Electroweak Nuclear Properties from Single Molecular Ions in a Penning Trap.

We present a novel technique to probe electroweak nuclear properties by measuring parity violation (PV) in single molecular ions in a Penning trap. The trap's strong magnetic field Zeeman shifts opposite-parity rotational and hyperfine molecular states into near degeneracy. The weak interaction-induced mixing between these degenerate states can be larger than in atoms by more than 12 orders of magnitude, thereby vastly amplifying PV effects. The single molecule sensitivity would be suitable for applications to nuclei across the nuclear chart, including rare and unstable nuclei.

Deceleration and Trapping of SrF Molecules.

We report on the electrostatic trapping of neutral SrF molecules. The molecules are captured from a cryogenic buffer-gas beam source into the moving traps of a 4.5-m-long traveling-wave Stark decelerator. The SrF molecules in X^{2}Σ^{+}(v=0,N=1) state are brought to rest as the velocity of the moving traps is gradually reduced from 190 m/s to zero. The molecules are held for up to 50 ms in multiple electric traps of the decelerator. The trapped packets have a volume (FWHM) of 1 mm^{3} and a velocity spread of 5(1) m/s, which corresponds to a temperature of 60(20) mK. Our result demonstrates a factor 3 increase in the molecular mass that has been Stark decelerated and trapped. Heavy molecules (mass>100 amu) offer a highly increased sensitivity to probe physics beyond the standard model. This work significantly extends the species of neutral molecules of which slow beams can be created for collision studies, precision measurement, and trapping experiments.

Large Shape Staggering in Neutron-Deficient Bi Isotopes.

The changes in the mean-square charge radius (relative to ^{209}Bi), magnetic dipole, and electric quadrupole moments of ^{187,188,189,191}Bi were measured using the in-source resonance-ionization spectroscopy technique at ISOLDE (CERN). A large staggering in radii was found in ^{187,188,189}Bi^{g}, manifested by a sharp radius increase for the ground state of ^{188}Bi relative to the neighboring ^{187,189}Bi^{g}. A large isomer shift was also observed for ^{188}Bi^{m}. Both effects happen at the same neutron number, N=105, where the shape staggering and a similar isomer shift were observed in the mercury isotopes. Experimental results are reproduced by mean-field calculations where the ground or isomeric states were identified by the blocked quasiparticle configuration compatible with the observed spin, parity, and magnetic moment.

Measurement of the first ionization potential of lawrencium, element 103.

The chemical properties of an element are primarily governed by the configuration of electrons in the valence shell. Relativistic effects influence the electronic structure of heavy elements in the sixth row of the periodic table, and these effects increase dramatically in the seventh row--including the actinides--even affecting ground-state configurations. Atomic s and p1/2 orbitals are stabilized by relativistic effects, whereas p3/2, d and f orbitals are destabilized, so that ground-state configurations of heavy elements may differ from those of lighter elements in the same group. The first ionization potential (IP1) is a measure of the energy required to remove one valence electron from a neutral atom, and is an atomic property that reflects the outermost electronic configuration. Precise and accurate experimental determination of IP1 gives information on the binding energy of valence electrons, and also, therefore, on the degree of relativistic stabilization. However, such measurements are hampered by the difficulty in obtaining the heaviest elements on scales of more than one atom at a time. Here we report that the experimentally obtained IP1 of the heaviest actinide, lawrencium (Lr, atomic number 103), is 4.96(+0.08)(-0.07) electronvolts. The IP1 of Lr was measured with (256)Lr (half-life 27 seconds) using an efficient surface ion-source and a radioisotope detection system coupled to a mass separator. The measured IP1 is in excellent agreement with the value of 4.963(15) electronvolts predicted here by state-of-the-art relativistic calculations. The present work provides a reliable benchmark for theoretical calculations and also opens the way for IP1 measurements of superheavy elements (that is, transactinides) on an atom-at-a-time scale.

Probing Sizes and Shapes of Nobelium Isotopes by Laser Spectroscopy.

