Spectroscopy of short-lived radioactive molecules

Experimental perspectives on the matter-antimatter asymmetry puzzle: developments in electron EDM and [Formula: see text] experiments

In the search for clues to the matter-antimatter puzzle, experiments with atoms or molecules play a particular role. These systems allow measurements with very high precision, as demonstrated by the unprecedented limits down to [Formula: see text] e cm on electron EDM using molecular ions, and relative measurements at the level of [Formula: see text] in spectroscopy of antihydrogen atoms. Building on these impressive measurements, new experimental directions offer potential for drastic improvements. We review here some of the new perspectives in those fields and their associated prospects for new physics searches. This article is part of the theme issue 'The particle-gravity frontier'.

Analytic gradients for relativistic exact-two-component equation-of-motion coupled-cluster singles and doubles method

A first implementation of analytic gradients for spinor-based relativistic equation-of-motion coupled-cluster singles and doubles method using an exact two-component Hamiltonian augmented with atomic mean-field spin-orbit integrals is reported. To demonstrate its applicability, we present calculations of equilibrium structures and harmonic vibrational frequencies for the electronic ground and excited states of the radium mono-amide molecule (RaNH2) and the radium mono-methoxide molecule (RaOCH3). Spin-orbit coupling is shown to quench Jahn-Teller effects in the first excited state of RaOCH3, resulting in a C3v equilibrium structure. The calculations also show that the radium atoms in these molecules serve as efficient optical cycling centers.

Relativistic coupled-cluster calculations of RaOH pertinent to spectroscopic detection and laser cooling

A relativistic coupled-cluster study of the low-lying electronic states in the radium monohydroxide molecule (RaOH), a radioactive polyatomic molecule of interest to laser cooling and to the search of new physics beyond the Standard Model, is reported. The level positions of the A2Π1/2 and C2Σ states have been computed with an accuracy of around 200 cm-1 to facilitate spectroscopic observation of RaOH using laser induced fluorescence spectroscopy, thereby exploiting the systematic convergence of electron-correlation and basis-set effects in relativistic coupled-cluster calculations. The energy level for the B2Δ3/2 state has also been calculated accurately to conclude that the B2Δ3/2 state lies above the A2Π1/2 state. This confirms X2Σ ↔ A2Π1/2 as a promising optical cycling transition for laser cooling RaOH.

Quantum-Enhanced Metrology for Molecular Symmetry Violation Using Decoherence-Free Subspaces

We propose a method to measure time-reversal symmetry violation in molecules that overcomes the standard quantum limit while leveraging decoherence-free subspaces to mitigate sensitivity to classical noise. The protocol does not require an external electric field, and the entangled states have no first-order sensitivity to static electromagnetic fields as they involve superpositions with zero average lab-frame projection of spins and dipoles. This protocol can be applied with trapped neutral or ionic species, and can be implemented using methods that have been demonstrated experimentally.

Ab initio study of electronic states and radiative properties of the AcF molecule

Relativistic coupled-cluster calculations of the ionization potential, dissociation energy, and excited electronic states under 35 000 cm-1 are presented for the actinium monofluoride (AcF) molecule. The ionization potential is calculated to be IPe = 48 866 cm-1, and the ground state is confirmed to be a closed-shell singlet and thus strongly sensitive to the T,P-violating nuclear Schiff moment of the Ac nucleus. Radiative properties and transition dipole moments from the ground state are identified for several excited states, achieving a mean uncertainty estimate of ∼450 cm-1 for the excitation energies. For higher-lying states that are not directly accessible from the ground state, possible two-step excitation pathways are proposed. The calculated branching ratios and Franck-Condon factors are used to investigate the suitability of AcF for direct laser cooling. The lifetime of the metastable (1)3Δ1 state, which can be used in experimental searches of the electric dipole moment of the electron, is estimated to be of order 1 ms.

Optimizing Quantum Control Pulses with Gaussian Process Priors: The Spectral Way

This study presents the Gaussian Process Prior Optimization for Pulse Shaping (GPPOPS) methodology, a novel approach to pulse shaping engineering. Its main objective is to efficiently identify laser pulse shapes that can achieve a desired task encoded in a cost function while being experimentally implementable. The AlH⁺ molecule was utilized as a test case to find pulse shapes that maximized vibronic transitions. The results demonstrate that optimal pulses can be readily implemented using current laser technology and that their control capabilities can withstand noise. The study emphasizes the benefits of constructing a surrogate approach to the control landscape during the optimization process. This approach is expected to be versatile, efficient and readily implementable in the laboratory. Its demonstrated robustness to noise sets it apart from other numerical pulse shaping engineering methods. By reducing the required experimental labor, this method has the potential to facilitate breakthroughs in quantum engineering.

