Multichannel Quantum Defect Calculations Research Articles

Spectroscopic study of the F[formula omitted] outer well state in H2, HD and D2

Two-photon UV-photolysis of hydrogen sulfide molecules is applied to produce hydrogen molecules in highly excited vibrational levels in the X1Σg+ electronic ground state, up to the dissociation energy and into the quasibound region. Photolysis precursors H2S, HDS and D2S are used to produce vibrationally hot H2, HD and D2. The wave function density at large internuclear separation is excited via two-photon transitions in the F1Σg+ - X1Σg+ system to probe ro-vibrational levels in the first F1Σg+ outer well state of gerade symmetry. Combining with accurate knowledge of the X1Σg+ (v,J) levels from advanced ab initio calculations, energies of rovibrational levels in the F1Σg+ state are determined. For the H2 isotopologue a three-laser scheme is employed yielding level energies at accuracies of 4×10−3 cm−1 for F(v=0,J) up to J=21 and for some low J values of F(v=1). A two-laser scheme was applied to determine level energies in H2 for F(v=0−4) levels as well as for various F levels in HD and D2, also up to large rotational quantum numbers. The latter measurements in the two-laser scheme are performed at lower resolution and the accuracy is strongly limited to 0.5 cm−1 by ac-Stark effects. For H2 a new quasibound resonance X1Σg+ (v=6, J=23) is detected through the Q(23) and O(23) transitions in the F0-X6 band. Also a quasi-bound resonance in D2 is assigned, for the first time in this species: X1Σg+ (v=17 , J=15). The experimental results on F(v,J) level energies are compared with previously reported theoretical results from multi-channel quantum-defect calculations as well as with results from newly performed non-adiabatic quantum calculations.

Absorption spectrum of H2 between the third and the fourth dissociation thresholds (132 500 – 139 000 cm−1)

Over a thousand spectral lines in the absorption spectrum of molecular hydrogen (H2) to the npσ 1Σu+ and npπ 1Πu± Rydberg levels (n ≥ 4) were measured and assigned for rotational levels with N’=0 – 4 in the spectral range between 132 500 and 139 000 cm−1. The experimental energies, the absorption cross sections, and Einstein A coefficients were compared with ab initio multi-channel quantum defect (MQDT) calculations. The assigned lines include 31P(1), 225 R(0) or P(2), 291 R(1) or P(3), 109 R(2) lines, 71 R(3) lines, and over 300 Q(1–3) lines. Transition energies were determined up to excitation energies of 139 000 cm−1 above the ground state, thereby extending earlier works and leading to several reassignments. The overall agreement between experiment and first principles calculations, without adjustable parameters, is very good in view of the multi-state interferences treated within the MQDT-framework. The line intensities in terms of Einstein A coefficients are well represented in the MQDT-framework. These line intensities follow, in general, the 1/n3 scaling behavior as characteristic in Rydberg series, but many deviations occur which are explained by MQDT. Despite the mostly very good agreement between the observations and the outcome of the MQDT calculations for both level energies and line intensities, some pronounced deviations were found which are discussed. 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. So far, some 108 lines remained unassigned.

Photolysis Production and Spectroscopic Investigation of the Highest Vibrational States in H2 (X1Σg+ v = 13, 14).

Rovibrational quantum states in the X1Σg+ electronic ground state of H2 are prepared in the v = 13 vibrational level up to its highest bound rotational level J = 7, and in the highest bound vibrational level v = 14 (for J = 1) by two-photon photolysis of H2S. These states are laser-excited in a subsequent two-photon scheme into F1Σg+ outer well states, where the assignment of the highest (v,J) states is derived from a comparison of experimentally known levels in F1Σg+, combined with ab initio calculations of X1Σg+ levels. The assignments are further verified by excitation of F1Σg+ population into autoionizing continuum resonances, which are compared with multichannel quantum defect calculations. Precision spectroscopic measurements of the F-X intervals form a test for the ab initio calculations of ground state levels at high vibrational quantum numbers and large internuclear separations, for which agreement is found.

