Precision-Spectroscopic Determination of the Binding Energy of a Two-Body Quantum System: The Hydrogen Atom and the Proton-Size Puzzle.

Precision measurements in Rydberg states of H with principal quantum number n in the range between 20 and 30 are reported. In the presence of homogeneous electric fields with strengths below 2 V cm^{-1}, these Rydberg states are subject to a linear Stark effect with accurately calculable Stark shifts. From the spectral positions of field-independent and field-dependent Rydberg-Stark states, we derive the n=20 and 24 Bohr energies, and the ionization energy with respect to the 2 ^{2}S_{1/2}(f=0,1) [short 2S(0,1)] metastable states. Combining these results with the 2S(1)-1S(1) transition frequency [C. G. Parthey et al., Phys. Rev. Lett. 107, 203001 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.203001; A. Matveev et al., Phys. Rev. Lett. 110, 230801 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.230801] and the 1S hyperfine splitting [L. Essen et al., Nature (London) 229, 110 (1971)NATUAS0028-083610.1038/229110a0], we determine the ionization frequency of the 1S(0) ground state to be 3 288 087 922 407.2(3.7)_{stat}(1.8)_{syst} kHz, which is the most precise value ever determined for the binding energy of a two-body quantum system. Using the 2S(0)-2P_{1/2}(1) interval [N. Bezginov et al., Science 365, 1007 (2019)SCIEAS0036-807510.1126/science.aau7807], we determine the Rydberg frequency to be cR_{∞}=3 289 841 960 204(15)_{stat}(7)_{syst}(13)_{2S-2P} kHz in a procedure that is insensitive to the value of the proton charge radius. These new results are discussed in the context of the proton-size puzzle.

Cold Ion-Molecule Chemistry: The Very Different Reactions of He⁺ with CO and NO.

The ion-molecule reactions He+ + CO → He + C+ + O and He+ + NO → He + N+ + O have been measured at collision energies between 0 and kB · 10 K. Strong variations of the rate coefficients are observed below kB · 5 K. The rate of the He+ + CO reaction decreases by ~30% whereas that of the He+ + NO reaction increases by a factor of ~1.5. These observations are interpreted in the realm of an adiabatic-channel capture model as arising from interactions between the ion charge and the dipole and quadrupole moments of CO and NO. We show that the different low-energy behavior of these reactions originates from the closed- vs. open-shell electronic structures of CO and NO.

Imaging-Assisted Single-Photon Doppler-Free Laser Spectroscopy and the Ionization Energy of Metastable Triplet Helium.

Skimmed supersonic beams provide intense, cold, collision-free samples of atoms and molecules and are one of the most widely used tools in atomic and molecular laser spectroscopy. High-resolution optical spectra are typically recorded in a perpendicular arrangement of laser and supersonic beams to minimize Doppler broadening. Typical Doppler widths are nevertheless limited to tens of MHz by the residual transverse-velocity distribution in the gas-expansion cones. We present an imaging method to overcome this limitation that exploits the correlation between the positions of the atoms and molecules in the supersonic expansion and their transverse velocities, and thus their Doppler shifts. With the example of spectra of (1s)(np) ^{3}P_{0-2}←(1s)(2s) ^{3}S_{1} transitions to high Rydberg states of metastable triplet He, we demonstrate the suppression of the residual Doppler broadening and a reduction of the full linewidths at half maximum to only about 1 MHz in the UV. Using a retroreflection arrangement for the laser beam and a cross-correlation method, we determine Doppler-free spectra without any signal loss from the selection, by imaging, of atoms within ultranarrow transverse-velocity classes. As an illustration, we determine the ionization energy of triplet metastable He and confirm the significant discrepancy between recent experimental [G. Clausen et al., Phys. Rev. Lett. 127, 093001 (2021)PRLTAO0031-900710.1103/PhysRevLett.127.093001] and high-level theoretical [V. Patkós et al., Phys. Rev. A 103, 042809 (2021)PLRAAN2469-992610.1103/PhysRevA.103.042809] values of this quantity.

