The Stark effect in autoionizing high-n Rydberg states decouples the Rydberg electron from the ion core through ℓ mixing with core-nonpenetrating high-ℓ states. The Rydberg states become long-lived, which is ideal for precision spectroscopy, and their structures reflect the fine and hyperfine structures of the ion-core levels. We report on precision measurements, in weak electric fields, of the fine and hyperfine structures of two distinct categories of high autoionizing molecular Rydberg-Stark states differing by the nature of the ion-core angular momentum: Rydberg states of para-H_{2} (total nuclear spin I=0,2) with a rotationally excited (N^{+}=2) H_{2}^{+} ion core and Rydberg states of ortho-D_{2} (I=0,2) with a rotationless (N^{+}=0) ion core. The spectra reveal striking differences which are interpreted as arising from the dominance of anisotropic charge-quadrupole interactions between the rotating quadrupolar ion core and the Rydberg electron in para-H_{2} and the absence of such interactions in rotationless ortho-D_{2} Rydberg states. In ortho-D_{2}, the dominant interaction, the magnetic Fermi-contact hyperfine interaction in the ion core, does not significantly affect the motion of the Rydberg electron. By analyzing these spectra based on a treatment combining multichannel quantum-defect theory and matrix diagonalization, we derive new experimental values of the hyperfine coupling constant b_{F}=139.84(5)  MHz of D_{2}^{+}(v^{+}=1,N^{+}=0), the spin-rotation coupling constant c_{e}=39.62(11)  MHz of H_{2}^{+}(v^{+}=1,N^{+}=2) and the fundamental vibrational interval of ortho-D_{2}^{+} [47 279 980.8(1.9) MHz]. The approach followed here in the study of molecular Rydberg-Stark states is general and broadly applicable to measurements of the fine and hyperfine structures of molecular cations.

We present a general theoretical treatment and calculations of the fine and hyperfine structures in the spectra of high-n molecular Rydberg states in static uniform electric fields. The treatment combines (i) multichannel quantum-defect theory and long-range polarization models to determine the field-free energies of ne Rydberg states of the molecules (e is the orbital-angular-momentum quantum number of the Rydberg electron), (ii) a matrix-diagonalization approach to calculate the Stark shifts including the hyperfine structure, and (iii) sequences of angular-momentum basis transformations to predict the line positions and intensities in Stark spectra as they would be observed in single or multiphoton excitation sequences. To clarify how the molecular rotation and the nuclear spins influence the fine and hyperfine structure of molecular Rydberg-Stark spectra, we compare calculated spectra of ortho-D2 with a D+2 ion core in the rotational ground state (N+ = 0) for total nuclear spins I of 0 (i.e., without hyperfine structure) and 2 (i.e., with hyperfine structure) with the corresponding spectra of para-H2 with an H+2 ion core in the first excited rotational state (N+ = 2) but zero nuclear spin (I = 0). The calculations show that the hyperfine interaction alone does not significantly modify the Stark effect, but splits each Stark state by almost exactly the hyperfine Fermi-contact splitting of the ion core. In contrast, the molecular rotation, which is coupled both to the ion-core electron spin by the magnetic spin-rotation interaction and to the Rydberg-electron orbital motion by the core-polarization and charge-quadrupole interactions, induces Stark-state-specific splittings that significantly differ from the spin-rotation splitting of the (N+ = 2) ion core.

The high resolution Rydberg absorption spectrum of 2-butyne C4H6 recorded previously at the SOLEIL synchrotron facility has been interpreted using multichannel quantum defect theory (MQDT). The calculations are based on the continuum scattering calculations of Xu et al., J. Chem. Phys. 136, 154303 (2012) and of Jacovella et al., J. Phys. Chem. A 119, 12339 (2015) pertaining to the dipole-allowed excited state symmetries in absorption from the ground state. In contrast to the traditional approach of calculating low-lying electronic states first and then attempting to extend the calculations to ever higher energy, here the analysis proceeds through the extension of these detailed calculations of the electronic continuum scattering down into the discrete region of the spectrum. The continuum reaction matrices and dipole transition moments are adapted to the discrete Rydberg region via the use of an energy-modified formulation of MQDT theory and associated energy dependences of the quantum defects. The analysis reproduces more than 40 Rydberg states from n ≈ 10 down to the 3d and 4s levels with an rms error of better than 20 cm−1. These belong to five Rydberg series with three different molecular symmetries. While the approach predicts many additional series, most of these are calculated and observed to carry only little oscillator strength. The analysis shows that the Rydberg spectrum is dominated by the excitation of an e″ symmetry electron of fδ and gπ type, in line with what previous studies of the above-threshold shape resonance of 2-butyne have shown. The present study is intended to serve as an example showing how first principles continuum calculations may be useful for the interpretation of highly bound discrete states in a range that poses problems for the standard ab initio techniques. The quantitative treatment of the dipole absorption cross sections is deferred to a future paper.

