Multichannel Quantum Defect Theory Research Articles

Inter-Series Interactions on the Atomic Photoionization Spectra Studied by the Phase-Shifted Multichannel-Quantum Defect Theory

Development in mathematical formulations of parameterizing the resonance structures using the phase-shifted multichannel quantum defect theory (MQDT) and their use in analyzing the effect of inter-series interactions on the autoionizing Rydberg spectra is reviewed. Reformulation of the short-range scattering matrix into the form analogous to S = SBSR in scattering theory are the crucial step in this development. Formulation adopts different directions and goals depending on whether autoionizing series converge to the same limit (degenerate) or to different limits (nondegenerate) because of the different nature of the perturbation. For the nondegenerate case, finding the simplest form of profile index functions of the autoionizing spectra with the minimal number of parameters is the main goal and some results are reviewed. For the degenerate case where perturbation acts uniformly throughout the entire series, isolation of the overlapped autoionizing series into the unperturbed autoionizing series is the key objective in research and some results in that direction are reviewed.

Even-parity Rydberg and autoionizing states of lutetium by laser resonance-ionization spectroscopy

Multi-step laser resonance ionization spectroscopy of lutetium (Lu) has been performed at TRIUMF's off-line laser ion source test stand. The even-parity Rydberg series $6s^2nd$ $^2D_{3/2}$, $6s^2nd$ $^2D_{5/2}$ and $6s^2ns$ $^2S_{1/2}$ were observed converging to the 6s$^2$ ionization potential. The experimental results has been compared to previous work. 51 levels of Rydberg series $6s^2nd$ $^2D_{5/2}$ and 52 levels of Rydberg series $6s^2ns$ $^2S_{1/2}$ were reported new. Additionally six even-parity autoionization (AI) series converging to Lu ionic states $5d6s$ $^3D_1$ and $5d6s$ $^3D_2$ were observed. The level energies of these AI states were measured. The configurations of the AI states were assigned by relativistic multichannel theory (RMCT) within the framework of multichannel quantum defect theory (MQDT).

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.

Effective control of cold collisions with radio-frequency fields

We study $^{87}\mathrm{Rb}$ cold collisions in a static magnetic field and a single-color radio-frequency (RF) field by employing the multichannel quantum defect theory in combination with the Floquet method to solve the two-body time-dependent Schr\"odinger equation. Our results show that RF fields can modify the two-body scattering length by a large scale through Feshbach resonances in both low- and high-static magnetic-field regimes. Such RF-induced Feshbach resonances can be applied to quenching experiments or control of interactions in spinor condensates. Here, we also show that, analogously to photoassociation, RF fields can also associate cold atoms into molecules at a useful rate.

Theoretical resonant electron-impact vibrational excitation, dissociative recombination and dissociative excitation cross sections of ro-vibrationally excited BeH+ ion

A theoretical study of resonant vibrational excitation, dissociative recombination and dissociative excitation processes of the beryllium monohydride cation, BeH+, induced by electron impact, is reported. Full sets of ro-vibrationally-resolved cross sections and of the corresponding Maxwellian rate coefficients are presented for the three processes. Particular emphasis is given to the high-energy behaviour. Potential curves of , and symmetries and the corresponding resonance widths, obtained from R-matrix calculations, provide the input for calculations which use a local complex-potential model for resonant collisions in each of the three symmetries. Rotational motion of nuclei and isotopic effects are also discussed. The relevant results are compared with those obtained using a multichannel quantum defect theory method. Full results are available from the Phys4Entry database.

Quantum defect theory for the orbital Feshbach resonance

In the ultracold gases of alkali-earth-metal-like atoms, a new type of Feshbach resonance, i.e., the orbital Feshbach resonance (OFR), has been proposed and experimentally observed in ultracold $^{173}\mathrm{Yb}$ atoms [R. Zhang et al., Phys. Rev. Lett. 115, 135301 (2015)]. When the OFR of the $^{173}\mathrm{Yb}$ atoms occurs, the energy gap between the open and closed channels is smaller by two orders of magnitude than the van der Waals energy. As a result, quantitative accurate results for the low-energy two-body problems can be obtained via multichannel quantum defect theory (MQDT), which is based on the exact solution of the Schr\"odinger equation with the van der Waals potential. In this paper we use MQDT to calculate the two-atom scattering length, effective range, and binding energy of two-body bound states for the systems with OFR. With these results we further study the clock-transition spectrum for the two-body bound states, which can be used to experimentally measure the binding energy. Our results are helpful for the quantitative theoretical and experimental research for the ultracold gases of alkali-earth-metal-like atoms with OFR.