Pulsed-ramped-field-ionisation zero-kinetic-energy photoelectron spectroscopy of the metastable rare-gas atoms Ar, Kr and Xe.

The photoionisation of the metastable rare-gas atoms Rg = Ar, Kr and Xe is investigated at the Rg+ […](ns)2(np)5 2P3/2 ← Rg[…](ns)2(np)5((n + 1)s) 13P2 photoionisation threshold (n = 3, 4 and 5 for Ar, Kr and Xe) using the technique of pulsed-ramped-field-ionisation zero-kinetic-energy (PRFI-ZEKE) photoelectron spectroscopy. This technique, which monitors the field ionisation of high Rydberg states induced by a slowly growing electric-field ramp after a prepulse of opposite polarity, was recently introduced to record photoelectron spectra with high resolution and high sensitivity [Harper, Chen, Boyé-Péronne and Gans, Phys. Chem. Chem. Phys., 2022, 117, 9353]. A tunable UV laser system with a bandwidth of 30 MHz is used here to establish the factors determining the resolution and overall accuracy of this new method. In particular, the effects of stray electric fields, and of the magnitude of the prepulse and the field ramp on PRFI-ZEKE photoelectron spectra are studied by combining experiments with numerical simulations of the field-ionisation of high Rydberg states and of the electron flight times from the ionisation spot to the detector. A spectral resolution of 0.05 cm-1 is demonstrated in the photoelectron spectrum of metastable Ar.

Reaction of an Ion and a Free Radical near 0 K: He+ + NO → He + N+ + O.

The reactions between ions and free radicals are among the fastest chemical reactions. They are predicted to proceed with large rates, even near 0 K, but so far, this prediction has not been verified experimentally. We report on measurements of the rate coefficient of the reaction between the ion He+ and the free radical NO at collision energies in the range between 0 and ∼ kB·10 K. To avoid heating of the ions by stray electric fields, the reaction is observed within the large orbit of a Rydberg electron of principal quantum number n ≥ 30, which shields the ion from external electric fields without affecting the reaction. Low collision energies are reached by merging a supersonic beam of He Rydberg atoms with a supersonic beam of NO molecules and adjusting their relative velocity using a chip-based Rydberg-Stark decelerator and deflector. We observe a strong enhancement of the reaction rate at collision energies below ∼kB·2 K. This enhancement is interpreted on the basis of adiabatic-channel capture-rate calculations as arising from the near-degenerate rotational levels of opposite parity resulting from the Λ-doubling in the X 2Π1/2 ground state of NO. With these new results, we examine the reliability of broadly used approximate analytic expressions for the thermal rate constants of ion-molecule reactions at low temperatures.

Multipole-moment effects in ion-molecule reactions at low temperatures: part III - the He+ + CH4 and He+ + CD4 reactions at low collision energies and the effect of the charge-octupole interaction.

We present experimental and theoretical studies of the He+ + CH4 and He+ + CD4 reactions at collision energies in the kB·(0-10) K range. Helium atoms in a supersonic beam are excited to a low-field-seeking Rydberg-Stark state and merged with a supersonic beam of CH4 or CD4 using a curved surface-electrode deflector. The ion-molecule reactions are studied within the orbit of the helium Rydberg [He(n)] electron, which suppresses stray-electric-fields-induced heating and makes it possible to reach very low collision energies. The collision energy is varied by adjusting the velocity of the He(n) atoms with the surface deflector, keeping the velocity of the methane beam constant. The reaction product ions (C(H/D)p+ with p∈ {1,2,3}) are collected in a time-of-flight mass spectrometer and monitored as a function of the collision energy. No significant energy-dependence of the total reaction yields of either reactions is observed. The measured relative reaction rate coefficient for the He+ + CH4 reaction is approximately twice higher than the one for the He+ + CD4 reaction. The CH+, CH2+ and CH3+ (CD+, CD2+ and CD3+) ions were detected in ratios 0.28(±0.04) : 1.00(±0.11) : 0.11(±0.04) [0.35(±0.07) : 1.00(±0.16):0.04+0.09-0.04]. We also present calculations of the capture rate coefficients for the two reactions, in which the interaction between the charge of the helium ion and the octupole moment of the methane molecule is included. The rotational-state-specific capture rate coefficients are calculated for states with J = (0-3) at collision energies below kB·15 K. After averaging over the rotational states of methane populated at the rotational temperature of the supersonic beam, the calculations only predict extremely weak enhancements (in the order of ∼0.4%) of the rate coefficients compared to the Langevin rate constant kL over the collision-energy range considered.