Ab initio non-adiabatic study of the 4pσ B'' 1Σ+u state of H2

ABSTRACTFully ab initio non-adiabatic multichannel quantum defect calculations of the 4pσ B'' 1∑u+ energy levels, line intensities and widths, based on the latest quantum-chemical clamped-nuclei calculations of Wolniewicz and collaborators are presented for H2. The B″ state corresponds to the inner well of the state. The B'' v ≥ 1 levels are rapidly predissociated through vibrational coupling with the 3pσ B’ 1Σ+u continuum so that coupled-equation calculations become unstable. Multichannel quantum defect theory, on the other hand, is demonstrated to be particularly suited to this situation. Experimental data as level energies, line intensities and dissociation widths were revisited and corrected. Reinvestigating previously published spectra, several new lines were assigned.

Experimental and theoretical studies of the [formula omitted] and [formula omitted] ([formula omitted]–6) states of D2: Energies, natural widths, absorption line intensities, and dynamics

Over a thousand spectral lines in the photoexcitation spectrum of molecular deuterium (D2) to np1Σu+ 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.

Velocity-map imaging of near-threshold photoelectrons in Ne and Ar

The photoionization of Ne and Ar has been studied in the region between the ${}^{2}$${P}_{3/2}$ and ${}^{2}$${P}_{1/2}$ thresholds using a velocity-map imaging (VMI) spectrometer. The VMI technique provides a two-dimensional overview of the ionization cross section versus photon energy and emission angle. In these regions the neutral Rydberg states converging to the ${}^{2}$${P}_{1/2}$ ion state affect both the ionization cross section and the asymmetry parameter of the photoelectron angular distribution, which both display Fano line shapes. The results are compared with relativistic multichannel quantum-defect calculations.

Synchrotron vacuum ultraviolet radiation studies of the D Π1u state of H2

The 3pπD Π1u state of the H2 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 Π1u 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 Π1u− 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 Π1u 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 Π1u vibrational series. The combined results yield accurate information on the characteristic Beutler–Fano profiles associated with the strongly predissociated Πu+ parity components of the D Π1u 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.

Complex rotation method for the Dirac Hamiltonian

We show that the method of the complex rotation can be applied to the Dirac Hamiltonian. We compute positions and widths of resonance levels of hydrogenlike ions ~with Z51 and Z510), described relativisti- cally, in the presence of the uniform dc electric field ~relativistic Stark effect !. We show that, for small Z, positions of the resonance levels, given by the relativistic approach, agree well with known nonrelativistic results. The relativistic treatment introduces corrections on the same order both for the resonance positions and widths, and may, therefore, alter widths considerably. The complex rotation method is a well-known tool, allow- ing to calculate positions and widths of resonances in atomic systems @1-7#. To mention just a few applications, the method has been used in nonrelativistic quantum-mechanical calculations of resonance parameters of doubly excited states @8,9# or Stark resonances @10-12# in such systems as He, H 2 ,o r Ps 2 . The above mentioned applications of the complex rotation procedure neglected relativistic effects. Recent developments of the experimental technique perfected experimental data to a degree where relativistic effects become observable. For example, in recent publications @13,14# of 2lnl8 resonances in helium the authors show that theoretical predictions based on the nonrelativistic approach differ considerably from the experimental data. Only by inclusion of the spin-orbit effects in the scheme of an R-matrix multichannel quantum-defect calculation @15# were the experimental results explained. Another manifestation of the relativistic effects has been reported in Ref. @16#, where a peak in the electron-He 1 (1s) scattering has been observed, which is forbidden in the pure LS-coupling scheme. The recent experimental studies @17# of the effect of the strong electric field on helium hint at the important role played by the relativistic effects. Also, forbid- den in the LS coupling, doubly excited states have been ob- served in a single-photon excitation from the ground state of helium @18#. These findings indicate that, in the spectra of the doubly excited states, or in the process of the interaction of atomic states with electric field, relativistic effects may play quite an important role. Incorporation of the relativistic effects into the scheme of calculation and, in particular, proper modifi- cations of the complex rotation procedure, allowing to take full account of the relativistic effects, seem to be necessary. In the present paper we propose a modification of the complex rotation method, taking full account of the relativ- istic effects. We develop the complex rotation procedure for the Dirac Hamiltonian.

