95.30.Dr, 98.80.Bp The observation of spectral features at high redshift (z 2-3) provides an opportunity to probe minute variations of some fundamental constants over time intervals of 10 10 years, corresponding to 80% of the lifetime of the Universe. For the fine structure constant evidence has been reported for a temporal drift at 5 significance [1]. Variation of another fundamental constant, the dimensionless proton-electron mass ratio m p =m e , may be probed through spectra of molecules. Recently, an indication for a possible decrease of was reported at = 2:45 0:59 10 ÿ5 over a time interval of 12 10 9 years [2,3]. This result is derived from a set of 76 H 2 spectral lines in two absorption systems at z 2:59 and z 3:02 in the line of sight towards quasars Q0405 ÿ 443 and Q0347 ÿ 383 [4]. From observations of the NH 3 inversion splitting in the astrophysical object B0218 357 at z 0:68, a tight constraint upon variation at = 0:6 1:9 10 ÿ6 was deduced [5]. These seemingly contradictory results might be reconciled by invoking the concept of a phase transition having occurred at z 1, transiting from a matter-dominated to a darkenergy-dominated Universe; variation of constants is hypothesized to occur only before the phase transition, henceThe comparison of spectral lines over cosmological time scales depends on the availability of spectral transitions that can be observed at high accuracy and at high redshift. Molecular hydrogen is the most abundant molecule in the Universe by orders of magnitude. The abundance of the deuterated HD species competes with other abundant molecules such as CO and CH such that it is worthwhile to consider the opportunity of using HD absorption for probing mass-variation effects. HD lines in the Lyman bands have indeed been observed in the object Q1232 082 at z 2:34 [7].To facilitate this opportunity, a set of highly accurate zero-redshift (laboratory) transition wavelengths of HD electronic absorption lines is required. Here we report on the spectral calibration of zero-redshift HD lines in the B 1 u ÿ X 1 g Lyman and the C 1 u ÿ X 1 g Werner bands, referred to as Lv and Wv bands with v the vibrational quantum number, in the extreme ultraviolet range 100-11...

The 3pπD (1)Π(u) state of the H(2) molecule was reinvestigated with different techniques at two synchrotron installations. The Fourier transform spectrometer in the vacuum ultraviolet wavelength range of the DESIRS beamline at the SOLEIL synchrotron was used for recording absorption spectra of the D (1)Π(u) state at high resolution and high absolute accuracy, limited only by the Doppler contribution at 100 K. From these measurements, line positions were extracted, in particular, for the narrow resonances involving (1)Π(u) (-) states, with an accuracy estimated at 0.06 cm(-1). The new data also closely match multichannel quantum defect calculations performed for the Π(-) components observed via the narrow Q-lines. The Λ-doubling in the D (1)Π(u) state was determined up to v=17. The 10 m normal incidence scanning monochromator at the beamline U125/2 of the BESSY II synchrotron, combined with a home-built target chamber and equipped with a variety of detectors, was used to unravel information on ionization, dissociation, and intramolecular fluorescence decay for the D (1)Π(u) vibrational series. The combined results yield accurate information on the characteristic Beutler-Fano profiles associated with the strongly predissociated Π(u) (+) parity components of the D (1)Π(u) levels. Values for the parameters describing the predissociation width as well as the Fano-q line shape parameters for the J=1 and J=2 rotational states were determined for the sequence of vibrational quantum numbers up to v=17.

We report on the realization of a heavy "Bohr atom," through the spectroscopic observation of a Rydberg series of bound quantum states at principal quantum numbers n=140 to 230. The system is made heavy by replacing an electron inside a hydrogen atom by a composite H- particle, thus forming a H+H- Coulombically bound system obeying the physical laws of a generalized atom with appropriate mass scaling.