Multipole-moment effects in ion-molecule reactions at low temperatures: part II - charge-quadrupole-interaction-induced suppression of the He+ + N2 reaction at collision energies below kB·10 K.

We report on an experimental and theoretical investigation of the He+ + N2 reaction at collision energies in the range between 0 and kB·10 K. The reaction is studied within the orbit of a highly excited Rydberg electron after merging a beam of He Rydberg atoms (He(n), n is the principal quantum number), with a supersonic beam of ground-state N2 molecules using a surface-electrode Rydberg-Stark decelerator and deflector. The collision energy Ecoll is varied by changing the velocity of the He(n) atoms for a fixed velocity of the N2 beam and the relative yields of the ionic reaction products N+ and N2+ are monitored in a time-of-flight mass spectrometer. We observe a reduction of the total reaction-product yield of ∼30% as Ecoll is reduced from ≈kB·10 K to zero. An adiabatic capture model is used to calculate the rotational-state-dependent interaction potentials experienced by the N2 molecules in the electric field of the He+ ion and the corresponding collision-energy-dependent capture rate coefficients. The total collision-energy-dependent capture rate coefficient is then determined by summing over the contributions of the N2 rotational states populated at the 7.0 K rotational temperature of the supersonic beam. The measured and calculated rate coefficients are in good agreement, which enables us to attribute the observed reduction of the reaction rate at low collision energies to the negative quadrupole moment, Qzz, of the N2 molecules. The effect of the sign of the quadrupole moment is illustrated by calculations of the rotational-state-dependent capture rate coefficients for ion-molecule reactions involving N2 (negative Qzz value) and H2 (positive Qzz value) for |J, M〉 rotational states with J ≤ 5 (M is the quantum number associated with the projection of the rotational angular momentum vector J⃑ on the collision axis). With decreasing value of |M|, J⃑ gradually aligns perpendicularly to the collision axis, leading to increasingly repulsive (attractive) interaction potentials for diatomic molecules with positive (negative) Qzz values and to reaction rate coefficients that decrease (increase) with decreasing collision energies.

Reactions of H2, HD, and D2 with H2+, HD+, and D2+: Product-Channel Branching Ratios and Simple Models.

We present measurements of the product-channel branching ratios of the reactions (i) HD+ + HD forming H2D+ + D (38.1(30)%) and HD2+ + H (61.9(30)%), (ii) HD+ + D2 forming HD2+ + D (61.4(35)%) and D3+ + H (38.6(35)%), and (iii) D2+ + HD forming HD2++ D (60.5(20)%) and D3+ + H (39.5(20)%) at collision energies Ecoll near zero, i.e., below kB × 1 K. These branching ratios are compared with branching ratios predicted using three simple models: a combinatorial model (M1), a model (M2) describing the reactions as H-, H+-, D-, and D+-transfer processes, and a statistical model (M3) that relates the reaction rate coefficients to the translational and rovibrational state densities of the HnD3-n+ + H/D (n = 0, 1, 2 or 3) product channels. The experimental data are incompatible with the predictions of models M1 and M2 and reveal that the branching ratios exhibit clear correlations with the product state densities.