Multichannel quantum defect calculation of the phase lag in the coherent control of HI

Multichannel quantum defect theory (MQDT) is applied within a unified framework to compute the ionization and dissociation channel phases of HI. Our numerical results illustrate the mathematical origin of a channel phase within the MQDT formalism, and are consistent with the existing theory of this phenomenon, based on the collision formalism and with experimental measurements. The present study explains why previous MQDT calculations predicted that the channel phase vanishes identically.

Dissociative recombination of NO+: calculations andcomparison with experiment

Multichannel quantum defect calculations for NO+dissociative recombination (DR) for electron energies from thresholdto 8 eV are presented. The calculations use electronic energiesand autoionization widths of valence states obtained from ab initio R-matrix calculations with the correspondingpotential curves calibrated using available spectroscopic data.Six valence states open to dissociation are included in thefinal calculations. Excellent agreement with the measured crosssections is obtained for the low-energy DR, up to 3 eV and, forthe first time, the peak observed in the cross section at highenergy is accounted for. The importance of the variousdissociative states at different electron energies, as well asthe direct and indirect processes, is discussed. Compared toprevious theoretical studies, the inclusion of a thirddissociative state of 2Π symmetry and the largerautoionization width of the B' 2Δ state are found to beparticularly important for the agreement with experiment.

Photoelectron angular distributions of rotationally selected NO Rydberg states.

The photoelectron angular distributions from autoionizing $\mathrm{ns}$ and $\mathrm{nf}$ Rydberg states of NO are presented. A striking dependence of the angular distribution on the rotational level in the excited Rydberg complex is observed: The sign of the asymmetry parameter $\ensuremath{\beta}$ alternates for consecutive rotational levels. A multichannel quantum defect calculation shows qualitative agreement with the experimental results and indicates the role of predissociation in the decay of these Rydberg states.

The f Rydberg series in the absorption spectrum of N2

The nf Rydberg levels of 14N2 converging to the X 2Σ+g ground state of N+2 have been studied from n=4–9 in the high-resolution absorption spectra of supersonically expanding nitrogen at wavelengths ranging from 843.2 to 802.6 Å (118 600–124 600 cm−1). The best experimental results, achieving rotational temperatures on the order of 20 to 40 K and a resolution of 0.5 cm−1, were obtained by photographing the jet absorption against the background continuum from a synchrotron radiation source. Complementary data for 14N2 and 15N2 come from the analyses of spectra recorded under equilibrium conditions at 70 K with a resolution of 1 cm−1, using the He continuum as background source. The observations are interpreted with the help of multichannel quantum defect calculations and lead to the conclusion that, to varying degrees and with the exception of 4f(v=0), all the complexes studied here show the effects of interactions with core excited d and s Rydberg levels built on the A 2Πu first excited state of N+2. Also, the 9f(v=0) complex is shown to be perturbed by 10p(v=0), and the strength of the p–f interaction has been determined.

Rydberg molecule in a magnetic field

Rydberg states of the NO molecule have been probed by two-color resonantly enhanced multiphoton ionization in a magnetic field of 0.93 T. Penetrating s and d states show strong interactions with the intramolecular field while nonpenetrating f states show stronger interactions with the extemal magnetic field. Competition between the molecular core anisotropy and the extemal field anisotropy leads to a greater variety of situations than in a Rydberg atom, ranging from a « weak field » regime to a « strong field » regime. These different situations are illustrated by a multichannel quantum defect calculation on the np states of NO including the Zeeman effect. An extreme situation can be achieved in which the Rydberg molecule looses its molecular character and shows an almost pure atomic structure within each rotational channel.

