New Nuclear Magnetic Moment of ^{209}Bi: Resolving the Bismuth Hyperfine Puzzle

Precision spectroscopy on 9Be overcomes limitations from nuclear structure

Many powerful tests of the standard model of particle physics and searches for new physics with precision atomic spectroscopy are hindered by our lack of knowledge of nuclear properties. Ideally, these properties may be derived from precise measurements of the most sensitive and theoretically best-understood observables, often found in hydrogen-like systems. Although these measurements are abundant for the electric properties of nuclei, they are scarce for the magnetic properties, and precise experimental results are limited to the lightest of nuclei1-4. Here we focus on 9Be, which offers the unique possibility to use comparisons between different charge states available for high-precision spectroscopy in Penning traps to test theoretical calculations typically obscured by nuclear structure. In particular, we perform high-precision spectroscopy of the 1s hyperfine and Zeeman structure in hydrogen-like 9Be3+. We determine the effective Zemach radius with an uncertainty of 500 ppm, and the bare nuclear magnetic moment with an uncertainty of 0.6 parts per billion- uncertainties unmatched beyond hydrogen. Moreover, we compare our measurements with the measurements conducted on the three-electron charge state 9Be+ (ref. 5), which enables testing the calculation of multi-electron diamagnetic shielding effects of the nuclear magnetic moment at the parts per billion level. Furthermore, we test the quantum electrodynamics methods used for the calculation of the hyperfine splitting. Our results serve as a crucial benchmark for transferring high-precision results of nuclear magnetic properties across different electronic configurations.

Opportunities for fundamental physics research with radioactive molecules

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

Testing quantum electrodynamics in extreme fields using helium-like uranium

Quantum electrodynamics (QED), the quantum field theory that describes the interaction between light and matter, is commonly regarded as the best-tested quantum theory in modern physics. However, this claim is mostly based on extremely precise studies performed in the domain of relatively low field strengths and light atoms and ions1-6. In the realm of very strong electromagnetic fields such as in the heaviest highly charged ions (with nuclear charge Z ≫ 1), QED calculations enter a qualitatively different, non-perturbative regime. Yet, the corresponding experimental studies are very challenging, and theoretical predictions are only partially tested. Here we present an experiment sensitive to higher-order QED effects and electron-electron interactions in the high-Z regime. This is achieved by using a multi-reference method based on Doppler-tuned X-ray emission from stored relativistic uranium ions with different charge states. The energy of the 1s1/22p3/2 J = 2 → 1s1/22s1/2 J = 1 intrashell transition in the heaviest two-electron ion (U90+) is obtained with an accuracy of 37 ppm. Furthermore, a comparison of uranium ions with different numbers of bound electrons enables us to disentangle and to test separately the one-electron higher-order QED effects and the bound electron-electron interaction terms without the uncertainty related to the nuclear radius. Moreover, our experimental result can discriminate between several state-of-the-art theoretical approaches and provides an important benchmark for calculations in the strong-field domain.

Stringent test of QED with hydrogen-like tin

Inner-shell electrons naturally sense the electric field close to the nucleus, which can reach extreme values beyond 1015 V cm-1 for the innermost electrons1. Especially in few-electron, highly charged ions, the interaction with the electromagnetic fields can be accurately calculated within quantum electrodynamics (QED), rendering these ions good candidates to test the validity of QED in strong fields. Consequently, their Lamb shifts were intensively studied in the past several decades2,3. Another approach is the measurement of gyromagnetic factors (g factors) in highly charged ions4-7. However, so far, either experimental accuracy or small field strength in low-Z ions5,6 limited the stringency of these QED tests. Here we report on our high-precision, high-field test of QED in hydrogen-like 118Sn49+. The highly charged ions were produced with the Heidelberg electron beam ion trap (EBIT)8 and injected into the ALPHATRAP Penning-trap setup9, in which the bound-electron g factor was measured with a precision of 0.5 parts per billion (ppb). For comparison, we present state-of-the-art theory calculations, which together test the underlying QED to about 0.012%, yielding a stringent test in the strong-field regime. With this measurement, we challenge the best tests by means of the Lamb shift and, with anticipated advances in the g-factor theory, surpass them by more than an order of magnitude.

