Multichannel Quantum Defect Theory Parameters Research Articles

Spectroscopy and scattering matrices with nitrogen atom: Rydberg states and optical oscillator strengths

The scattering matrices of e + N+ with Jπ = 1.5+ in discrete energy regions are calculated using the eigenchannel R-matrix method. We obtain good parameters of multichannel quantum defect theory (MQDT) that vary smoothly as the function of the energy resulting from the analytical continuation property of the scattering matrices. By employing the MQDT, all discrete energy levels for N could be calculated accurately without missing anyone. The MQDT parameters (i.e., scattering matrices) can be calibrated with the available precise spectroscopy values. In this work, the optical oscillator strengths for the transition between the ground state and Rydberg series are obtained, which provide rich data for the diagnostic analysis of plasma.

Spectroscopy and scattering: Analytical properties of scattering matrices in discrete and continuum regions

The scattering matrices of $e\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}{\mathrm{O}}^{+}(2{p}^{3}\phantom{\rule{0.16em}{0ex}}^{4}S_{3/2},\phantom{\rule{0.16em}{0ex}}^{2}D_{3/2,5/2})$ with ${J}^{\ensuremath{\pi}}={3}^{\ensuremath{-}}$ in various energy regions including discrete and adjacent continuum are calculated using our modified eigenchannel $R$-matrix method. The analytical properties of the scattering matrices for this multichannel scattering process with strong interchannel interactions are unveiled by our method. Based on the scattering matrices, all energy levels (including an infinite number of Rydberg states and autoionization resonance states without missing any one) can be calculated accurately in the framework of multichannel quantum defect theory (MQDT). The MQDT parameters (i.e., scattering matrices) can be checked and/or calibrated with available precise spectroscopy data. In the present work, the calculation precision of the scattering matrices of ${J}^{\ensuremath{\pi}}={3}^{\ensuremath{-}}$ is determined to be about 2%, which should meet the needs of future calculations for the important $e\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}{\mathrm{O}}^{+}$ collision process in astrophysics research.

Intimate relationship between spectroscopy and collisions: a scenario to calculate relevant atomic data for astrophysics

An extended atomic data base with sufficiently high precision in energy levels and transition/collision rates is required for satellite observation in astrophysics studies and energy development research in inertial confinement fusion and magnetic confinement fusion. We summarize in this paper a scenario for performing calculations leading to such large-scale atomic data with high precision based on the analytical continuation properties of the scattering matrices, connecting spectroscopy and collisions. Based on the scenario, we calculate directly the scattering matrices with spectroscopic accuracy, i.e. the accurate multi-channel quantum defect theory parameters in both bound and continuum energy regions based on the recently developed eigenchannel R-matrix approach. Applications of the related atomic processes are presented to demonstrate the advantages enjoyed by this approach, which is hoped to meet the requirements in the stages of precision physics for astrophysics and energy research.

Determination of the binding energies of the np Rydberg states of H2, HD, and D2 from high-resolution spectroscopic data by multichannel quantum-defect theory

Multichannel quantum-defect theory (MQDT) is used to calculate the electron binding energies of np Rydberg states of H2, HD, and D2 around n = 60 at an accuracy of better than 0.5 MHz. The theory includes the effects of rovibronic channel interactions and the hyperfine structure, and has been extended to the calculation of the asymmetric hyperfine structure of Rydberg states of a heteronuclear diatomic molecule (HD). Starting values for the eigenquantum-defect parameters of MQDT were extracted from ab initio potential-energy functions for the low-lying p Rydberg states of molecular hydrogen and subsequently refined in a global weighted fit to available experimental data on the singlet and triplet Rydberg states of H2 and D2. The electron binding energies of high-np Rydberg states derived in this work represent important quantities for future determinations of the adiabatic ionization energies of H2, HD, and D2 at sub-MHz accuracy.

