Multichannel Quantum Defect Analysis Research Articles

Observations of the high vibrational levels of the B′′B̄ 1Σu+ state of H2

Double-resonance laser spectroscopy via the EF (1)Σg (+),v(')=6,J(')=0-2 state was used to probe the high vibrational levels of the B('')B̄ (1)Σu (+) state of molecular hydrogen. Resonantly enhanced multiphoton ionization spectra were recorded by detecting ion production as a function of energy using a time of flight mass spectrometer. New measurements of energies for the v = 51-66 levels for the B('')B̄ state of H2 are reported, which, taken with previous results, span the v = 46-69 vibrational levels. Results for energy levels are compared to theoretical close-coupled calculations [L. Wolniewicz, T. Orlikowski, and G. Staszewska, J. Mol. Spectrosc. 238, 118-126 (2006)]. The average difference between the 84 measured energies and calculated energies is -3.8 cm(-1) with a standard deviation of 5.3 cm(-1). This level of agreement showcases the success of the theoretical calculations in accounting for the strong rovibronic mixing of the (1)Σu (+) and (1)Πu (+) states. Due to the ion-pair character of the outer well, the observed energies of the vibrational levels below the third dissociation limit smoothly connect with previously observed energies of ion-pair states above this limit. The results provide an opportunity for testing a heavy Rydberg multi-channel quantum defect analysis of the high vibrational states below the third dissociation limit.

High-resolution measurements and multichannel quantumdefect analysis of the Kr(4p5(2P1/2)nd', J = 2,3)autoionizing resonances

Using two-step laser excitation of metastable Kr(4p55s 3P2,0) atoms via selected Kr(4p55p J = 1,2) levels, we haverecorded the low-lying autoionizing resonances Kr(2P1/2 nd', J = 2,3) (n = 6,7) at high resolution in two different experiments(atomic beam spectroscopy and optogalvanic spectroscopy in a discharge).Accurate values for the resonance positions (quantum defects) and the(reduced) widths have been determined and profile indices are reported.For comparison, multichannel quantum defect theory (MQDT) analyses,using energy-dependent MQDT parameters, have been carried out for theodd Kr(J = 1,2,3) levels, yielding good agreement in the quantumdefects and partial agreement in the predicted reduced widths for thend' resonances with the experimental values. Moreover, simplifiedphase-shifted quantum defect theory analyses of the measured bound oddKr(J = 2 and 3) Rydberg levels were carried out with the aimof providing improved insight into the dominant decay mechanism of the resonances.We also present a summary and comparative discussion of the reducedwidths for the nd'[K]J resonances of all the rare-gas atoms Ne,Ar, Kr and Xe.

Multichannel quantum defect analysis of the double resonance photoionization series of H2O

A new analysis is presented of the recent photoionization spectrum of H2O, excited by double resonance via several rotational sublevels of the (100) vibrational level of the C̃(1B1) state. Evidence for a previously unsuspected strong f series indicates significant d orbital contamination of the nominal p orbital in the intermediate state. This is the first report of an f series in the Rydberg state of any asymmetric top. Previous d series analyses of single-photon photoionization spectra terminating on the (100) level of H2O+ are also corrected and extended to a wider range of excited rotational electronic states. The d series appears to contain absent lines, indicative of predissociation. Some lines remain unassigned, but there is no systematic evidence of either s or p series.

Laser-reduced fluorescence study of the carbon monoxide nd triplet Rydberg series: Experimental results and multichannel quantum defect analysis

The ndσ and ndδ (n=4...9, v=0) triplet Rydberg series of carbon monoxide have been observed for the first time and rotationally resolved with an accuracy of 0.03 cm−1 using a three-step excitation scheme. A multichannel quantum defect theory (MQDT) analysis shows strong perturbations for n=5, 8, and 9 and predicts the positions of the sσ and dπ levels. There is significant mixing between the sσ and dσ states, with a mixing angle between 42 and 45 degrees, as well as some smaller interaction with the np series. The ionization limit for CO is found to be 113 027.5(3) cm−1.

High-resolution measurement and quantum-defect analysis for the Ne nd' J= 1, 2 and 3 autoionizing resonances

Using resonant two-photon excitation of a metastable Ne(2p53s 3P0.2) beam by two single-mode CW dye lasers, we have measured reduced widths Gamma r=n*3 Gamma n for the four Ne(2p5(2P12/) nd' (K)s) autoionizing resonance series ((K)s=(3/2)3, (3/2)2, (5/2)2, and (5/2)3). The resulting values are Gamma r=167(7), 350(7), 87(2), and 73(3) cm-1, respectively, in good agreement with predictions by a semiempirical multichannel quantum-defect analysis involving complex quantum defects.