SI-traceable frequency dissemination at 1572.06 nm in a stabilized fiber network with ring topology.

Frequency dissemination in phase-stabilized optical fiber networks for metrological frequency comparisons and precision measurements are promising candidates to overcome the limitations imposed by satellite techniques. However, in an architecture shared with telecommunication data traffic, network constraints restrict the availability of dedicated channels in the commonly-used C-band. Here, we demonstrate the dissemination of an SI-traceable ultrastable optical frequency in the L-band over a 456 km fiber network with ring topology, in which data traffic occupies the full C-band. We characterize the optical phase noise and evaluate a link instability of 4.7 × 10-16 at 1 s and 3.8 × 10-19 at 2000 s integration time, and a link accuracy of 2 × 10-18. We demonstrate the application of the disseminated frequency by establishing the SI-traceability of a laser in a remote laboratory. Finally, we show that our metrological frequency does not interfere with data traffic in the telecommunication channels. Our approach combines an unconventional spectral choice in the telecommunication L-band with established frequency-stabilization techniques, providing a novel, cost-effective solution for ultrastable frequency-comparison and dissemination, and may contribute to a foundation of a world-wide metrological network.

Multipole-moment effects in ion-molecule reactions at low temperatures: part I - ion-dipole enhancement of the rate coefficients of the He+ + NH3 and He+ + ND3 reactions at collisional energies Ecoll/kB near 0 K.

The energy dependence of the rates of the reactions between He+ and ammonia (NY3, Y = {H,D}), forming NY2+, Y and He as well as NY+, Y2 and He, and the corresponding product branching ratios have been measured at low collision energies Ecoll between 0 and kB·40 K using a recently developed merged-beam technique [Allmendinger et al., ChemPhysChem, 2016, 17, 3596]. To avoid heating of the ions by stray electric fields, the reactions are observed within the large orbit of a highly excited Rydberg electron. A beam of He Rydberg atoms was merged with a supersonic beam of ammonia using a curved surface-electrode Rydberg-Stark deflector, which is also used for adjusting the final velocity of the He Rydberg atoms, and thus the collision energy. A collision-energy resolution of about 200 mK was reached at the lowest Ecoll values. The reaction rate coefficients exhibit a sharp increase at collision energies below ∼kB·5 K and pronounced deviations from Langevin-capture behaviour. The experimental results are interpreted in terms of an adiabatic capture model describing the rotational-state-dependent orientation of the ammonia molecules by the electric field of the He+ atom. The model faithfully describes the experimental observations and enables the identification of three classes of |JKMp〉 rotational states of the ammonia molecules showing different low-energy capture behaviour: (A) high-field-seeking states with |KM| ≥ 1 correlating to the lower component of the umbrella-motion tunnelling doublet at low fields. These states undergo a negative linear Stark shift, which leads to strongly enhanced rate coefficients; (B) high-field-seeking states subject to a quadratic Stark shift at low fields and which exhibit only weak rate enhancements; and (C) low-field-seeking states with |KM| ≥ 1. These states exhibit a positive Stark shift at low fields, which completely suppresses the reactions at low collision energies. Marked differences in the low-energy reactivity of NH3 and ND3-the rate enhancements in ND3 are more pronounced than in NH3-are quantitatively explained by the model. They result from the reduced magnitudes of the tunnelling splitting and rotational intervals in ND3 and the different occupations of the rotational levels in the supersonic beam caused by the different nuclear-spin statistical weights. Thermal capture rate constants are derived from the model for the temperature range between 0 and 10 K relevant for astrochemistry. Comparison of the calculated thermal capture rate coefficients with the absolute reaction rates measured above 27 K by Marquette et al. (Chem. Phys. Lett., 1985, 122, 431) suggests that only 40% of the close collisions are reactive.