The ionization energy of HD has been determined to be E-I(HD) = 124 568.484 66(7) cm(-1) by two-photon Doppler-free vacuum-ultraviolet pulsed laser spectroscopy, near-infrared continuous-wave laser spectroscopy, and Rydberg-series extrapolation by multichannel quantum-defect theory (MQDT). From this value, the dissociation energy of HD is deduced to be D0(HD) = 36 405.782 53(7) cm(-1), representing a fivefold improvement over previous values and resolving a 3.2 sigma disagreement with ab initio calculations of the four-particle nonadiabatic relativistic energy and of quantum-electrodynamic corrections up to order m alpha(6). Interactions between d, f , and g Rydberg series have been observed and had to be included in the MQDT extrapolation of the Rydberg series.

J. Hussels, N. Hölsch, C.-F. Cheng, 3 E. J. Salumbides, H. L. Bethlem, K. S. E. Eikema, Ch. Jungen, M. Beyer, F. Merkt, ∗ and W. Ubachs † Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026 China Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom (Dated: February 2, 2022)

We discuss the accuracy of various published ab initio calculations of highly excited Born-Oppenheimer bound and doubly excited states in diatomic molecules. We show that some of these results appear questionable and in a few cases even clearly unreliable, a fact which may also affect the prediction of collision cross sections based on such data. Our analysis uses Quantum Defect Theory scaling laws and is supported by variational R-matrix calculations. Some simple recipes are discussed, which may help users of ab initio quantum chemistry packages to assess the quality of their results.

Multichannel quantum defect theory is adapted to treat simultaneous rotational and vibrational preionization in H2. The strongly preionized spectrum between the N+ = 0 and N+ = 2 rotational thresholds of photoionization of H 2 X 1 ∑ g + ( J ″ = 0 , v ″ = 0 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203746608/2f2626dc-8555-4899-8d1e-59e7f2e652dc/content/eq3131.tif"/> to produce H 2 + X 2 ∑ g + ( N + , v + = 0 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203746608/2f2626dc-8555-4899-8d1e-59e7f2e652dc/content/eq3132.tif"/> is computed as example and good agreement is obtained with the photoionization data of Dehmer and Chupka.

Effects of electronic orbital angular momentum in triatomic molecules are reviewed, known collectively under the name Renner-Teller effect. The focus is on the years between 1960 and 1980, when numerous examples of the Renner-Teller effect became known experimentally. In the same years, Renner's original theory was refined and extended in various groups in order to account for the new observations. The method developed in A. J. Merer's research group in Vancouver is discussed in some detail. This effort, based on the theory of Hougen, Bunker, and Johns for large amplitude nuclear bending motion (1970), led to the first quantitative interpretation of the quasilinear bending level structure of the NH2 radical - itself the first known example of the Renner-Teller effect observed by Dressler and Ramsay in 1958. Alternative approaches, refinements, and extensions of the theory implemented after 1980 are also described, the most important extension being the inclusion of the stretching vibrational degrees of freedom, which allows the description of anharmonic Fermi interactions. Finally, the manifestations of the Renner-Teller effect expected in Rydberg states are discussed, and a sketch of the corresponding theory is presented. It is shown that the Renner-Teller effect can also play an important role in continuum processes, such as the recombination of electrons with linear ions. (C) 2019 Elsevier Inc. All rights reserved.

Nuclear-spin-symmetry conservation makes the observation of transitions between quantum states of ortho- and para-H_{2} extremely challenging. Consequently, the energy-level structure of H_{2} derived from experiment consists of two disjoint sets of level energies, one for para-H_{2} and the other for ortho-H_{2}. We use a new measurement of the ionization energy of para-H_{2} [E_{I}(H_{2})/(hc)=124 417.491 098(31)  cm^{-1}] to determine the energy separation [118.486 770(50)  cm^{-1}] between the ground states of para- and ortho-H_{2} and thus link the energy-level structure of the two nuclear-spin isomers of this fundamental molecule. Comparison with recent theoretical results [M. Puchalski et al., Phys. Rev. Lett. 122, 103003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103003] enables the derivation of an upper bound of 1.5 MHz for a hypothetical global shift of the energy-level structure of ortho-H_{2} with respect to that of para-H_{2}.