Probing fundamental particles with molecules

Molecular spectroscopy constrains the size of the electron's electric dipole moment.

Intensity-Borrowing Mechanisms Pertinent to Laser Cooling of Linear Polyatomic Molecules

A study of the intensity-borrowing mechanisms important to optical cycling transitions in laser-coolable polyatomic molecules arising from non-adiabatic coupling, contributions beyond the Franck-Condon approximation, and Fermi resonances is reported. It has been shown to be necessary to include non-adiabatic coupling to obtain computational accuracy that is sufficient to be useful for laser cooling of molecules. The predicted vibronic branching ratios using perturbation theory based on the non-adiabatic mechanisms have been demonstrated to agree well with those obtained from variational discrete variable representation calculations for representative molecules including CaOH, SrOH, and YbOH. The electron-correlation and basis-set effects on the calculated transition properties, including the vibronic coupling constants, the spin-orbit coupling matrix elements, and the transition dipole moments, and on the calculated branching ratios have been thoroughly studied. The vibronic branching ratios predicted using the present methodologies demonstrate that RaOH is a promising radioactive molecule candidate for laser cooling.

Zwitterions Functionalized by Optical Cycling Centers: Toward Laser-Coolable Polyatomic Molecular Cations

Functionalization of large aromatic compounds and biomolecules with optical cycling centers (OCC) is of considerable interest for the design and engineering of molecules with a highly selective optical photoresponse. Both internal and external dynamics in such molecules can be precisely controlled by lasers, enabling their efficient cooling and opening up broad prospects for high-precision spectroscopy, ultracold chemistry, enantiomer separation, and various other fields. The way the OCC is bonded to a molecular ligand is crucial to the optical properties of the OCC, first of all, for the degree of closure of the optical cycling loop. Here we introduce a novel type of functionalized molecular cation where a positively charged OCC is bonded to various organic zwitterions with a particularly high permanent dipole moment. We consider strontium(I) complexes with betaine and other zwitterionic ligands and show the possibility of creating efficient and highly closed population cycling for dipole-allowed optical transitions in such complexes.

New Developments in the Production and Research of Actinide Elements

This article briefly reviews topics related to actinide research discussed at the virtual workshop Atomic Structure of Actinides & Related Topics organized by the University of Mainz, the Helmholtz Institute Mainz, and the GSI Helmholtz Centre for Heavy Ion Research, Darmstadt, Germany, and held on the 26–28 May 2021. It includes references to recent theoretical and experimental work on atomic structure and related topics, such as element production, access to nuclear properties, trace analysis, and medical applications.

Accurate ab initio calculations of RaF electronic structure appeal to more laser-spectroscopical measurements

Recently, a breakthrough has been achieved in laser-spectroscopic studies of short-lived radioactive compounds with the first measurements of the radium monofluoride molecule (RaF) UV/vis spectra. We report results from high-accuracy ab initio calculations of the RaF electronic structure for ground and low-lying excited electronic states. Two different methods agree excellently with experimental excitation energies from the electronic ground state to the ²Π_1/2 and ²Π_3/2 states, but lead consistently and unambiguously to deviations from experimental-based adiabatic transition energy estimates for the ²Σ_1/2 excited electronic state, and show that more measurements are needed to clarify spectroscopic assignment of the ²Δ state.

Development of 222Rn Emanation Sources with Integrated Quasi 2π Active Monitoring