High-resolution spectroscopy and quantum-defect model for the gerade triplet np and nf Rydberg states of He2

Photoionization spectra and Rydberg-state-resolved threshold-ionization spectra of the gerade triplet np Rydberg states of (4)He2 located in the vicinity of the X(+) (2)Σ(u)(+) (ν(+) = 0) ionization threshold were recorded from the 2sσ a (3)Σ(u)(+) metastable state. An accuracy of 0.01 cm(-1) was achieved for the experimental term values of the observed Rydberg states. The data were combined with spectroscopic data on low-lying triplet np and nf Rydberg states from the literature to derive energy- and internuclear-distance-dependent eigenquantum-defect parameters of multichannel quantum-defect theory (MQDT). The MQDT calculations reproduce the experimental data within their experimental uncertainties and enabled the derivation of potential-energy curves for the lowest triplet p Rydberg states (n = 2-5) of He2. The eigenquantum-defect parameters describing the p -f interaction were found to be larger than 0.002 at the energies corresponding to the high-n Rydberg states, so that the p -f interaction plays an important role in the autoionization dynamics of np Rydberg states with v(+) = 0. By extrapolating the experimental term values of triplet np Rydberg states of (4)He2 in the range of principal quantum number n between 87 and 110, the positions of the (v(+) = 0, N(+) = 3) and (v(+) = 0, N(+) = 5) levels of the ground state of (4)He(+)(2) were determined to lie 70.937(3) cm(-1) and 198.369(6) cm(-1), respectively, above the (v(+) = 0, N(+) = 1) ground rotational level.

Spectrum of the Autoionizing Triplet Gerade Rydberg States of H2 and its Analysis Using Multichannel Quantum-Defect Theory

A new spectrum of the autoionizing triplet states of gerade symmetry of H2 has been recorded from the υ″ = 1–4, N″ = 1–3 rovibrational levels of the metastable c 3Π(u)– state in a supersonic beam. The spectrum consists of overlapping ns and nd Rydberg series with n in the range between 4 and 45 converging to the υ+ = 1–4, N+ = 0–5 levels of the X+ 2Σ(g)+ ground state of H2+. Numerous perturbations caused by s–d and rovibrational channel interactions are revealed in the spectrum and were fully assigned by combining double-resonance experiments and ab initio multichannel quantum-defect theory (MQDT). The energy- and internuclear-distance-dependent eigenquantum-defect parameters of MQDT were derived from available ab initio calculations of the low-lying electronic states of H2 and the ground state of H2(+) and were subsequently refined in a global fit to experimental data. The positions of 552 triplet ns and nd Rydberg levels of H2 (361 of which were measured in the present study) could be reproduced with a root-mean-square deviation of 0.2 cm(–1).

Analysis of the J=1 energy levels of Mg III by multichannel quantum defect theory

The J=1 energy levels of Mg III are analyzed with multichannel quantum defect theory (MQDT). Fitting MQDT parameters to minimize deviation between the observed and theoretical energy values, we determined the MQDT parameters (μα, Uiα) for J=1 odd-parity levels. Using these parameters, we predict the energy levels 2s22p5(2Po1/2)nd 2[3/2]1 (9⩽n⩽16), 2s22p5(2Po3/2)nd 2[3/2]1 (7,9⩽n⩽25), 2s22p5(2Po3/2)nd 2[1/2]1 (9⩽n⩽25), 2s22p5 (2Po1/2)ns 2[1/2]1 (9⩽n⩽17) and 2s22p5(2Po3/2)ns 2[3/2]1 (10⩽n⩽26) of Mg III. In addition, the inter-channel perturbations are analyzed.

Radiative lifetimes of Rydberg 6p n d J =2 states of Pb I by multichannel quantum defect theory

Energy levels of the odd-parity 6pnd J=2 Rydberg states of Pb I are analysed by the multichannel quantum defect theory (MQDT) in the frame of a five-channel three-limit calculation model. With optimal MQDT parameters, channel admixture coefficients are obtained and used to calculate the theoretical lifetimes of the levels by comparing to the previously measured lifetimes. The predicted lifetimes for higher-lying Rydberg states are given and discussed. These predicted lifetimes are very different from those obtained by the four-channel two-limit model previously used, which means that introduction of the additional interacting channel is important for studying the 6pnd J=2 Rydberg states of Pb I.