Potential energy surface of the Rydberg states of the NO molecule in an intense IR radiation field

A method taking into account valence (non-Rydberg) and dissociative configurations has been developed for calculation of potential energy surfaces of the NO molecule in an intense IR radiation field. The resonance rovibronic structure of the Rydberg molecule–laser field quantum system has been analyzed within the steady-state formalism of the radiation collision matrix using multi-channel quantum defect theory. Special conditions for field control of predissociation involving intermediate Rydberg and valence states have been formulated.

Cross Sections and Rate Coefficients for Vibrational Excitation of HeH+ Molecule by Electron Impact

Cross sections and thermally-averaged rate coefficients for vibration (de-)excitation of HeH + by an electron impact are computed using a theoretical approach that combines the multi-channel quantum defect theory and the UK R-matrix code. Fitting formulas with a few numerical parameters are derived for the obtained rate coefficients. The interval of applicability of the formulas is from 40 to 10,000 K.

Resonance ionization spectroscopy in dysprosium

We report on resonance ionization spectroscopy (RIS) of high-lying energy levels in dysprosium. We developed efficient excitation schemes and re-determined the first ionization potential (IP) via analysis of Rydberg convergences. For this purpose both two- and three-step excitation ladders were investigated. An overall ionization efficiency of 25(4) % could be demonstrated in the RISIKO mass separator of Mainz University, using a three-step resonance ionization scheme. Moreover, an extensive analysis of the even-parity 6sns- and 6snd-Rydberg-series convergences, measured via two-step excitation was performed. To account for strong perturbations in the observed s-series, the approach of multichannel quantum defect theory (MQDT) was applied. Considering all individual series limits we extracted an IP-value of 47901.76(5) cm−1, which agrees with the current literature value of 47901.7(6) cm−1, but is one order of magnitude more precise.

Observation of broad p -wave Feshbach resonances in ultracold Rb85−Rb87 mixtures

We observe new Feshbach resonances in ultracold mixtures of $^{85}$Rb and $^{87}$Rb atoms in the $^{85}$Rb$|2, +2\rangle$+$^{87}$Rb$|1, +1\rangle$ and $^{85}$Rb$|2, -2\rangle$+$^{87}$Rb$|1, -1\rangle$ scattering channels. The positions and properties of the resonances are predicted and characterized using the semi-analytic multichannel quantum-defect theory by Gao. Of particular interest, a number of broad entrance-channel dominated p-wave resonances are identified, implicating exciting opportunities for studying a variety of p-wave interaction dominated physics.

Electron impact on vibrationally cold

The dissociative recombination and vibrational excitation processes induced by electron impact on vibrationally cold are investigated in the framework of the multichannel quantum defect theory for electron energies below 1 eV. The thermal rate coefficients for the electron temperature range from 10 to 5000 K are reported.

Quantum-state-controlled Penning-ionization reactions between ultracold alkali-metal and metastable helium atoms

In an ultracold, optically trapped mixture of $^{87}$Rb and metastable triplet $^4$He atoms we have studied trap loss for different spin-state combinations, for which interspecies Penning ionization is the main two-body loss process. We observe long trapping lifetimes for the purely quartet spin-state combination, indicating strong suppression of Penning ionization loss by at least two orders of magnitude. For the other spin-mixtures we observe short lifetimes that depend linearly on the doublet character of the entrance channel. We compare the extracted loss rate coefficient with recent predictions of multichannel quantum-defect theory for reactive collisions involving a strong exothermic loss channel and find near-universal loss for doublet scattering. Our work demonstrates control of reactive collisions by internal atomic state preparation.