In this work, a novel approach for the standardization of low-level 222Rn emanation is presented. The technique is based on the integration of a 222Rn source, directly, with an α-particle detector, which allows the residual 222Rn to be continuously monitored. Preparation of the device entails thermal physical vapor deposition of 226RaCl2 directly onto the surface of a commercially available ion implanted Si-diode detector, resulting in a thin-layer geometry. This enables continuous collection of well resolved α-particle spectra of the nuclei, decaying within the deposited layer, with a detection efficiency of approximately 0.5 in a quasi 2π geometry. The continuously sampled α-particle spectra are used to derive the emanation by statistical inversion. It is possible to achieve this with high temporal resolution due to the small background and the high counting efficiency of the presented technique. The emanation derived in this way exhibits a dependence on the relative humidity of up to 15% in the range from 20% rH to 90% rH. Traceability to the SI is provided by employing defined solid-angle α-particle spectrometry to characterize the counting efficiency of the modified detectors. The presented technique is demonstrated to apply to a range covering the release of at least 1 to 210 222Rn atoms per second, and it results in SI-traceable emanation values with a combined standard uncertainty not exceeding 2%. This provides a pathway for the realization of reference atmospheres covering typical environmental 222Rn levels and thus drastically improves the realization and the dissemination of the derived unit of the activity concentration concerning 222Rn in air.

Fock-space relativistic coupled cluster study on the RaF molecule promising for the laser cooling

The potential energy curves of the ground and five low-lying excited terms of the RaF molecule are calculated using the Fock-space relativistic coupled theory. The electronic term energies, equilibrium internuclear distances, transition and permanent dipole moments, sequences of vibrational energies, harmonic vibrational frequencies, Franck-Condon factors, and radiative lifetimes are predicted. The calculated spectroscopic constants are in good agreement with the available theoretical and experimental data. The scheme for the direct laser cooling involving the first excited A²П_1/2 state is proposed. The data obtained in this study suggests the A²П_1/2 → X²Σ⁺ channel in the RaF molecule is the almost ideal case for direct laser cooling. It is quite possible that the effective cooling scheme for the RaF molecule can be realized using only one pump laser.

On the Feasibility of Rovibrational Laser Cooling of Radioactive RaF+ and RaH+ Cations

Polar radioactive molecules have been suggested to be exceptionally sensitive systems in the search for signatures of symmetry-violating effects in their structure. Radium monofluoride (RaF) possesses an especially attractive electronic structure for such searches, as the diagonality of its Franck-Condon matrix enables the implementation of direct laser cooling for precision experiments. To maximize the sensitivity of experiments with short-lived RaF isotopologues, the molecular beam needs to be cooled to the rovibrational ground state. Due to the high kinetic energies and internal temperature of extracted beams at radioactive ion beam (RIB) facilities, in-flight rovibrational cooling would be restricted by a limited interaction timescale. Instead, cooling techniques implemented on ions trapped within a radiofrequency quadrupole cooler-buncher can be highly efficient due to the much longer interaction times (up to seconds). In this work, the feasibility of rovibrationally cooling trapped RaF+ and RaH+ cations with repeated laser excitation is investigated. Due to the highly diagonal nature between the ionic ground state and states in the neutral system, any reduction of the internal temperature of the molecular ions would largely persist through charge-exchange without requiring the use of cryogenic buffer gas cooling. Quasirelativistic X2C and scalar-relativistic ECP calculations were performed to calculate the transition energies to excited electronic states and to study the nature of chemical bonding for both RaF+ and RaH+. The results indicate that optical manipulation of the rovibrational distribution of trapped RaF+ and RaH+ is unfeasible due to the high electronic transition energies, which lie beyond the capabilities of modern laser technology. However, more detailed calculations of the structure of RaH+ might reveal possible laser-cooling pathways.

The role of QED effects in transition energies of heavy-atom alkaline earth monofluoride molecules: A theoretical study of Ba+, BaF, RaF, and E120F

Heavy-atom alkaline earth monofluoride molecules are considered as prospective systems to study spatial parity or spatial parity and time-reversal symmetry violating effects such as the nuclear anapole moment or the electron electric dipole moment. A comprehensive and highly accurate theoretical study of the electronic structure properties and transition energies in such systems can simplify the preparation and interpretation of the experiments. However, almost no attempts to calculate quantum electrodynamics (QED) effects' contribution into characteristics of these neutral heavy-atom molecules have been performed. Recently, we have formulated and implemented such an approach to calculate QED contributions to transition energies of molecules [L. V. Skripnikov, J. Chem. Phys. 154, 201101 (2021)]. In this paper, we perform a benchmark theoretical study of the transition energies in the Ba⁺ cation and BaF molecule. The deviation of the calculated values from the experimental ones is of the order 10 cm^-1 and is more than an order of magnitude better than the "chemical accuracy," 350 cm^-1. The achievement of such an agreement has been provided, in particular, by the inclusion of the QED effects. The latter appeared to be not less important than the high-order correlation effects beyond the coupled cluster with single, double, and perturbative triple cluster amplitude level. We compare the role of QED effects for transition energies with heavier molecules-RaF and E120F, where E120 is the superheavy Z = 120 homolog of Ra.