Energy levels of Rydberg 6 pnd and [formula omitted] states of PbI by multichannel quantum defect theory

Energy levels of the odd-parity 6 pnd and 6png J=3 Rydberg states of atomic lead are analyzed by the multichannel quantum defect theory (MQDT) with previous experimental energy levels. Calculated energy levels and optimal MQDT parameters were obtained by the fitting process. Theoretical energy positions of 127 levels are given. Some unknown moderately lying levels and high-lying levels are predicted. Admixture coefficients are calculated to interpret the perturbation of the perturbing channel to the 6 pnd and 6 png series.

Energy levels of perturbed 6pnd J = 2 Rydberg states of Pb I by multichannel quantum defect theory

Energy levels of the odd-parity 6p n d J = 2 Rydberg states of atomic lead are analyzed by the multichannel quantum defect theory (MQDT) with previous experimental energy levels. The 6p n d (6 ≤ n ≤ 63) J = 2 Rydberg energy levels are calculated and optimal MQDT parameters were obtained. Using these parameters, admixture coefficients for each level are calculated to designate the level denotations. The results show that strong channel mixings exist for the levels near the 6p6d (3/2)[5/2] 2 o and 6p6d (3/2)[3/2] 2 o pertubers. The five-channel model different from that in literature is used to predict 21 energy positions of 6p n d (1/2)[3/2] 2 o levels and to determine the denotations of all the 6pnd J = 2 Rydberg states under 59788 cm －1 for Pb I.

Calculations of radiative lifetimes of Rydberg6pndJ=2states of Pb I by multichannel quantum defect theory

Recently measured radiative lifetimes of the Rydberg series $6pnd\frac{1}{2}[\frac{5}{2}{]}_{2}^{o}$ and $\frac{1}{2}[\frac{3}{2}{]}_{2}^{o}$ $(n=6--13)$ of Pb I [Li et al., Phys. Rev. A 57, 3443 (1998)] have been compared with theoretical values obtained by means of multichannel quantum defect theory (MQDT) analyses. The MQDT parameters were obtained from experimentally determined energy levels. The channel admixture coefficients were calculated and used to evaluate the theoretical lifetimes. In addition, lifetime values for highly excited Rydberg states have been predicted.

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.

Relativistic Multichannel Theory: Scaling Behavior of Multichannel Quantum Defect Theory Parameters (μα, Uiα) Along the Ne-Like Iso-electronic Sequence

The compact physical parameters (μα, Uiα) in multichannel quantum defect theory (MQDT) can be directly calculated with relativistic multichannel theory (RMCT). Here we report a systematic study of the MQDT parameters (μα, Uiα) with RMCT along the Ne-like iso-electronic sequence (including Ca10+, Fe16+, Ge22+, Ag37+ ions). We find that the physical parameters (μα, Uiα) show a very interesting scaling behavior along the iso-electronic sequence.

Eigenchannel R-matrix calculation of the even-parity 6pnf J=2,3,4 autoionizing levels of barium

The 6pnf J=2,3,4 autoionizing levels of barium are studied through a combination of the eigenchannel R-matrix and the multichannel quantum defect theory (MQDT) methods. The calculation reproduces well the spectra of 6pnf series observed in excitation from 5d6p levels and confirms that the 6pnf levels have very large autoionization rates. Calculated MQDT parameters are compared with those obtained empirically from experiment and used to analyse channel interactions.

ANALYSIS OF GaII SPECTRUM BY MULTICHANNEL QUANTUM DEFECT THEORY

In this paper we have analysed the spectrum of Gall by means of multichannel quantum-defect theory (MQDT). Here the MQDT parameters for even-parity J = 0,1,2,3 and odd-parity J=1,2 bound levels involving three limits are determined through a fit of the calculated results to experimental data. The unknown energy levels of eleven Rydberg series are predicted by using these optinum parameters. The interaction between these series are discussed. The predicted energy values are in good agreement with the experimental data from ref. [1] .

Multichannel quantum defect theory of the hyperfine structure of high Rydberg states.

The multichannel quantum defect theory (MQDT) of fine structure has been extended to hyperfine structure by dividing the configuration space into three parts: The {alpha} region, the {ital i} region, and the {ital i}{sub {ital F}} region, according to the competition among short-range interaction, spin-orbit interaction, and hyperfine interaction. Then an unperturbative theory of hyperfine structure in high Rydberg states is derived. The MQDT parameters of hyperfine structure have been categorized into two parts: one is contributed by short-range and spin-orbit interactions and has been given by an analogy with the MQDT parameters of fine structure; the other is contributed by spin-orbit and hyperfine interactions and has been given analytically. The hyperfine structure in high Rydberg states can then be calculated directly from the MQDT parameters of fine structure.