Bound and free quantum resonances of molecular hydrogen exhibiting wave-function density at large internuclear separation, 4–5 a.u., are excited via multi-step laser spectroscopy. Highly excited vibrational levels of H are prepared via two-photon UV-photolysis of HS. Subsequent two-photon Doppler-free precision measurements are performed connecting levels with outer-well levels. Detection and spectroscopic labelling of the quantum states is assisted by further laser excitation into the auto-ionisation continuum employing a third UV-laser. Level energies of high rotational states () in the outer-well state are accurately determined. The three-laser study demonstrates a method for probing resonances in the H ionisation continuum with wave-function density at large internuclear separation 4–5 a.u., large angular momenta J, and energy range 131,100–133,000 cm−1, a hitherto unexplored territory. GRAPHICAL ABSTRACT

The ionization energy of ortho-H_{2} has been determined to be E_{I}^{o}(H_{2})/(hc)=124 357.238 062(25)  cm^{-1} from measurements of the GK(1,1)-X(0,1) interval by Doppler-free, two-photon spectroscopy using a narrow band 179-nm laser source and the ionization energy of the GK(1,1) state by continuous-wave, near-infrared laser spectroscopy. E_{I}^{o}(H_{2}) was used to derive the dissociation energy of H_{2}, D_{0}^{N=1}(H_{2}), at 35 999.582 894(25)  cm^{-1} with a precision that is more than one order of magnitude better than all previous results. The new result challenges calculations of this quantity and represents a benchmark value for future relativistic and QED calculations of molecular energies.

Over a thousand spectral lines in the photoexcitation spectrum of molecular deuterium (D2) to np 1Σu+ and 1Πu+ Rydberg levels (n⩾4) were measured for rotational levels N′=1–6 in the 117000–137000cm−1 spectral range by two different types of experiments at two synchrotron radiation sources: a vacuum ultraviolet (VUV) Fourier-transform (FT) spectrometer at SOLEIL, Paris and a 10m-normal-incidence monochromator (NIM) at BESSY II, Berlin. The experimental energies, the absorption cross sections, Einstein A-coefficients, and line widths are compared with ab initio multi-channel quantum defect (MQDT) calculations for these levels. More than 350 R(0) or P(2) lines were assigned, some 280 R(1) or P(3) lines, some 270 R(2) or P(4) lines, over 100 R(3) or P(5) lines, over 90 R(4) lines, and 24 R(5) lines to extract information on the N′=1–6 excited levels. Transition energies were determined up to excitation energies of 137000cm−1 above the ground state, thereby extending earlier work by various authors and considerably improving the spectral accuracy (<0.1cm−1), leading to several reassignments. The absorption and the dissociation, ionization and fluorescence excitation cross sections from the NIM experiment are measured on absolute scale and are used to calibrate intensities in the VUV-FT spectra. The overall agreement between experiment and first principles calculations, without adjustable parameters, is excellent in view of the multi-state interferences treated within the MQDT-framework: For the low N′ values the averaged deviations between those observed in the FT-SOLEIL spectra and those calculated with MQDT are ∼0.1cm−1 with a spread of ∼0.5cm−1. The line intensities in terms of Einstein coefficients are well represented in the MQDT-framework, as are the level widths representing the lifetimes associated with the sum of the three decay channels. These line intensities follow, in general, the 1/n3 scaling behavior as characteristic in Rydberg series, but deviations occur and those are explained by MQDT. The decay dynamics of the excited N Rydberg levels is analyzed on the basis of the measured quantum yields for ionization, dissociation and fluorescence observed in the NIM experiment in terms of absolute cross sections for the distinctive channels. In particular in the n=4 manifolds dissociation is found to play a major role, where in the n=5 manifolds the behavior is most erratic due to strong competition between decay channels. At n=6, ionization takes over as the dominant channel. Despite the excellent agreement between observations and the outcome of the MQDT calculations for both level energies and dynamics, some pronounced deviations are found as in the splitting of the 5pπ,v=4–6, N′=1 levels. The shortcomings of the MQDT calculations are ascribed to the treatment of the excited states in terms of a 1snp single electron configuration, therewith neglecting possible interferences with 1snf or 2s core excited states. Some 27 lines remained unassigned; in view of their observation in fluorescence it is stipulated that these lines probe levels in the nf manifold.