Isotope Shifts of Radium Monofluoride Molecules

Isotope shifts of ^{223-226,228}Ra^{19}F were measured for different vibrational levels in the electronic transition A^{2}Π_{1/2}←X^{2}Σ^{+}. The observed isotope shifts demonstrate the particularly high sensitivity of radium monofluoride to nuclear size effects, offering a stringent test of models describing the electronic density within the radium nucleus. Ab initio quantum chemical calculations are in excellent agreement with experimental observations. These results highlight some of the unique opportunities that short-lived molecules could offer in nuclear structure and in fundamental symmetry studies.

CERN-MEDICIS: A Review Since Commissioning in 2017

The CERN-MEDICIS (MEDical Isotopes Collected from ISolde) facility has delivered its first radioactive ion beam at CERN (Switzerland) in December 2017 to support the research and development in nuclear medicine using non-conventional radionuclides. Since then, fourteen institutes, including CERN, have joined the collaboration to drive the scientific program of this unique installation and evaluate the needs of the community to improve the research in imaging, diagnostics, radiation therapy and personalized medicine. The facility has been built as an extension of the ISOLDE (Isotope Separator On Line DEvice) facility at CERN. Handling of open radioisotope sources is made possible thanks to its Radiological Controlled Area and laboratory. Targets are being irradiated by the 1.4 GeV proton beam delivered by the CERN Proton Synchrotron Booster (PSB) on a station placed between the High Resolution Separator (HRS) ISOLDE target station and its beam dump. Irradiated target materials are also received from external institutes to undergo mass separation at CERN-MEDICIS. All targets are handled via a remote handling system and exploited on a dedicated isotope separator beamline. To allow for the release and collection of a specific radionuclide of medical interest, each target is heated to temperatures of up to 2,300°C. The created ions are extracted and accelerated to an energy up to 60 kV, and the beam steered through an off-line sector field magnet mass separator. This is followed by the extraction of the radionuclide of interest through mass separation and its subsequent implantation into a collection foil. In addition, the MELISSA (MEDICIS Laser Ion Source Setup At CERN) laser laboratory, in service since April 2019, helps to increase the separation efficiency and the selectivity. After collection, the implanted radionuclides are dispatched to the biomedical research centers, participating in the CERN-MEDICIS collaboration, for Research & Development in imaging or treatment. Since its commissioning, the CERN-MEDICIS facility has provided its partner institutes with non-conventional medical radionuclides such as Tb-149, Tb-152, Tb-155, Sm-153, Tm-165, Tm-167, Er-169, Yb-175, and Ac-225 with a high specific activity. This article provides a review of the achievements and milestones of CERN-MEDICIS since it has produced its first radioactive isotope in December 2017, with a special focus on its most recent operation in 2020.

Fine and hyperfine interactions in 171YbOH and 173YbOH

The odd isotopologues of ytterbium monohydroxide, ^171,173YbOH, have been identified as promising molecules to measure parity (P) and time reversal (T) violating physics. Here, we characterize the òΠ_1/2(0,0,0)-X̃²Σ⁺(0,0,0) band near 577 nm for these odd isotopologues. Both laser-induced fluorescence excitation spectra of a supersonic molecular beam sample and absorption spectra of a cryogenic buffer-gas cooled sample were recorded. In addition, a novel spectroscopic technique based on laser-enhanced chemical reactions is demonstrated and used in absorption measurements. This technique is especially powerful for disentangling congested spectra. An effective Hamiltonian model is used to extract the fine and hyperfine parameters for the òΠ_1/2(0,0,0) and X̃²Σ⁺(0,0,0) states. A comparison of the determined X̃²Σ⁺(0,0,0) hyperfine parameters with recently predicted values [Denis et al., J. Chem. Phys. 152, 084303 (2020); K. Gaul and R. Berger, Phys. Rev. A 101, 012508 (2020); and Liu et al., J. Chem. Phys. 154,064110 (2021)] is made. The measured hyperfine parameters provide experimental confirmation of the computational methods used to compute the P,T-violating coupling constants W_d and W_M, which correlate P,T-violating physics to P,T-violating energy shifts in the molecule. The dependence of the fine and hyperfine parameters of the òΠ_1/2(0,0,0) and X̃²Σ⁺(0,0,0) states for all isotopologues of YbOH are discussed, and a comparison to isoelectronic YbF is made.