Multichannel quantum defect analysis of preionizing Rydberg states of Li2 including rovibronic interactions

The multichannel quantum defect analysis of the preionization spectrum of Li2 published recently by Schwarz et al.1 is reconsidered and unified. In addition to the rotational–electronic interactions taken into account in Ref. 1, nuclear vibrational motion and vibrational–electronic interactions between Rydberg l complexes associated with different vibrational limits are included. A quantum defect matrix is constructed which depends linearly on the internuclear distance and whose elements are determined from the experimental data by a nonlinear least-squares fitting procedure. The resulting R-dependent quantum defect matrix is used to calculate the preionization profiles of the resonance peaks.

Observation of the Stark effect in autoionizing Rydberg states of Ar with a multichannel quantum-defect analysis

The Stark spectra of autoionizing Rydberg states of Ar converging to the second ionization limit 3p5 2P1/2 have been investigated, experimentally and theoretically, as a function of electric field strength, in the range 15-2000 V cm-1. The levels with effective principal quantum number v=12-19, are excited by single-photon absorption from the ground state using a coherent extreme ultraviolet laser source (bandwidth approximately 1.0 cm-1) generated by four-wave sum-frequency mixing of the outputs of two pulsed dye lasers; a detailed Stark map is obtained for the first time. A multichannel quantum-defect-theory analysis of the field-induced-state mixing is carried out, reproducing positions, widths and shapes of the experimentally observed features. In addition, this analysis provides new insight into the dynamical decay of the autoionizing states.

Photodissociation of K2 (X 1Σ+g–B 1Πu)

A semiclassical model based on an orbital following picture to describe the dissociation dynamics of K*2 (B 1Πu) is outlined. The results of this simple model are in complete quantitative agreement with an exact quantum calculation by Dubs and Julienne based on a half-collision multichannel quantum defect analysis (accompanying paper). These theoretical works give a complete description of the process and indicate that dissociation occurs adiabatically from the Hund’s case (a) to the Hund’s case (c) basis, followed by a sudden recoupling at long range to the Hund’s case (e) basis. The experimentally observed bound–free excitation spectrum and the polarization of the atomic product fluorescence are in excellent agreement with the result of a full thermally averaged calculation based on this theoretical dynamical model.

High resolution absorption spectrum of palladium in the 4d subshell excitation region

The authors report high resolution absorption spectra of palladium in the 1500-1300 AA region. The observations were made in the first order of a 3 m vacuum spectrograph equipped with a 6000 lines/mm holographic grating using synchrotron radiation as the background source of continuum. More than 45 new transitions are reported, all of which can be classified into Rydberg series due to excitation of one electron from the 4d subshell: 4d10 1S0 to 4d9(2D5/2) n p (9(n<or=30)nf(6(n<or=16) to 4d9(2D3/2) n p (8(n<or=17). The ionization energies obtained are 67241.3+or-0.8 cm-1 and 70779.8+or-0.8 cm-1 for the 2D5/2 and 2D3/2 states of Pd II respectively. To study the interchannel interactions, a graphical multichannel quantum defect analysis of the observed energy levels is presented.

A simple version of the multichannel quantum defect analysis of inelastic atomic processes involving molecular Rydberg states

A system of algebraic equations is suggested for the T matrix describing the collision of atoms occurring with participation of the Rydberg molecular states. The equations used ensure the unitarity of the S matrix and allow one to establish the direct connection between the phenomenological parameters of the theory and the adiabatic characteristics of the terms. The peculiarities of the resonant structure of the inelastic scattering are studied. The relative role of the population mechanism of the continuum states and of the quasi-discrete molecular Rydberg states is considered.

Three-step laser spectroscopy and multichannel quantum defect analysis of odd-parity Rydberg states of neutral ytterbium

High-lying odd-parity levels of neutral ytterbium are investigated by the method of selective three-step laser spectroscopy. Excitation from the ground state 4f146s2 is performed by means of three dye lasers and the Rydberg levels are detected by using the field ionisation method. Three different levels are used as starting levels of the transitions to Rydberg levels. Thus Rydberg levels pertaining to 6snp J=0-2 and 6snf J=2, 3 series as well as some 4f135d26s levels are observed. The new experimental data are analysed by means of the multichannel quantum defect theory. The theoretical analysis consists of a J by J parametrisation of the observed energy spectra. The perturbations of the Rydberg series 6snp J=1, 6snp 3P0 and 6snf J=3 by levels of the 4f135d26s configuration are clearly interpreted. The limitations of the MQDT models derived solely from energy data are discussed. A revised value of the first ionisation limit is proposed.