Until recently, ground-state nuclear moments of the heaviest nuclei could only be inferred from nuclear spectroscopy, where model assumptions are required. Laser spectroscopy in combination with modern atomic structure calculations is now able to probe these moments directly, in a comprehensive and nuclear-model-independent way. Here we report on unique access to the differential mean-square charge radii of ^{252,253,254}No, and therefore to changes in nuclear size and shape. State-of-the-art nuclear density functional calculations describe well the changes in nuclear charge radii in the region of the heavy actinides, indicating an appreciable central depression in the deformed proton density distribution in ^{252,254}No isotopes. Finally, the hyperfine splitting of ^{253}No was evaluated, enabling a complementary measure of its (quadrupole) deformation, as well as an insight into the neutron single-particle wave function via the nuclear spin and magnetic moment.

Relativistic Coupled Cluster Calculations with Variational Quantum Electrodynamics Resolve the Discrepancy between Experiment and Theory Concerning the Electron Affinity and Ionization Potential of Gold.

The first ionization potential (IP) and electron affinity (EA) of the gold atom have been determined to an unprecedented accuracy using relativistic coupled cluster calculations up to the pentuple excitation level including the Breit and QED contributions. We reach meV accuracy (with respect to the experimental values) by carefully accounting for all individual contributions beyond the standard relativistic coupled cluster approach. Thus, we are able to resolve the long-standing discrepancy between experimental and theoretical IP and EA of gold.

Identification of the predicted 5s-4f level crossing optical lines with applications to metrology and searches for the variation of fundamental constants.

We measure optical spectra of Nd-like W, Re, Os, Ir, and Pt ions of particular interest for studies of a possibly varying fine-structure constant. Exploiting characteristic energy scalings we identify the strongest lines, confirm the predicted 5s-4f level crossing, and benchmark advanced calculations. We infer two possible values for optical M2/E3 and E1 transitions in Ir^{17+} that have the highest predicted sensitivity to a variation of the fine-structure constant among stable atomic systems. Furthermore, we determine the energies of proposed frequency standards in Hf^{12+} and W^{14+}.

Theoretical predictions of properties and volatility of chlorides and oxychlorides of group-4 elements. I. Electronic structures and properties of MCl4 and MOCl2 (M = Ti, Zr, Hf, and Rf).

Relativistic, infinite order exact two-component, density functional theory electronic structure calculations were performed for MCl4 and MOCl2 of group-4 elements Ti, Zr, Hf, and element 104, Rf, with the aim to predict their behaviour in gas-phase chromatography experiments. RfCl4 and RfOCl2 were shown to be less stable than their lighter homologs in the group, tetrachlorides and oxychlorides of Zr and Hf, respectively. The oxychlorides turned out to be stable as a bent structure, though the stabilization energy with respect to the flat one (C(2v)) is very small. The trend in the formation of the tetrachlorides from the oxychlorides in group 4 is shown to be Zr < Hf < Rf, while the one in the formation of the oxychlorides from the chlorides is opposite. All the calculated properties are used to estimate adsorption energy of these species on various surfaces in order to interpret results of gas-phase chromatography experiments, as is shown in Paper II.

Theoretical predictions of properties and volatility of chlorides and oxychlorides of group-4 elements. II. Adsorption of tetrachlorides and oxydichlorides of Zr, Hf, and Rf on neutral and modified surfaces.

With the aim to interpret results of gas-phase chromatography experiments on volatility of group-4 tetrachlorides and oxychlorides including those of Rf, adsorption enthalpies of these species on neutral, and modified quartz surfaces were estimated on the basis of relativistic, two-component Density Functional Theory calculations of MCl4, MOCl2, MCl6(-), and MOCl4(2) with the use of adsorption models. Several mechanisms of adsorption were considered. In the case of physisorption of MCl4, the trend in the adsorption energy in the group should be Zr > Hf > Rf, so that the volatility should change in the opposite direction. The latter trend complies with the one in the sublimation enthalpies, ΔH(sub), of the Zr and Hf tetrachlorides, i.e., Zr < Hf. On the basis of a correlation between these quantities, ΔH(sub)(RfCl4) was predicted as 104.2 kJ/mol. The energy of physisorption of MOCl2 on quartz should increase in the group, Zr < Hf < Rf, as defined by increasing dipole moments of these molecules along the series. In the case of adsorption of MCl4 on quartz by chemical forces, formation of the MOCl2 or MOCl4(2-) complexes on the surface can take place, so that the sequence in the adsorption energy should be Zr > Hf > Rf, as defined by the complex formation energies. In the case of adsorption of MCl4 on a chlorinated quartz surface, formation of the MCl6(2-) surface complexes can occur, so that the trend in the adsorption strength should be Zr ≤ Hf < Rf. All the predicted sequences, showing a smooth change of the adsorption energy in the group, are in disagreement with the reversed trend Zr ≈ Rf < Hf, observed in the "one-atom-at-a-time" gas-phase chromatography experiments. Thus, currently no theoretical explanation can be found for the experimental observations.