Approaching meV level for transition energies in the radium monofluoride molecule RaF and radium cation Ra+ by including quantum-electrodynamics effects

Highly accurate theoretical predictions of transition energies in the radium monofluoride molecule, ²²⁶RaF, and radium cation, ²²⁶Ra⁺, are reported. The considered transition X²Σ_1/2 → A²Π_1/2 in RaF is one of the main features of this molecule and can be used to laser-cool RaF for a subsequent measurement of the electron electric dipole moment. For molecular and atomic predictions, we go beyond the Dirac-Coulomb Hamiltonian and treat high-order electron correlation effects within the coupled cluster theory with the inclusion of quadruple and ever higher amplitudes. The effects of quantum electrodynamics (QED) are included non-perturbatively using the model QED operator that is now implemented for molecules. It is shown that the inclusion of the QED effects in molecular and atomic calculations is a key ingredient in resolving the discrepancy between the theoretical values obtained within the Dirac-Coulomb-Breit Hamiltonian and the experiment. The remaining deviation from the experimental values is within a few meV. This is more than an order of magnitude better than the "chemical accuracy," 1 kcal/mol = 43 meV, that is usually considered as a guiding thread in theoretical molecular physics.

Probing Fundamental Symmetries of Deformed Nuclei in Symmetric Top Molecules

Precision measurements of Schiff moments in heavy, deformed nuclei are sensitive probes of beyond standard model T, P violation in the hadronic sector. While the most stringent limits on Schiff moments to date are set with diamagnetic atoms, polar polyatomic molecules can offer higher sensitivities with unique experimental advantages. In particular, symmetric top molecular ions possess K doublets of opposite parity with especially small splittings, leading to full polarization at low fields, internal comagnetometer states useful for rejection of systematic effects, and the ability to perform sensitive searches for T, P violation using a small number of trapped ions containing heavy exotic nuclei. We consider the symmetric top cation ^{225}RaOCH_{3}^{+} as a prototypical and candidate platform for performing sensitive nuclear Schiff measurements and characterize in detail its internal structure using relativistic ab initio methods. The combination of enhancements from a deformed nucleus, large polarizability, and unique molecular structure make this molecule a promising platform to search for fundamental symmetry violation even with a single trapped ion.

Optical Mass Spectrometry of Cold RaOH^{+} and RaOCH_{3}^{+}

We present an all-optical mass spectrometry technique to identify trapped ions. The new method uses laser-cooled ions to determine the mass of a cotrapped dark ion with a sub-dalton resolution within a few seconds. We apply the method to identify the first controlled synthesis of cold, trapped RaOH^{+} and RaOCH_{3}^{+}. These molecules are promising for their sensitivity to time and parity violations that could constrain sources of new physics beyond the standard model. The nondestructive nature of the mass spectrometry technique may help identify molecular ions or highly charged ions prior to optical spectroscopy. Unlike previous mass spectrometry techniques for small ion crystals that rely on scanning, the method uses a Fourier transform that is inherently broadband and comparatively fast. The technique's speed provides new opportunities for studying state-resolved chemical reactions in ion traps.

Electronic structure parameter of nuclear magnetic quadrupole moment interaction in metal monofluorides

The electronic structure parameter (W_M) of the nuclear magnetic quadrupole moment (MQM) interaction in numerous open-shell metal monofluorides (viz., MgF, CaF, SrF, BaF, RaF, and PbF) is computed in the fully relativistic coupled-cluster framework. The electron-correlation effects are found to be very important for the precise calculation of W_M in the studied molecular systems. The molecular MQM interaction parameter scales nearly as Z² in the alkaline earth metal monofluorides, where Z is the nuclear charge of metal. Our study identifies ²²³RaF as a good candidate for the experimental search of the nuclear MQM, which can help unravel the physics beyond the standard model in the hadron sector of matter.

Finite-Field Calculations of Transition Properties by the Fock Space Relativistic Coupled Cluster Method: Transitions between Different Fock Space Sectors

Reliable information on transition matrix elements of various property operators between molecular electronic states is of crucial importance for predicting spectroscopic, electric, magnetic and radiative properties of molecules. The finite-field technique is a simple and rather accurate tool for evaluating transition matrix elements of first-order properties in the frames of the Fock space relativistic coupled cluster approach. We formulate and discuss the extension of this technique to the case of transitions between the electronic states associated with different sectors of the Fock space. Pilot applications to the evaluation of transition dipole moments between the closed-shell-like states (vacuum sector) and those dominated by single excitations of the Fermi vacuum (the 1h1p sector) in heavy atoms (Xe and Hg) and simple molecules of heavy element compounds (I2 and TlF) are reported.