A multichannel quantum defect analysis of two-state couplings in diatomic molecules

A multichannel quantum defect analysis (MCQDA) for non-Coulomb potentials is applied to two-channel coupling in diatomic molecules. Given the exact 2×2 scattering matrix S(E) obtained at a single energy above the dissociation threshold E&amp;gt;0, we can extract an analytic, energy-insensitive 2×2 matrix Y(E) which can be extrapolated across thresholds and yield a complete description of predissociating molecules. The predicted widths, shifts, and line shapes obtained from MCQDA are in quantitative agreement with the exact numerical results and confirm the remarkable simplicity that can be achieved in describing diatomic systems near dissociation limits. The analysis is equally applicable to either adiabatic avoided crossings or diabatic curve crossings. The validity of MCQDA is independent of coupling strength and can quantitatively describe strongly overlapped predissociating resonance states. The application of MCQDA to the bound state spectrum, when both channels are closed, is discussed.

A multichannel quantum defect analysis of diatomic predissociation and inelastic atomic scattering

Given an NT×NT interaction matrix W∞(R) which describes the dissociation of a diatomic molecule into NT asymptotic atomic channel states, we can generate exact numerical solutions to the close-coupled scattering equations. At total energies E above the highest dissociation threshold we obtain an NT×NT scattering matrix S(E) which defines the asymptotic structure of the NT- fold degenerate multichannel scattering or continuum wave functions. This matrix varies rapidly with energy and is nonanalytic at thresholds. However, based on a multichannel quantum defect analysis (MCQDA) of the coupled equations we find that the numerical S(E) matrix can be made to yield a real, symmetric matrix Y(E) which is analytic in E. This matrix can then be analytically continued across threshold to provide rigorous analytic descriptions of the multichannel diatomic wave functions in the predissociating and bound-state regions of the energy spectrum. Since the extraction of Y(E) is predicated on assigning a reference potential 𝒱γ(R) to each channel, the detailed energy variation of Y(E) is dependent on the choice of potentials. Fortunately, the physics contained in W∞(R) generally dictates an obvious set of reference potentials which usually make Y(E) slowly varying. As E is reduced below threshold we can use Y(E), often well represented as a constant over a wide range of energies, to provide a description of the predissociating molecule, including such observable properties as linewidths, level shifts, and branching ratios. At still lower energies, when all channels are closed, Y(E) offers a complete, nonperturbative description of the configuration interaction between bound electronic-rotational states of the molecule. Although many insights in this paper are provided by a WKB analysis of the reference solutions associated with each reference potential, the MCQDA yields a complete quantum mechanical description of the exact close-coupled wave functions. The quality of these wave functions is limited only by the accuracy of the molecular potentials and interaction matrix elements that are used to construct W∞(R), and by the number NT and specific set of channels we choose to include in the close-coupled theory. The analysis is equally valid when applied to either adiabatic avoided crossings or diabatic curve crossings. More importantly, the formal structure of the close-coupled wave functions dictated by MCQDA yields a rigorous framework for the analysis of strongly interacting continuum, predissociating, and bound state channels without recourse to perturbation theory.

On the Ne(2p5ns',nd') autoionisation resonances: high-resolution measurement and quantum defect analysis

Using mass spectrometric ion detection, the authors have studied the low-lying Ne(2p514s', 12d') autoionisation resonances by transverse two-photon laser excitation of a metastable Ne(2p53s 3P2) atom beam via the Ne(2p53p 1D2) intermediate state. The resonance width of a fitted Beutler-Fano profile was determined as Gamma (14s', J=1)=(6.0+or-0.5)GHz, Gamma (12d', J=1-3)=(2.0+or-0.5)GHz in very good agreement with values deduced in a multichannel quantum defect analysis of available spectroscopic data.