Ionization Energy of the Metastable 2

In a recent breakthrough in first-principles calculations of two-electron systems, Patkós, Yerokhin, and Pachucki [Phys. Rev. A 103, 042809 (2021)PLRAAN2469-992610.1103/PhysRevA.103.042809] have performed the first complete calculation of the Lamb shift of the helium 2 ^{3}S_{1} and 2 ^{3}P_{J} triplet states up to the term in α^{7}m. Whereas their theoretical result of the frequency of the 2 ^{3}P←2 ^{3}S transition perfectly agrees with the experimental value, a more than 10σ discrepancy was identified for the 3 ^{3}D←2 ^{3}S and 3 ^{3}D←2 ^{3}P transitions, which hinders the determination of the He^{2+} charge radius from atomic spectroscopy. We present here a new measurement of the ionization energy of the 2 ^{1}S_{0} state of He [960 332 040.491(32) MHz] which we use in combination with the 2 ^{3}S_{1}←2 ^{1}S_{0} interval measured by Rengelink et al. [Nat. Phys. 14, 1132 (2018).NPAHAX1745-247310.1038/s41567-018-0242-5] and the 2 ^{3}P←2 ^{3}S_{1} interval measured by Zheng et al. [Phys. Rev. Lett. 119, 263002 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.263002] and Cancio Pastor et al. [Phys. Rev. Lett. 92, 023001 (2004)PRLTAO0031-900710.1103/PhysRevLett.92.023001] to derive experimental ionization energies of the 2 ^{3}S_{1} state [1152 842 742.640(32) MHz] and the 2 ^{3}P centroid energy [876 106 247.025(39) MHz]. These values reveal disagreements with the α^{7}m Lamb shift prediction by 6.5σ and 10σ, respectively, and support the suggestion by Patkós et al. of an unknown theoretical contribution to the Lamb shifts of the 2 ^{3}S and 2 ^{3}P states of He.

Charge-Transfer-Induced Predissociation in Rydberg States of Molecular Cations: MgAr.

Very little is known about the Rydberg states of molecular cations, i.e., Rydberg states having a doubly charged ion core. With the example of MgAr+, we present general features of the structure and dynamics of the Rydberg states of molecular cations, which we find are subject to the process of charge-transfer-induced predissociation. Our study focuses on the spectrum of low-n Rydberg states with potential-energy functions associated with the Mg+(3d and 4s) + Ar(1S0) dissociation asymptotes. In particular, we have recorded spectra of the 3dπΩ' (Ω' = 1/2, 3/2) Rydberg states, extending from the lowest (v' = 0) vibrational levels to their dissociation limits. This spectral range encompasses the region where the onset of predissociation by interaction with the mostly repulsive 2Σ and 2Π charge-transfer states associated with the Mg(3s2) + Ar+(2P1/2,3/2) dissociation asymptotes is observed. This interaction leads to very strong perturbations of the 3dπ Rydberg states of MgAr+, revealed by vibrational progressions exhibiting large and rapid variations of the vibrational intervals, line widths, and spin-orbit splittings. We attribute the anomalous sign and magnitude of the spin-orbit coupling constant of the 3dπ state to the interaction with a 2Π Rydberg state correlating to the Mg+(4p) + Ar(1S0) dissociation limit. To analyze our spectra and elucidate the underlying process of charge-transfer-induced predissociation, we implemented a model that allowed us to derive the potential-energy functions of the charge-transfer states and to quantitatively reproduce the experimental results. This analysis characterizes the main features of the dynamics of the Rydberg series converging to the ground state of MgAr2+. We expect that the results and analysis reported here are qualitatively valid for a broader range of singly charged molecular cations, which are inherently prone to charge-transfer interactions.

Spectroscopic characterization of a thermodynamically stable doubly charged diatomic molecule: MgAr2.