A new Collinear Apparatus for Laser Spectroscopy and Applied Science (COALA)

We present a new collinear laser spectroscopy setup that has been designed to overcome systematic uncertainty limits arising from high-voltage and frequency measurements, beam superposition, and collisions with residual gas that are present in other installations utilizing this technique. The applied methods and experimental realizations are described, including an active stabilization of the ion-source potential, new types of ion sources that have not been used for collinear laser spectroscopy so far, dedicated installations for pump-and-probe measurements, and a versatile laser system referenced to a frequency comb. The advanced setup enables us to routinely determine transition frequencies, which was so far demonstrated only for a few cases and with lower accuracy at other facilities. It has also been designed to perform accurate high-voltage measurements for metrological applications. Demonstration and performance measurements were carried out with Ca⁺ and In⁺ ions.

Laser spectroscopy of indium Rydberg atom bunches by electric field ionization

This work reports on the application of a novel electric field-ionization setup for high-resolution laser spectroscopy measurements on bunched fast atomic beams in a collinear geometry. In combination with multi-step resonant excitation to Rydberg states using pulsed lasers, the field ionization technique demonstrates increased sensitivity for isotope separation and measurement of atomic parameters over previous non-resonant laser ionization methods. The setup was tested at the Collinear Resonance Ionization Spectroscopy experiment at ISOLDE-CERN to perform high-resolution measurements of transitions in the indium atom from the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {5s}^2\text {5d}\,^2\text {D}_{5/2}$$\end{document}5s25d2D5/2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {5s}^2\text {5d}\,^2\text {D}_{3/2}$$\end{document}5s25d2D3/2 states to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {5s}^2n$$\end{document}5s2np \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^2$$\end{document}2P and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {5s}^2n\text {f}\,^2$$\end{document}5s2nf2F Rydberg states, up to a principal quantum number of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=72$$\end{document}n=72. The extracted Rydberg level energies were used to re-evaluate the ionization potential of the indium atom to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$46,670.107(4)\,\hbox {cm}^{-1}$$\end{document}46,670.107(4)cm-1. The nuclear magnetic dipole and nuclear electric quadrupole hyperfine structure constants and level isotope shifts of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {5s}^2\text {5d}\,^2\text {D}_{5/2}$$\end{document}5s25d2D5/2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {5s}^2\text {5d}\,^2\text {D}_{3/2}$$\end{document}5s25d2D3/2 states were determined for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{113,115}$$\end{document}113,115In. The results are compared to calculations using relativistic coupled-cluster theory. A good agreement is found with the ionization potential and isotope shifts, while disagreement of hyperfine structure constants indicates an increased importance of electron correlations in these excited atomic states. With the aim of further increasing the detection sensitivity for measurements on exotic isotopes, a systematic study of the field-ionization arrangement implemented in the work was performed at the same time and an improved design was simulated and is presented. The improved design offers increased background suppression independent of the distance from field ionization to ion detection.

Relativistic Fock Space Coupled Cluster Method for Many-Electron Systems: Non-Perturbative Account for Connected Triple Excitations

The Fock space relativistic coupled cluster method (FS-RCC) is one of the most promising tools of electronic structure modeling for atomic and molecular systems containing heavy nuclei. Until recently, capabilities of the FS-RCC method were severely restricted by the fact that only single and double excitations in the exponential parametrization of the wave operator were considered. We report the design and the first computer implementation of FS-RCC schemes with full and simplified non-perturbative account for triple excitations in the cluster operator. Numerical stability of the new computational scheme and thus its applicability to a wide variety of molecular electronic states is ensured using the dynamic shift technique combined with the extrapolation to zero-shift limit. Pilot applications to atomic (Tl, Pb) and molecular (TlH) systems reported in the paper indicate that the breakthrough in accuracy and predictive power of the electronic structure calculations for heavy-element compounds can be achieved. Moreover, the described approach can provide a firm basis for high-precision modeling of heavy molecular systems with several open shells, including actinide compounds.