The D 1 Πu -X 1 Σ + g absorption system of molecular deuterium has been re-investigated using the VUV Fourier -Transform (FT) spectrometer at the DESIRS beamline of the synchrotron SOLEIL and photon-induced fluorescence spectrometry (PIFS) using the 10 m normal incidence monochromator at the synchrotron BESSY II. Using the FT spectrometer absorption spectra in the range 72 -82 nm were recorded in quasi static gas at 100 K and in a free flowing jet at a spectroscopic resolution of 0.50 and 0.20 cm −1 respectively . The narrow Q-branch transitions, probing states of Π − symmetry, were observed up to vibrational level v = 22. The states of Π + symmetry, known to be broadened due to predissociation and giving rise to asymmetric Beutler-Fano resonances, were studied up to v = 18. The 10 m normal incidence beamline setup at BESSY II was used to simultaneously record absorption, dissociation, ionization and fluorescence decay channels from which information on the line intensities, predissociated widths, and Fano q-parameters were extracted. R-branch transitions were observed up to v = 23 for J = 1-3 as well as several transitions for J = 4 and 5 up to v = 22 and 18 respectively. The Q-branch transitions are found to weakly predissociate and were observed from v = 8 to the final vibrational level of the state v = 23. The spectroscopic study is supported by two theoretical frameworks. Results on the Π − symmetry states are compared to ab initio multi-channel-quantum defect theory (MQDT) calculations, demonstrating that these calculations are accurate to within 0.5 cm −1 . Furthermore, the calculated line intensities of Q-lines agree well with measured values. For the states of Π + symmetry a perturbative model based on a single bound state interacting with a predissociation continuum was explored, yielding good agreement for predissociation widths, Fano q-parameters and line intensities.

Absorption spectroscopy in the vacuum ultraviolet (VUV) domain was performed on the hydrogen-deuteride molecule with a novel Fourier-Transform spectrometer based upon wavefront division interferometry. This unique instrument, which is a permanent endstation of the undulator-based beamline DESIRS on the synchrotron SOLEIL facility, opens the way to Fourier-Transform spectroscopy in the VUV range. The HD spectral lines in the Lyman and Werner bands were recorded in the 87-112 nm range from a quasi-static gas sample in a windowless configuration and with a Doppler-limited resolution. Line positions of some 268 transitions in the B 1 Σ + u (v ′ = 0 − 30) ← X 1 Σ + g (v ′′ = 0) Lyman bands and 141 transitions in the C 1 Πu(v ′ = 0 − 10) ← X 1 Σ + g (v ′′ = 0) Werner bands were deduced with uncertainties of 0.04 cm −1 (1σ) which correspond to ∆λ/λ ∼ 4 × 10 −7. This extensive laboratory database is of relevance for comparison with astronomical observations of H 2 and HD spectra from highly redshifted objects, with the goal of extracting a possible variation of the proton-to-electron mass ratio (µ = mp/me) on a cosmological time scale. For this reason also calculations of the so-called sensitivity coefficients K i were performed in order to allow for deducing constraints on ∆µ/µ. The K i coefficients, associated with the line shift that each spectral line undergoes as a result of a varying value for µ, were derived from calculations as a function of µ solving the Schrödinger equation using ab initio potentials.

A series of discrete resonances was observed in the spectrum of H 2 , which can be unambiguously assigned to bound quantum states in the 1/R Coulombic potential of the H + H -ion-pair system. Two-step laser excitation was performed, using tunable extreme ultraviolet radiation at λ ) 94-96 nm in the first step, and tunable ultraviolet radiation in the range λ ) 310-350 nm in the second step. The resonances, detected via H + and H 2 + ions produced in the decay process, follow a sequence of principal quantum numbers (n ) 140-230) associated with a Rydberg formula in which the Rydberg constant is mass scaled. The series converges upon the ionic H + H -dissociation threshold. This limit can be calculated without further assumptions from known ionization and dissociation energies in the hydrogen system and the electronegativity of the hydrogen atom. A possible excitation mechanism is discussed in terms of a complex resonance. Detailed measurements are performed to unravel and quantify the decay of the heavy Rydberg states into molecular H 2 + ions, as well as into atomic fragments, both H(n ) 2) and H(n ) 3). Lifetimes are found to scale as n 3 .

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