Although numerous doubly positively charged diatomic molecules (diatomic dications) are known from investigations using mass spectrometry and ab initio quantum chemistry, only three of them, NO2+, N22+ and DCl2+, have been studied using rotationally resolved optical spectroscopy and only about a dozen by vibrationally resolved double-ionization methods. So far, no thermodynamically stable diatomic dication has been characterized spectroscopically, primarily because of experimental difficulties associated with their synthesis in sufficient densities in the gas phase. Indeed, such molecules typically involve, as constituents, rare-gas, halogen, chalcogen, and metal atoms. We report here on a new approach to characterize molecular dications based on high-resolution photoelectron spectroscopy of the singly charged parent molecular cation and present the first spectroscopic characterization of a thermodynamically stable diatomic dication, MgAr2+. From the fully resolved vibrational and partially resolved rotational structures of the photoelectron spectra of 24MgAr+ and 26MgAr+, we determined the potential-energy function of the electronic ground state of MgAr2+, its dissociation (binding) energy (D0 = 10 690(3) cm-1), and its harmonic (ωe(24MgAr2+) = 327.02(11) cm-1) and anharmonic (ωexe(24MgAr2+) = 2.477(15) cm-1) vibrational constants. The analysis enables us to explain quantitatively how the strong bond arises in this dication despite the fact that Ar and Mg2+ both have a full-shell rare-gas electronic configuration.

The H2+ + HD reaction at low collision energies: H3+/H2D+ branching ratio and product-kinetic-energy distributions.

The fully state-selected reactions between H2+ molecules in the X+ 2Σg+(v+ = 0, N+ = 0) state and HD molecules in the X 1Σg+(v = 0, J = 0) state forming H3+ + D and H2D+ + H have been studied at collision energies Ecoll between 0 and kB·30 K with a resolution of about 75 mK at the lowest energies. H2 molecules in a supersonic beam were prepared in Rydberg-Stark states with principal quantum number n = 27 and merged with a supersonic beam of ground-state HD molecules using a curved surface-electrode Rydberg-Stark decelerator and deflector. The reaction between H2+ and HD was studied within the orbit of the Rydberg electron to avoid heating of the ions by stray electric fields. The reaction was observed for well-defined and adjustable time intervals, called reaction-observation windows, between two electric-field pulses. The first pulse swept all ions away from the reaction volume and its falling edge defined the beginning of the reaction-observation window. The second pulse extracted the product ions toward a charged-particle detector located at the end of a time-of-flight tube and its rising edge defined the end of the reaction-observation window. Monitoring and analysing the time-of-flight distributions of the H3+ and H2D+ products in dependence of the duration of the reaction-observation window enabled us to obtain information on the kinetic-energy distribution of the product ions and determine branching ratios of the H3+ + D and H2D+ + H reaction channels. The mean product-kinetic-energy release is 0.46(5) eV, representing 27(3)% of the available energy, and the H3+ + D product branching ratio is 0.225(20). The relative reaction rates correspond closely to Langevin capture rates down to the lowest energies probed experimentally (≈kB·50 mK).

Manipulating beams of paramagnetic atoms and molecules using inhomogeneous magnetic fields.

We review methods to manipulate the motion of pulsed supersonic atomic and molecular beams using time-independent and -dependent inhomogeneous magnetic fields. In addition, we discuss current and possible future applications and research directions.

Complete characterization of the 3p Rydberg complex of a molecular ion: MgAr+. II. Global analysis of the A+ 2Π and B+ 2Σ+ (3pσ,π) states.

We report a global study of the 3p Rydberg complex of the MgAr+ molecular ion. High-resolution spectroscopic data on the two spin-orbit components of the A+ electronic state were obtained by isolated-core multiphoton Rydberg-dissociation spectroscopy up to vibrational levels as high as v' = 29, covering more than 90% of the potential wells. Accurate adiabatic potential-energy functions of the A+ and B+ states, which together form the 3p Rydberg complex, were obtained in a global direct-potential-fit analysis of the present data and the extensive data on the B+ state reported in Paper I [D. Wehrli et al., J. Chem. Phys. 153, 074310 (2020)]. The dissociation energies of the B+ state, the two spin-orbit components of the A+ state, and the X+ state of MgAr+ are obtained with uncertainties (1 cm-1) more than two orders of magnitude smaller than in previous studies.