Relativistic coupled cluster study of diatomic compounds of Hg, Cn, and Fl.

The structure and energetics of eight diatomic heavy-atom molecules are presented. These include the species MAu, M2, and MHg, with M standing for the Hg, Cn (element 112), and Fl (element 114) atoms. The infinite-order relativistic 2-component Hamiltonian, known to closely reproduce 4-component results at lower computational cost, is used as framework. High-accuracy treatment of correlation is achieved by using the coupled cluster scheme with single, double, and perturbative triple excitations in large converged basis sets. The calculated interatomic separation and bond energy of Hg2, the only compound with known experimental data, are in good agreement with measurements. The binding of Fl to Au is stronger than that of Cn, predicting stronger adsorption on gold surfaces. The bond in the M2 species is strongest for Fl2, being of chemical nature; weaker bonds appear in Cn2 and Hg2, which are bound by van der Waals interactions, with the former bound more strongly due to the smaller van der Waals radius. The same set of calculations was also performed using the relativistic density functional theory approach, in order to test the performance of the latter for these weakly bound systems with respect to the more accurate coupled cluster calculations. It was found that for the MAu species the B3LYP functional provides better agreement with the coupled cluster results than the B88/P86 functional. However, for the M2 and the MHg molecules, B3LYP tends to underestimate the binding energies.

Ab initio studies of atomic properties and experimental behavior of element 119 and its lighter homologs.

Static dipole polarizabilities of element 119 and its singly charged cation are calculated, along with those of its lighter homologs, Cs and Fr. Relativity is treated within the 4-component Dirac-Coulomb formalism and electron correlation is included by the single reference coupled cluster approach with single, double, and perturbative triple excitations (CCSD(T)). Very good agreement with available experimental values is obtained for Cs, lending credence to the predictions for Fr and element 119. The atomic properties in group-1 are largely determined by the valence ns orbital, which experiences relativistic stabilization and contraction in the heavier elements. As a result, element 119 is predicted to have a relatively low polarizability (169.7 a.u.), comparable to that of Na. The adsorption enthalpy of element 119 on Teflon, which is important for possible future experimental studies of this element, is estimated as 17.6 kJ/mol, the lowest among the atoms considered here.

Theoretical predictions of properties of group-2 elements including element 120 and their adsorption on noble metal surfaces.

Trends in properties of group-2 elements Ca through element 120 and their M(2) and MAu dimers were determined on the basis of atomic and molecular relativistic density functional theory calculations. The relativistic contraction and stabilization of the ns AO with increasing atomic number were shown to result in the inversion of trends both in atomic and molecular properties in group 2 beyond Ba, so that element 120 should be chemically similar to Sr. Due to the same reason, bonding in (120)(2) and 120Au should be the weakest among the considered here M(2) and MAu. Using calculated dissociation energies of M(2), the sublimation enthalpy, ΔH(sub), of element 120 of 150 kJ/mol was estimated via a correlation between these quantities in group 2. Using the M-Au binding energies, the adsorption enthalpies, ΔH(ads), of element 120 of 172 kJ/mol on gold, 127 kJ/mol on platinum, and 50 kJ/mol on silver were estimated via a correlation with known ΔH(ads) in the group. These moderate values of ΔH(ads) are indicative of a possibility of chromatography adsorption studies of element 120 on these noble metal surfaces.

A supersonic laser ablation beam source with narrow velocity spreads.