Multichannel quantum-defect analysis of the bound even-parity spectrum of neutral barium

Extensive new data on the bound even-parity spectrum of neutral barium have been provided recently by two-step optogalvanic spectroscopy. Highly excited members of the Rydberg series $6sns^{3}S_{1}$, $6snd^{3}D_{1}$, $^{3}D_{3}$, and $6sng$ as well as perturbing levels of these series belonging to $5dnd$ configurations have been observed. By means of multichannel quantumdefect theory (MQDT), we have performed the analysis of all available energy data relevant to the $J=1,3,4,5$ even-parity bound spectra of barium. The behavior of $6sns^{3}S_{1}$, $6snd^{3}D_{1}$, $^{3}D_{3}$ series perturbed by levels pertaining to the $5dns (n=7,8)$ and $5dnd (n=6,7)$ configurations is clearly interpreted. The MQDT analyses of $J=1 \mathrm{and} 3$ spectra complementary to that previously performed on the $J=2$ spectrum offer the possibility of studying the anomalous fine structures of highly excited $6snd$ configurations. The MQDT analyses of $J=3\ensuremath{-}5$ spectra explain the observed energies of $6sng^{3}G_{3,4,5}$ and $^{1}G_{4}$ Rydberg levels; the fine structures of the $6sng$ series are only partially resolved in the vicinity of $5d7d$ $J=3 \mathrm{to} 5$ perturbing levels. Since the $J=0$ and $J=2$ bound even-parity spectra of Ba have already been analyzed by MQDT, we have now a full MQDT description of the bound even-parity spectrum for $J$ values ranging from 0 to 5.

High resolution spectroscopy on 6sns Rydberg states of barium

Extensive new data on perturbed and unperturbed levels of the 6s n s1S0 and 6s n s3S1 Rydberg series of Barium have been obtained in a high-resolution laser atomic-beam experiment. Special attention has been paid to the region aboven=15 where the3S1 series is strongly perturbed. The results on hyperfine energies and isotopic field shift ratios are compared with calculations using wavefunctions obtained from a Multi Channel Quantum Defect analysis. The applicability of various approximations to these wavefunctions is discussed. Good agreement between experiment and calculation is obtained.

Lifetimes of Rydberg levels in the perturbed 6snd1,3D2series of barium I

Using two-step laser excitation in an atomic beam and time-delayed field ionisation detection, we have measured the lifetimes of the Rydberg levels of Ba I belonging to the perturbed series 6snd 1D2 (n = 17-35) and 6snd 3D2 (n = 17-28) and also the lifetime of the perturbing 5d7d 1D2 level. The expected shortening has been observed for the lifetimes of those levels which are strongly mixed with the perturber. The measured values have been satisfactorily interpreted by a parametric method based upon the wavefunctions previously obtained from a multichannel quantum defect analysis of the energies.

Highly excited levels of neutral ytterbium. II. Multichannel quantum defect analysis of odd- and even-parity spectra

For pt.I see ibid., vol.13, no.6, p.1073 (1980). Data on the bound even-parity spectrum of Yb have been presented in the preceding paper (Carnus et al., 1980). These data provide an excellent opportunity for the application of multichannel quantum defect theory (MQDT) to this spectrum. The bound even-parity J=0, 2 spectra and the bound odd-parity J=1 spectrum are analysed with MQDT models. The behaviour of the even-parity 4f146sns 1S0 (n>or=7) and 4f146snd 1.3D2 (n>or=8) Rydberg series perturbed by levels of the 4f146p2 and 4f135d6s6p configurations is well interpreted; in the same way the known bound levels of the 4f146snp 1.3P1 Rydberg series (n>or=12) perturbed by levels of the 4f135d26s configuration are well interpreted. The mutual interaction of the singlet and triplet levels of J=1 and J=2 Rydberg series is analysed. Some assignments of levels are changed and predicted energy values are given for many levels.

Multichannel quantum-defect analysis of the bound even-parity J=2 spectrum of neutral barium

Extensive new data on the bound even-parity J=2 spectrum of Ba provide an excellent opportunity for the application of multichannel quantum-defect theory (MODT) to this spectrum. The parametrisation of the J=2 energy levels is successfully carried out using a nine-channel MQDT model involving four limits. The influence of large spin-orbit coupling effects and configuration interaction is analysed. The mutual interaction of the 6snd1D2 and 6snd3D2 Rydberg series as well as the perturbations of these by levels pertaining to the 5dns (n=7,8), 5dnd (n=6,7) and 6p2 configurations are clearly interpreted.

Absorption spectrum of krypton in the vacuum uv region

The absorption spectrum of atomic krypton in the wavelength region 840–1240 A has been investigated with a 6.65-m vacuum spectrograph. The expected five ns and nd Rydberg series have been observed. The series have been extended as far as n = 60 for nd (3/2)°1 and n = 59 for nd′(3/2)°1. The ionization energies obtained are 112 914.6 ± 0.1 cm−1 and 118 284.6 ± 0.2 cm−1 for 2P°3/2 and 2P°1/2 states of Kr ii, respectively. Strong interactions have been observed as perturbations and autoionization; a graphical multichannel quantum defect analysis of the observed energy levels is presented.