Multichannel Quantum Defect Theory Research Articles

Theoretical approaches for doubly-excited Rydberg states in quasi-two-electron systems: two-electron dynamics far away from the nucleus

ABSTRACT We report on recent progress regarding the theoretical treatment of doubly-excited Rydberg states of atoms with two valence electrons. Building upon state-of-the-art techniques, we demonstrate that an approach based on configuration interaction with exterior complex scaling (CI-ECS) is capable of describing high Rydberg states () and does not rely on the assumptions of R-matrix multichannel quantum-defect theory. We show that CI-ECS allows the simultaneous, accurate treatment of a range of doubly-excited Rydberg states broader than previously possible. The implementation of the method with numerical basis functions is explained in detail. As an example, CI-ECS calculations of the doubly-excited states of Mg and Sr are presented, and excellent agreement is found with available experimental data. The CI-ECS method opens new perspectives for studying collective two-electron dynamics in doubly-excited Rydberg states of alkaline-earth metal atoms, and is also of interest for the field of Rydberg-based quantum simulation.

Precision Measurements in Few-Electron Molecules: The Ionization Energy of Metastable ^{4}He_{2} and the First Rotational Interval of ^{4}He_{2}^{+}.

Molecular helium represents a benchmark system for testing abinitio calculations on few-electron molecules. We report on the determination of the adiabatic ionization energy of the a ^{3}Σ_{u}^{+} state of He_{2}, corresponding to the energy interval between the a ^{3}Σ_{u}^{+} (v^{''}=0, N^{''}=1) state of He_{2} and the X^{+} ^{2}Σ_{u}^{+} (v^{+}=0, N^{+}=1) state of He_{2}^{+}, and of the lowest rotational interval of He_{2}^{+}. These measurements rely on the excitation of metastable He_{2} molecules to high Rydberg states using frequency-comb-calibrated continuous-wave UV radiation in a counterpropagating laser-beam setup. The observed Rydberg states were extrapolated to their series limit using multichannel quantum-defect theory. The ionization energy of He_{2} (a ^{3}Σ_{u}^{+}) and the lowest rotational interval of He_{2}^{+} (X^{+} ^{2}Σ_{u}^{+}) are 34 301.207 002(23)±0.000 037_{syst} cm^{-1} and 70.937 589(23)±0.000 060_{syst} cm^{-1}, respectively.

Multichannel interactions of two atoms in an optical tweezer

The multichannel Na-Cs interactions are characterized by a series of measurements using two atoms in an optical tweezer, along with a multichannel quantum defect theory (MQDT). The triplet and singlet scattering lengths are measured by performing Raman spectroscopy of the Na-Cs motional states and least-bound molecular state in the tweezer. Magnetic Feshbach resonances are observed for only two atoms at fields which agree well with the MQDT. Our methodology, which promotes the idea of an effective theory of interaction, can be a key step towards the understanding and the description of more complex interactions. The tweezer-based measurements in particular will be an important tool for atom-molecule and molecule-molecule interactions, where high densities are experimentally challenging and where the interactions can be dominated by intra-species processes.

Observation of state-to-state hyperfine-changing collisions in a Bose-Fermi mixture of Li6 and K41 atoms

Hyperfine-changing collisions are of fundamental interest for the studying of ultracold heteronuclear mixtures. Here, we report the state-to-state study of the hyperfine-changing-collision dynamics in a Bose-Fermi mixture of $^6$Li and $^{41}$K atoms. The collision products are directly observed and the spin-changing dynamics is measured. Based on a two-body collision model, the experimental results are simultaneously fitted from which the spin-changing rate coefficient of $ 1.9(2)\times 10^{-12}~\rm{cm^3\cdot s^{-1}}$ is gained, being consistent with the multi-channel quantum defect theory calculation. We further show that the contact parameter of $^6$Li-$^{41}$K mixture can be extracted from the measured spin-changing dynamics. The obtained results are consistent with the first order perturbation theory in the weakly-interacting limit. Our system offers great promise for studying spin-changing interactions in heteronuclear mixtures.

Dissociative Recombination of Cold HeH^{+} Ions.