A supersonic beam source for SrF and BaF molecules is constructed by combining the expansion of carrier gas (a mixture of 2% SF6 and 98% argon) from an Even-Lavie valve with laser ablation of a barium/strontium metal target at a repetition rate of 10 Hz. Molecular beams with a narrow translational velocity spread are produced at relative values of Δv/v = 0.053(11) and 0.054(9) for SrF and BaF, respectively. The relative velocity spread of the beams produced in our source is lower in comparison with the results from other metal fluoride beams produced in supersonic laser ablation sources. The rotational temperature of BaF is measured to be 3.5 K. The source produces 6 × 108 and 107 molecules per steradian per pulse in the X2Σ+ (ν = 0, N = 1) state of BaF and SrF molecules, respectively, a state amenable to Stark deceleration and laser cooling.

Theoretical predictions of trends in spectroscopic properties of gold containing dimers of the 6p and 7p elements and their adsorption on gold.

Fully relativistic, four-component density functional theory electronic structure calculations were performed for the MAu dimers of the 7p elements, 113 through 118, and their 6p homologs, Tl through Rn. It was shown that the M-Au bond strength should decrease from the 6p to 7p homologs in groups 13 and 14, while it should stay about the same in groups 15 through 17 and even increase in group 18. This is in contrast with the decreasing trend in the M-M bond strength in groups 15 through 17. The reason for these trends is increasingly important relativistic effects on the np AOs of these elements, particularly their large spin-orbit splitting. Trends in the adsorption energies of the heaviest elements and their homologs on gold are expected to be related to those in the binding energies of MAu, while sublimation enthalpies are closely connected to the binding energies of the MM dimers. Lack of a correlation between the MAu and MM binding energies means that no correlation can also be expected between adsorption enthalpies on gold and sublimation enthalpies in groups 15 through 17. No linear correlation between these quantities is established in the row of the 6p elements, as well as no one is expected in the row of the 7p elements.

Theoretical predictions of trends in spectroscopic properties of homonuclear dimers and volatility of the 7p elements.

Fully relativistic density functional theory electronic structure calculations were performed for homonuclear dimers of the 7p elements, 113-118 and their 6p homologs, Tl through Rn. All the dimers of the heaviest elements, with the exception of (118)(2), were found to be weaker bound than their lighter homologs. The difference in the dissociation energy (D(e)) between the 6p and 7p homologs was shown to decrease from group 15 to group 17, with a reversal of the trend in group 18. A remarkable feature is a shift of the maximum in D(e)(M(2)) from group 15 in the third through sixth rows to group 16 in the seventh row. Strong relativistic effects on the 7p atomic orbitals, particularly, their large spin-orbit splitting, were shown to be responsible for these trends. Using the calculated D(e)(M(2)), the sublimation enthalpies, DeltaH(sub), of macroamounts, or formation enthalpies of gaseous atoms, DeltaH(f)(g), of the heaviest elements were estimated using a linear correlation between these quantities in the chemical groups. The newly estimated values are in good agreement with those obtained via a linear extrapolation from the lighter homologs in the groups.

Detection of the 5p - 4f orbital crossing and its optical clock transition in Pr9.

Recent theoretical works have proposed atomic clocks based on narrow optical transitions in highly charged ions. The most interesting candidates for searches of physics beyond the Standard Model are those which occur at rare orbital crossings where the shell structure of the periodic table is reordered. There are only three such crossings expected to be accessible in highly charged ions, and hitherto none have been observed as both experiment and theory have proven difficult. In this work we observe an orbital crossing in a system chosen to be tractable from both sides: Pr[Formula: see text]. We present electron beam ion trap measurements of its spectra, including the inter-configuration lines that reveal the sought-after crossing. With state-of-the-art calculations we show that the proposed nHz-wide clock line has a very high sensitivity to variation of the fine-structure constant, [Formula: see text], and violation of local Lorentz invariance; and has extremely low sensitivity to external perturbations.

Atomic properties of element 113 and its adsorption on inert surfaces from ab initio Dirac-Coulomb calculations.