Inner-shell electron energy loss spectra of NO 2 at high resolution: Comparison with multichannel quantum defect calculations of dipole oscillator strengths and transition energies

High-resolution electron energy loss spectra of the nitrogen ls and oxygen 1s inner shells of NO 2 have been obtained under conditions of high-impact energy (3 keV) and zero-degree scattering angle. The spectra have been placed on an absolute dipole oscillator strength scale. Multichannel quantum defect theory calculations of excitation energies and dipole oscillator strengths for N 1s and O 1s excitation are in quite good agreement with the measured spectra. The calculations are used to aid the assignment of features in the inner-shell spectra. A strong resonance present in both the N 1s and O 1s ionization continua is identified as excitation to the unbound 5b 2 (b 2 *) molecular orbital. A consideration of the present ISEELS work for NO 2 and earlier ISEELS measurements for other molecules shows that additional prominent structures observed in previously reported NO 2 inner-shell photoabsorption spectra obtained using synchrotron radiation are due to the presence of impurities.

Vacuum ultraviolet laser photoionization spectroscopy: A high-resolution study of spin-orbit autoionization in HI

The process of spin-orbit autoionization in HI has been studied using tunable coherent vacuum ultraviolet light, which had a spectral resolution of 0.01 Å. The high intensity of the coherent light source made it possible to record the spectrum under supersonic molecular beam conditions, where the HI had a rotational temperature of about 10 K. This spectrum of cold HI was very different from the high-resolution spectrum of 300 K HI recorded on the same apparatus, one difference being that it had very sharp resonances which were not present in the 300 K spectrum. These results are contrasted and compared with previous experimental work, and with a recent multichannel quantum defect calculation done by Lefebvre-Brion and co-workers. The similarities and differences between the autoionization in HI and the isoelectronic atom Xe are also discussed in light of these results.

Branching ratios for autoionisation of ν=3 Rydberg states in nitric oxide

An investigation is reported of the autoionising decay of the n=18-22 members of the nu =3 Rydberg series, converging to the X1 Sigma +( nu 2+3) state of NO+. Photoelectron spectra for two-colour multiphoton ionisation processes via the A2 Sigma +( nu '=3) intermediate state are recorded. Photoelectron analysis of the decaying 22p( nu =3) Rydberg state leads to branching ratios of 1.00:0.06:0.25 for autoionisation into the nu +=2, 1, 0 channels respectively. These branching ratios deviate from the Delta nu =-1 propensity rule for pure vibrational autoionisation. The effect of electronic coupling with a dissociative (valence) continuum is discussed. Experimental branching ratios are compared with results of two-step multichannel quantum-defect calculations by Guisti-Suzor and Jungen (1984) in which vibrational autoionisation and (pre)-dissociation are treated simultaneously.

Quantum defect analysis of HD photoionization

A multichannel quantum defect calculation is shown to reproduce most observed features in several portions of the HD photoabsorption spectrum. The rovibrational frame transformation theory of Atabek, Dill, and Jungen is reformulated in terms of a quantum defect matrix. The calculation accounts for spectral regions far from dissociation thresholds despite its neglect of g–u mixing.

Ab initio approach to the multichannel quantum defect calculation of the electronic autoionisation in the Hopfield series of N2

The two-step formulation of the multichannel quantum defect theory, applied to molecular electronic autoionistion by Giusti-Suzor (1980) and Lefebvre-Brion (1973) is used to calculate the total and partial photoionisation cross sections in the region of the Hopfield series on N2, the 700-730 AA wavelength range. The electronic quantities necessary for this treatment are obtained from ab initio calculations. The cross sections and the photoelectron angular distribution parameters are in satisfying agreement with experiment. The results clearly show that the absorption series correspond to the (B2 Sigma u+)nd sigma g series and the apparent emission series to the (B2 Sigma u+)nd pi g series.