The HeH^{+} cation is the simplest molecular prototype of the indirect dissociative recombination (DR) process that proceeds through electron capture into Rydberg states of the corresponding neutral molecule. This Letter develops the first application of our recently developed energy-dependent frame transformation theory to the indirect DR processes. The theoretical model is based on the multichannel quantum-defect theory with the vibrational basis states computed using exterior complex scaling of the nuclear Hamiltonian. The abinitio electronic R-matrix theory is adopted to compute quantum defects as functions of the collision energy and of the internuclear distance. The resulting DR rates are convolved over the beam energy distributions relevant to a recent experiment at the Cryogenic Storage Ring, giving good agreement between the experiment and the theory.

Model for vibronic excitation of CH+ by resonant scattering of electron

SynopsisA new model for theoretical study of vibronic (de-)excitation (including vibrational (de-)excitation) cross sections of CH+ by electron impact was developed based on the multichannel quantum defect theory (MQDT) close-channel-elimination procedure and vibrational-frame-transformation theory of Chang and Fano. The successful application of this model suggested a promising calculation method for vibronic (de-)excitation of diatomic ion core by resonant scattering of electron.

Electron dissociative attachement to ArH+, HD+, N2 + and CO2

SynopsisWe will present our recent results in the study of electron-induced reactivity of ionized and neutral molecules. The Configuration Interaction method and the Multichannel Quantum Defect Theory have been employed in order to obtain cross sections for collisions of electrons with ArH+, HD+, N2 and CO2.

Spectroscopy and photoionization of C+ ions by the relativistic eigenchannel R-matrix method

SynopsisThe scattering matrices of C+ are calculated by using our relativistic eigenchannel R-matrix method. With the merits of the analytical continuation properties of the scattering matrices, lots of atomic dynamical data with accuracy are obtained. Much physical quantities are acquired by applying the multichannel quantum defect theory (MQDT) procedure. The present calculated results are in good agreement with the available experimental data, which has been shown by the newly proposed projected high dimensional quantum defect graph (symmetrized), namely JHANGZ plot.

Calculations of long range interactions for 87Sr Rydberg states

A method for calculating the properties of Rydberg states and Rydberg–Rydberg interaction between two 87Sr atoms is described. The method is based on a multichannel quantum defect theory description of the Rydberg states that accounts for the hyperfine splitting of the 87Sr+ ground state. Results are given for the scalar and tensor polarizabilities and the eigenvalues of the C6 matrix for the 5sns FT = 9/2 series. These results illustrate the new features that arise due to the hyperfine splitting of the thresholds. In particular, there should be several couple Förster resonances above n = 50 unlike the case of 88Sr which has none.

Time delays in ultracold atomic and molecular collisions

We study the behavior of the Eisenbud-Wigner collisional time delay around Feshbach resonances in cold and ultracold atomic and molecular collisions. We carry out coupled-channels scattering calculations on ultracold Rb and Cs collisions. In the low-energy limit, the time delay is proportional to the scattering length, so exhibits a pole as a function of applied field. At high energy, it exhibits a Lorentzian peak as a function of either energy or field. For narrow resonances, the crossover between these two regimes occurs at an energy proportional to the square of the resonance strength parameter $s_\textrm{res}$. For wider resonances, the behavior is more complicated and we present an analysis in terms of multichannel quantum defect theory.

Electron-Induced Excitation, Recombination, and Dissociation of Molecular Ions Initiating the Formation of Complex Organic Molecules

We review the study of dissociative recombination and ro-vibrational excitation of diatomic and small polyatomic molecular ions initiating complex organic molecules formation. In particular, we show how Multichannel Quantum Defect Theory (MQDT) and R-matrix methods are used to compute cross sections and rate coefficients for cations in well defined ro-vibrational levels of the ground electronic state, from sub-meV up to few eV collision energies. The most recent MQDT results are compared with either other theoretical data, or with measured data obtained in storage-ring experiments.

Dissociative Recombination of CH+ Molecular Ion Induced by Very Low Energy Electrons

We used the multichannel quantum defect theory to compute cross sections and rate coefficients for the dissociative recombination of CH + initially in its lowest vibrational level v i + = 0 with electrons of incident energy below 0.2 eV. We have focused on the contribution of the 2 2 Π state which is the main dissociative recombination route at low collision energies. The final cross section is obtained by averaging the relevant initial rotational states ( N i + = 0 , ⋯ , 10 ) with a 300 K Boltzmann distribution. The Maxwell isotropic rate coefficients for dissociative recombination are also calculated for different initial rotational states and for electronic temperatures up to a few hundred Kelvins. Our results are compared to storage-ring measurements.