Fully relativistic ab initio Dirac-Coulomb Fock-space coupled cluster calculations were performed on Tl and element 113. The calculated polarizabilty of element 113, 29.85 au, is the smallest in group 13, except for B. The estimated atomic and van der Waals radii of element 113 are also the smallest among these elements. Using the calculated atomic properties and an adsorption model, adsorption enthalpies of elements Al through 113 on inert surfaces, such as Teflon and polyethylene, are predicted. The trends in the atomic properties and DeltaH(ads) in group 13 were found to reverse from In to element 113, reflecting the strong relativistic contraction and stabilization of the outer np(1/2) orbital, which are largest for element 113. The small values of DeltaH(ads) for element 113 on Teflon (14 kJ/mol) and polyethylene (16 kJ/mol) guarantee its transport from the target chamber to the chemistry set up, and the 6 kJ/mol difference relative to Tl values makes possible the separation and identification of the superheavy element on the inert surfaces.

Adsorption of inert gases including element 118 on noble metal and inert surfaces from ab initio Dirac-Coulomb atomic calculations.

The interaction of the inert gases Rn and element 118 with various surfaces has been studied on the basis of fully relativistic ab initio Dirac-Coulomb CCSD(T) calculations of atomic properties. The calculated polarizability of element 118, 46.3 a.u., is the largest in group 18, the ionization potential is the lowest at 8.91 eV, and the estimated atomic radius is the largest, 4.55 a.u. These extreme values reflect, in addition to the general trends in the Periodic Table, the relativistic expansion and destabilization of the outer valence 7p(3/2) orbital. Van der Waals coefficients C(3) and adsorption enthalpies DeltaH(ads) of Ne through element 118 on noble metals and inert surfaces, such as quartz, ice, Teflon, and graphite, were calculated in a physisorption model using the atomic properties obtained. The C(3) coefficients were shown to steadily increase in group 18, while the increase in DeltaH(ads) from Ne to Rn does not continue to element 118: The large atomic radius of the latter element is responsible for a decrease in the interaction energy. We therefore predict that experimental distinction between Rn and 118 by adsorption on these types of surfaces will not be feasible. A possible candidate for separating the two elements is charcoal; further study is needed to test this possibility.

Measurement of the first ionization potential of astatine by laser ionization spectroscopy.

The radioactive element astatine exists only in trace amounts in nature. Its properties can therefore only be explored by study of the minute quantities of artificially produced isotopes or by performing theoretical calculations. One of the most important properties influencing the chemical behaviour is the energy required to remove one electron from the valence shell, referred to as the ionization potential. Here we use laser spectroscopy to probe the optical spectrum of astatine near the ionization threshold. The observed series of Rydberg states enabled the first determination of the ionization potential of the astatine atom, 9.31751(8) eV. New ab initio calculations are performed to support the experimental result. The measured value serves as a benchmark for quantum chemistry calculations of the properties of astatine as well as for the theoretical prediction of the ionization potential of superheavy element 117, the heaviest homologue of astatine.

Prediction of the adsorption behavior of elements 112 and 114 on inert surfaces from ab initio Dirac-Coulomb atomic calculations.

The interaction of elements 112 and 114 with inert surfaces has been studied on the basis of fully relativistic ab initio Dirac-Coulomb CCSD(T) calculations of their atomic properties. The calculated polarizabilities of elements 112 and 114 are significantly lower than corresponding Hg and Pb values due to the relativistic contraction of the valence ns and np(12) orbitals, respectively, in the heavier elements. Due to the same reason, the estimated van der Waals radius of element 114 is smaller than that of Pb. The enthalpies of adsorption of Hg, Pb, and elements 112 and 114 on inert surfaces such as quartz, ice, and Teflon were predicted on the basis of these atomic calculations using a physisorption model. At the present level of accuracy, -DeltaH(ads) of element 112 on these surfaces is slightly (about 2 kJ/mol) larger than -DeltaH(ads)(Hg). The calculated -DeltaH(ads) of element 114 on quartz is about 7 kJ/mol and on Teflon is about 3 kJ/mol smaller than the respective values of -DeltaH(ads)(Pb). The trend of increasing -DeltaH(ads) in group 14 from C to Sn is thus reversed, giving decreasing values from Sn to Pb to element 114 due to the relativistic stabilization and contraction of the np(12) atomic orbitals. This is similar to trends shown by other atomic properties of these elements. The small difference in DeltaH(ads) of Pb and element 114 on inert surfaces obtained within a picture of physisorption contrasts with the large difference (more than 100 kJ/mol) in the chemical reactivity between these elements.