Absorption and photoionization spectra of H2 have been recorded at a resolution of 0.09 and 0.04 cm−1, respectively, between 125 600 cm−1 and 126 000 cm−1. The observed Rydberg states belong to series (n = 10 − 14) converging on the first vibrationally excited level of the X 2Σg+ state of H2+, and of lower members of series converging on higher vibrational levels. The observed resonances are characterized by the competition between autoionization, predissociation, and fluorescence. The unprecedented resolution of the present experimental data leads to a full characterization of the predissociation/autoionization profiles of many resonances that had not been resolved previously. Multichannel quantum defect theory is used to predict the line positions, widths, shapes, and intensities of the observed spectra and is found to yield quantitative agreement using previously determined quantum defect functions as the unique set of input parameters.

A number of unassigned lines in the absorption spectrum of diatomic hydrogen are attributed to nominally forbidden transitions from the ground state to the nf manifold of states (Rydberg electron with l = 3 orbital momentum). They appear via weak l- mixing interactions leading to local level perturbations. Our analysis is based on multichannel quantum defect theory and uses known theoretical information from the literature. The upper levels of most of these transitions are known to give rise to molecular fluorescence, and they are shown to be singlet-triplet mixed. We conclude that the well-known metastable c(3)Pi(-)(u) state can be populated via one-photon absorption of uv photons followed by cascade emission 4f -> 3d -> 2p.

Variational ab initio R-matrix theory combined with generalized multichannel quantum defect theory is used to calculate singly excited Rydberg states of the hydrohelium molecular ion, HeH+, for (1.3)Sigma(+), (1.3)Pi, (1.3)Delta, (1.3)Phi, and (1.3)Gamma symmetry. Bound levels are calculated for n values up to n approximate to 10, and continuum states up to approximate to 3 eV above the HeH2+ threshold. The calculations span the range of internuclear distances R from 1 to 5 bohrs. The present work follows a preliminary study on the (1.3)Delta states of HeH+ [Bouhali, Bezzaouia, Telmini, and Jungen, EPJ Web Conf. 84, 04004 (2015)] which was also based on R-matrix theory. Further-although limited to rather small R values-the present work extends the recent ab initio computations of Jungen and Jungen [Mol. Phys. 113, 2333 (2015)] to higher excitation energies which are not accessible to standard quantum-chemical methods. Where a comparison with the calculations of Jungen and Jungen and other older results can be made, namely for n <= 5, very good agreement with previous ab initio results is obtained.

The DESIRS beamline of the SOLEIL synchrotron facility, equipped with a vacuum ultraviolet Fourier-transform spectrometer has been used to measure P(N″=1) (N-N″=-1) absorption transitions of the D2 molecule. Some 44 P-lines were assigned and their transition frequencies determined up to excitation energies of 134,000 cm−1 above the ground state, thereby extending the earlier work by various authors, and considerably improving the spectral accuracy (<0.1 cm−1). The assignments have been aided by first principles multichannel quantum defect theory (MQDT) calculations. These calculations also provide predictions of the autoionization widths of the upper levels which agree well with the observed resonance widths.

The absolute absorption cross sections for photoexcitation of D2 to N=0 Rydberg levels have been measured at a resolution of 0.001nm in the 123,500–135,000cm−1 spectral range. The experimental energies and line intensities are compared with ab initio multichannel quantum defect (MQDT) calculations of the n⩾4 npσ1Σu+ N=0 levels of D2. The calculations provide theoretical values of level positions, line intensities and autoionization widths. They are based on quantum–mechanical clamped-nuclei potential energy curves and dipole transition moments available for the lowest Rydberg members of the npσ series. The overall agreement between experiment and theory is good. The decay dynamics of the excited N=0 Rydberg levels is discussed based on the observed quantum yields for ionization, dissociation and fluorescence, and is compared with the yields previously observed in the analogous states of the H2 isotopomer.

The predissociation profiles of the R(0), R(1) and R(2) lines of the 3pπ1Πu+,v = 3 ←X1Σg+,v′′ = 0 absorption transition in H2 are calculated in a multichannel quantum defect theory approach, implemented on the basis of state-of-the-art potential energy curves (PEC) from the Wolniewicz group. It is shown that the profiles may be very accurately represented by the Fano profile formula although the resonance parameters thus determined do not exactly coincide with the meaning given to them in Fano's original derivation. The recent high-resolution spectrum of the same transitions taken with the SOLEIL synchrotron is well reproduced by the calculations.

We discuss some aspects of a simple expression for the low-energy dissociative recombination cross section that applies when the recombination process is dominated by the indirect mechanism. In most previous applications, this expression has been applied to capture into vibrationally excited Rydberg states with the assumption that capture is always followed by prompt dissociation. Here we consider the dissociative recombination of larger polyatomic ions and electrons. More specifically, we consider capture into electronically core-excited Rydberg states, and begin to assess its potential importance for larger systems.