Analysis of vibrational autoionization of CaF Rydberg states.

We report calculations of vibrational autoionization rates of CaF Rydberg states, based on the results of a global multi-channel quantum defect theory (MQDT) fit. Our goal is to use intuitive physical models to interpret and extend the results from the MQDT calculations and, in particular, to characterize the physical mechanisms for the interaction between the Rydberg electron and the ion-core. The calculations indicate that, among the six strongly l-mixed core-penetrating (CP) Rydberg series of CaF, the n.36 p^Π Rydberg series has the fastest Δv = 1 vibrational autoionization rate, which is at least four times larger than that for the other CP Rydberg series, in agreement with experimental results. We first demonstrate that the rotational level dependence of the vibrational autoionization rate of the n.36 p^Π series is satisfactorily explained by l-uncoupling interactions, which differ for the positive and negative Kronig symmetry levels. Next, we interpret the relative vibrational autoionization rates of all six CP Rydberg series in the context of a valence-precursor (VP) model. The VP model is a consequence of Mulliken's rule, which states that the innermost lobe of the Rydberg wavefunction remains invariant in both the nodal position and shape for members of the same Rydberg series. The electronic properties of the six VP states, which are the terminus states (lowest-n) of each of the six CP Rydberg series, are further characterized in terms of a ligand-field model, providing insight into the intimate relationship between the Rydberg electron density in the ion-core region and the vibrational autoionization rate.

Spectrum of Field-Ionized Triplet Gerade Rydberg States of H2 and Comparison to Multichannel Quantum-Defect Theory.

A spectrum of field-ionized triplet Rydberg states of gerade symmetry H2 has been measured, excited from the υ″ = 0, N″ = 1-3 rovibrational levels of the metastable c3Πu-2pπ state in a 6 keV fast molecular beam. The field-ionized spectrum is kinetic energy labeled in order to separate it from the well-studied υ+ ≥ 1 autoionization spectrum. The spectrum consists of both ns and nd Rydberg series with n between 10 and 28 converging to the υ+ = 0, N+ = 1-3 levels of the X+ 2Σg+ ground state of H2+. Transitions with changes in vibration and/or rotation are also identified. The spectral positions of 59 transitions in the field ionization spectrum are identified and assigned quantum numbers using the predictions of multichannel quantum-defect theory (MQDT). The transition energies and subsequent effective quantum defects are compared between the experiment and theory. Most of the observed transitions, within the experimental uncertainty of 0.2 cm-1, agree with the energies predicted by MQDT.

The modulating action of electric field on magnetically tuned Feshbach resonance

We investigate the modulating action of an external electric field on the magnetically tuned Feshbach resonance in ultracold heteronuclear atomic collision by using the multichannel quantum-defect theory (MQDT). The coupling between different partial wave states induced by an electric field is included into the singlet and triplet quantum defect matrices y(0) and y(1). By taking the truncated -C6/R6 - C8/R8 - C10/R10 potential as the reference potential, the threshold behaviors of four quantum-defect parameters for the lowest three partial waves are described. The results calculated by using the MQDT agree with those calculated using the coupled channel method. Moreover, we present an analytical expression used for describing the variation of the position and width of the magnetically tuned Feshbach resonance modulated by an electric field.