Quantum-defect parametrization of perturbative two-photon ionization cross sections.

A multichannel quantum-defect theory (MQDT) parametrization of two-photon ionization (2PI) of atoms, suitable for use with ab initio calculations of perturbative 2PI amplitudes in the presence of intermediate- and/or final-state Rydberg resonances is developed. The rapid energy variation of such amplitudes is extracted in terms of elementary functions of energy and a set of MQDT parameters, which are ``smooth'' functions of energy. As an example, results of numerical computations of MQDT parameters for 2PI of atomic hydrogen (1s, 2s, and 3s) by circularly polarized light are presented. MQDT parameters for the many-channel case are derived, and an analysis of their energy dependence across Rydberg thresholds is given. The two-channel case is analyzed using phase-shifted Coulomb functions, and simple analytic formulas are given for the energy dependence of the amplitude as a function of a small set of physical parameters.

Multiphoton ionization of rare gases using multichannel-quantum-defect theory.

We apply multichannel-quantum-defect theory (MQDT) to multiphoton ionization of rare gases in lowest-order perturbation theory. We determine MQDT parameters of J = 1,3 odd-parity states, J = 0,2 even-parity states in xenon and krypton by fitting experimental energy levels and constructing Lu-Fano plots. We present calculations of two- and three-photon ionization of xenon and krypton in the autoionization region between the two thresholds. We compare autoionization spectra and also photoelectron angular distributions to experimental data (S. T. Pratt, P. M. Dehmer, and J. L. Dehmer, Phys. Rev. A 35, 3793 (1986); J. L. Dehmer, S. T. Pratt, and P. M. Dehmer, ibid. $fat 36: , 4494 (1987)). Agreement between theory and experiment is reasonable, especially for krypton.

Multiconfiguration Hartree-Fock calculations for singlet terms in neutral strontium.

Multiconfiguration Hartree-Fock (MCHF) calculations are presented for singlet terms in neutral strontium (Sr i) belonging to (perturbed) sp, sd, and sf Rydberg series. We discuss briefly some particularly difficult MCHF calculations and the steps taken to overcome the difficulties. The ab initio wave functions are used to calculate radiative lifetimes as well as individual transition rates for electric dipole and quadrupole radiation. The calculated lifetimes are compared to recent experimental results. The observed trends are well reproduced by the calculations. We compare our wave functions with wave functions obtained from multichannel quantum-defect theory (MQDT) in either of two different ways. One is based on semiempirical fitting to the observed energy levels and the other on a recent ab initio R-matrix calculation of MQDT parameters. We find good agreement with the wave functions obtained in the latter calculation, confirming earlier conjectures about the degree of reliability of semiempirical MQDT fits to perturbed Rydberg series [C. Froese Fischer and J. E. Hansen, Phys. Rev. A 24, 631 (1981)].

Eigenchannel R-matrix calculation of the photoabsorption spectrum of strontium

Presents the first detailed theoretical calculation of the absorption spectrum of Sr out of the 5s2 1S0 ground state. The autoionisation region below the 5p3/2 threshold is investigated, photoionisation cross sections being calculated by combining the multichannel quantum defect theory (MQDT) with the eigenchannel R-matrix method. Small-scale variational R-matrix calculations enable one to evaluate LS-coupled short-range reaction matrices. A jj-coupled reaction matrix is then deduced using a geometrical frame transformation. Diagonalisation of this matrix gives the energy-dependent MQDT parameters required for the description of the 13 relevant interacting channels. The 13-channel MQDT model built with theoretical R-matrix parameters provides an accurate description of the positions and the shapes of the 4d3/2,5/2 np, nf and 5p1/2,3/2 ns, nd J=1 autoionising lines. Particular attention is paid to high lying resonances observed near the spin-orbit split 4d3/2,5/2 and 5p1/2,3/2 thresholds.