Complete characterization of the 3p Rydberg complex of a molecular ion: MgAr+. I. Observation of the Mg(3pσ)Ar+ B+ state and determination of its structure and dynamics.

We report on the experimental observation of the B+ 2Σ+ state of MgAr+ located below the Mg+(3p 2P3/2) + Ar(1S0) dissociation asymptote. Using the technique of isolated-core multiphoton Rydberg-dissociation spectroscopy, we have recorded rotationally resolved spectra of the B+ 2Σ+(v') ← X+ 2Σ+(v″ = 7) transitions, which extend from the vibrational ground state (v' = 0) to the dissociation continuum above the Mg+(3p 2P3/2) + Ar(1S0) dissociation threshold. The analysis of the rotational structure reveals a transition from Hund's angular-momentum-coupling case (b) at low v' values to case (c) at high v' values caused by the spin-orbit interaction. Measurements of the kinetic-energy release and the angular distribution of the Mg+ fragments detected in the experiments enabled the characterization of the dissociation mechanisms. The vibrational levels of the B+ state above v' = 6 are subject to predissociation into the Mg+(3p 2P1/2) + Ar(1S0) continuum, and the fragment angular distributions exhibit anisotropy ß parameters around 0.5, whereas direct dissociation into the continuum above the Mg+(3p 2P3/2) + Ar(1S0) asymptote is characterized by ß parameters approaching 2. Molecular ions excited to the B+ state with v' = 0-6 efficiently absorb a second photon to the repulsive part of the 2Σ+ state associated with the Mg+(3d 2D3/2,5/2) + Ar(1S0) continua. The interpretation of the data is validated by the results of ab initio calculations of the low-lying electronic states of MgAr+, which provided initial evidence for the existence of bound vibrational levels of the B+ state and for the photodissociation mechanisms of its low vibrational levels.

Precision Measurements in Few-Electron Molecules: The Ionization Energy of Metastable

Molecular helium represents a benchmark system for testing ab initio calculations on few-electron molecules. We report on the determination of the adiabatic ionization energy of the a ^{3}Σ_{u}^{+} state of He_{2}, corresponding to the energy interval between the a ^{3}Σ_{u}^{+} (v^{''}=0, N^{''}=1) state of He_{2} and the X^{+} ^{2}Σ_{u}^{+} (v^{+}=0, N^{+}=1) state of He_{2}^{+}, and of the lowest rotational interval of He_{2}^{+}. These measurements rely on the excitation of metastable He_{2} molecules to high Rydberg states using frequency-comb-calibrated continuous-wave UV radiation in a counterpropagating laser-beam setup. The observed Rydberg states were extrapolated to their series limit using multichannel quantum-defect theory. The ionization energy of He_{2} (a ^{3}Σ_{u}^{+}) and the lowest rotational interval of He_{2}^{+} (X^{+} ^{2}Σ_{u}^{+}) are 34 301.207 002(23)±0.000 037_{syst} cm^{-1} and 70.937 589(23)±0.000 060_{syst} cm^{-1}, respectively.

Spectroscopy of Highly Excited States of the Hydrogen Atom.

In this contribution, we describe the status of the development of a precision-spectroscopic experiment aimed at measuring transitions to states of high principal quantum number n of the hydrogen atom (H). These states form series (called Rydberg series) which converge for n → ∞ to the ionization threshold of H. The ionization energy of H can thus be determined directly by measuring the frequencies of transitions to high-n states and extrapolating the Rydberg series to n → ∞.