The study on high <i>n</i> Rydberg state of La II

We analyze ionic spectrum of lanthanum via intermediate state (Xe)<inline-formula><tex-math id="M191">\begin{document}$ 5d6d \; ^3F_2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M191.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M191.png"/></alternatives></inline-formula> in the energy region 89872-91783 cm<sup>–1</sup>, and the spectrum is obtained using five-laser resonance excitation in combination with a method of sequential ionization by a pulsed electric field and a constant electric field, and has been recalibrate in this work. Both of one strong and one weak autoionization Rydberg series converging to the La<sup>2+</sup> state are determined. Meanwhile, the two autoionization Rydberg series are assigned by relativistic multichannel theory (RMCT) within the framework of multi-channel quantum defect theory (MQDT). More specifically, the strong autoionization Rydberg series is assigned to <inline-formula><tex-math id="M192">\begin{document}$ 5dnp\left(\dfrac{5}{2},\dfrac{1}{2}\right)_3 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M192.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M192.png"/></alternatives></inline-formula> and/or <inline-formula><tex-math id="M193">\begin{document}$ 5dnp\left(\dfrac{5}{2},\dfrac{1}{2}\right)_2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M193.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M193.png"/></alternatives></inline-formula>, and the weak autoionization Rydberg series is assigned to <inline-formula><tex-math id="M194">\begin{document}$ 5dnf\left(\dfrac{5}{2},\dfrac{5}{2}\right)_3 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M194.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M194.png"/></alternatives></inline-formula> and/or <inline-formula><tex-math id="M195">\begin{document}$ 5dnf\left(\dfrac{5}{2},\dfrac{5}{2}\right)_2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M195.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M195.png"/></alternatives></inline-formula>. We focus on the behavior of quantum defect with excitation energy for high <inline-formula><tex-math id="M196">\begin{document}$ n $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M196.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M196.png"/></alternatives></inline-formula> Rydberg states, which are sensitive to the existence of a external field. We find the breakdown of quantum defect regular behavior for a specific Rydberg series and autoionization Rydberg series of La<sup>+</sup> as the effective quantum number <inline-formula><tex-math id="M197">\begin{document}$ n^\star>67 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M197.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M197.png"/></alternatives></inline-formula>. Due to that our calculations, which are obtained by relativistic multichannel theory and included configuration interactions, are in basically agreement with that for experimental low <inline-formula><tex-math id="M198">\begin{document}$ n $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M198.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M198.png"/></alternatives></inline-formula> (<inline-formula><tex-math id="M199">\begin{document}$ n^\star<67 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M199.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20181980_M199.png"/></alternatives></inline-formula>) Rydberg states as well as small stray electric fields, we suggest that plasma formed by photoionization of La atoms in the second excitation step may be responsible for the breakdown of quantum defect regular behavior.

Laser and microwave spectroscopy of even-parity Rydberg states of neutral ytterbium and multichannel-quantum-defect-theory analysis

New measurements of high-lying even parity $6sns\, {}^1 \! S_0$ and $6snd\,{}^{3,1}\!D_2$ levels of neutral $^{174}$Yb are presented in this paper. Spectroscopy is performed by a two-step laser excitation from the ground state $4f^{14}6s^2 \, {}^1 \! S_0$, and the Rydberg levels are detected by using the field ionization method. Additional two-photon microwave spectroscopy is used to improve the relative energy accuracy where possible. The spectroscopic measurements are complemented by a multichannel quantum defect theory (MQDT) analysis for the J=0 and the two-coupled J=2 even parity series. We compare our results with the previous analysis of Aymar {\it{et al}} \cite{Aymar_1980} and analyze the observed differences. From the new MQDT models, a revised value for the first ionization limit $I_{6s}=50443.07041(25)$ cm$^{-1}$ is proposed.

Low-energy collisions between electrons and hydrogen fluoride cations

We have studied slow electron collisions with hydrogen fluoride cations in the framework of multi-channel quantum defect theory. Assuming energy-independent interactions, the short-range reaction matrix has been evaluated in the second order of the Born expansion of the Lippmann–Schwinger equation. The isotopic effects on the cross sections and thermal rate coefficients for dissociative recombination, vibrational excitation and de-excitation have been investigated.

Broad Feshbach resonances in ultracold alkali-metal systems

A comprehensive search for "broad" Feshbach resonances (FRs) in all possible combinations of stable alkali-metal atoms is carried out, using a multi-channel quantum-defect theory assisted by the analytic wave functions for a long-range van-der-Waals potential. A number of new "broad" $s$-, $p$- and $d$-wave FRs in the lowest-energy scattering channels, which are stable against two-body dipolar spin-flip loss, are predicted and characterized. Our results also show that "broad" FRs of $p$- or $d$-wave type that are free of two-body loss do not exist between fermionic alkali-metal atoms for magnetic field up to 1000\,G. These findings constitute helpful guidance on efforts towards experimental study of high-partial-wave coupling induced many-body physics.

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

Cross sections for rotational excitation and de-excitation of the HeH+ ion by an electron impact are computed using a theoretical approach that combines the UK R-matrix code and the multi-channel quantum defect theory. The thermally-averaged rate coefficients derived from the obtained cross sections are fitted to an analytical formula valid for a wide range of temperatures.