Low-energy collisions between electrons and [formula omitted]: Cross sections and rate coefficients for all the vibrational states of the ion

We provide cross sections and Maxwell rate coefficients for reactive collisions of slow electrons with BeH+ ions on all the eighteen vibrational levels (X1Σ+,vi+=0,1,2,…,17) using a Multichannel Quantum Defect Theory (MQDT)—type approach. These data on dissociative recombination, vibrational excitation and vibrational de-excitation are relevant for magnetic confinement fusion edge plasma modeling and spectroscopy, in devices with beryllium based main chamber materials, such as the International Thermonuclear Experimental Reactor (ITER) and the Joint European Torus (JET). Our results are presented in graphical form and as fitted analytical functions, the parameters of which are organized in tables.

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.

Dissociative recombination and vibrational excitation of BF+ in low energy electron collisions

The latest molecular data—potential energy curves and Rydberg-valence interactions—characterising the super-excited electronic states of BF are reviewed in order to provide the input for the study of their fragmentation dynamics. Starting from this input, the main paths and mechanisms of BF+ dissociative recombination and vibrational excitation are analysed. Their cross sections are computed for the first time using a method based on the multichannel quantum defect theory (MQDT), and Maxwellian rate-coefficients are calculated and displayed in ready-to-be-used format for low temperature plasma kinetics simulations.

Experimental and Theoretical Studies of Low‐Energy Penning Ionization of NH3, CH3F, and CHF3

We present results from a joint theoretical and experimental study of the low-energy Penning ionization of NH3 , CH3 F, and CHF3 by metastable Ne(3 P2 ) and He(3 S1 ) atoms. We combine the merged neutral beams experiment, covering a range of collision energies between 0.1-150 K, with multichannel quantum defect theory calculations based on interaction potentials from symmetry-adapted perturbation theory. The three symmetric tops provide several distinct properties that make them interesting targets for cold chemistry studies. Of these three, only NH3 has a lone electron pair that leads to a strong binding with rare gas atoms. The CHF3 molecule has much smaller rotational constants than both NH3 and CH3 F, and thus has a considerably higher density of rotational states already at low energies. Their presence opens inelastic collision channels that reduce the observed reactive cross section. We show that this effect dominates the total rate coefficient in heavy molecules already at relatively low collision energies but is much less prominent for lighter molecules.

Direct optical access to the triplet manifold of states inH2

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 $\ensuremath{\ell}=3$ orbital momentum). They appear via weak $\ensuremath{\ell}\ensuremath{-}$ 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 $c{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{u}^{\ensuremath{-}}$ state can be populated via one-photon absorption of uv photons followed by cascade emission $4f\ensuremath{\rightarrow}3d\ensuremath{\rightarrow}2p$.

High-resolution measurement for photoabsorption cross sections in the autoionization regions of ar, kr and xe

Photoabsorption cross sections in the autoionization regions of Ar, Kr and Xe have been measured with resolutions of 0.0045 AA for Ar and 0.0074 AA for Kr and Xe using a high-resolution spectrometer installed in the Photon Factory, a 2.5 GeV synchrotron radiation facility in Tsukuba. The cross sections are parametrized with the aid of a lineshape formula which is based on the multichannel quantum-defect theory and has a form analogous to Fano's resonance formula. These are compared in detail with other experimental data and theoretical predictions available in the literature.

Associative ionization reaction N + O → NO+ + e– in slow collisions of atoms

The endothermic associative ionization reaction N(2D) + O(3P) → NO** → NO(1Σ+) +e- in slow collisions of the atoms has been considered in terms of the multichannel quantum defect theory. The dependences of the partial and total cross sections of the reaction on the energy of the colliding atoms in the range of 0–0.3 eV have been calculated. It has been shown that the cross sections have a pronounced resonance structure, which is formed as a result of the multichannel interaction of autoionization states of the intermediate Rydberg complex NO** with dissociative states. The temperature dependence of the reaction rate constant is presented. The results are compared with those of other calculations and available experimental data.

Absorption, autoionization, and predissociation in molecular hydrogen: High-resolution spectroscopy and multichannel quantum defect theory

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 (2)Σ(g)(+) 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.