Empirical Determination of the Bohr-Weisskopf Effect in Cesium and Improved Tests of Precision Atomic Theory in Searches for New Physics

The finite distribution of the nuclear magnetic moment across the nucleus gives a contribution to the hyperfine structure known as the Bohr-Weisskopf (BW) effect. We have obtained an empirical value of -0.24(18)% for this effect in the ground and excited s states of atomic ^{133}Cs. This value is found from historical muonic-atom measurements in combination with our muonic-atom and atomic many-body calculations. The effect differs by 0.5% in the hyperfine structure from the value found using the uniform magnetization distribution, which has been commonly employed in the precision heavy-atom community over the last several decades. We also deduce accurate values for the BW effect in other isotopes and states of cesium. These results enable cesium atomic wave functions to be tested in the nuclear region at an unprecedented 0.2% level, and are needed for the development of precision atomic many-body methods. This is important for increasing the discovery potential of precision atomic searches for new physics, in particular for atomic parity violation in cesium.

Direct measurement of the 3He+ magnetic moments

Helium-3 has nowadays become one of the most important candidates for studies in fundamental physics1-3, nuclear and atomic structure4,5, magnetometry and metrology6, as well as chemistry and medicine7,8. In particular, 3He nuclear magnetic resonance (NMR) probes have been proposed as a new standard for absolute magnetometry6,9. This requires a high-accuracy value for the 3He nuclear magnetic moment, which, however, has so far been determined only indirectly and with a relative precision of 12 parts per billon10,11. Here we investigate the 3He+ ground-state hyperfine structure in a Penning trap to directly measure the nuclear g-factor of 3He+ [Formula: see text], the zero-field hyperfine splitting [Formula: see text] Hz and the bound electron g-factor [Formula: see text]. The latter is consistent with our theoretical value [Formula: see text] based on parameters and fundamental constants from ref. 12. Our measured value for the 3He+ nuclear g-factor enables determination of the g-factor of the bare nucleus [Formula: see text] via our accurate calculation of the diamagnetic shielding constant13 [Formula: see text]. This constitutes a direct calibration for 3He NMR probes and an improvement of the precision by one order of magnitude compared to previous indirect results. The measured zero-field hyperfine splitting improves the precision by two orders of magnitude compared to the previous most precise value14 and enables us to determine the Zemach radius15 to [Formula: see text] fm.

Shape and Size Tuning of BiIII-Centered Polyoxopalladates: High Resolution 209Bi NMR and 205/206Bi Radiolabeling for Potential Pharmaceutical Applications

We have discovered five bismuth(III)-containing polyoxopalladates (POPs) which were fully characterized by solution and solid-state physicochemical techniques: the cube-shaped [BiPd₁₂O₃₂(AsPh)₈]^5- (BiPd₁₂AsL), [BiPd₁₂O₃₂(AsC₆H₄N₃)₈]^5- (BiPd₁₂AsL_N), and [BiPd₁₂O₃₂(AsC₆H₄COO)₈]^13- (BiPd₁₂AsL_C) as well as the star-shaped [BiPd₁₅O₄₀(PO)₁₀H₆]^11- (BiPd₁₅P) and [BiPd₁₅O₄₀(PPh)₁₀]^7- (BiPd₁₅PL), respectively. The organically modified capping groups phenylarsonate, p-azidophenylarsonate, and p-carboxyphenylarsonate were chosen as the azido (-N₃) and carboxyl (-COOH) groups open up opportunities to covalently conjugate (via click reaction, amide coupling, etc.) with targeting vectors. The synthesis of p-azidophenylarsonate is reported here for the first time. The effects of the Bi^III template and the organoarsonate vs -posphonate capping groups on the resulting POP shape (cube vs star) are discussed. The ²⁰⁹Bi NMR (I = 9/2) spectra of BiPd₁₂AsL, BiPd₁₂AsL_N, and BiPd₁₂AsL_C revealed narrow peaks (ν_1/2 ∼ 200 Hz) at 5470 ppm with a longitudinal relaxation time in the millisecond range (at 8.46 T). The absence of a quadrupolar relaxation contribution could be attributed to the allocation of Bi^III in the highly symmetrical cuboid POP host cage. Similar peaks were absent in the ²⁰⁹Bi-NMR spectra of the star-shaped POPs BiPd₁₅P and BiPd₁₅PL due to the less symmetric coordination environment around the central Bi^III ion. Further, ^205/206Bi-radiolabeled POPs have been synthesized by incorporating a ^205/206Bi^III ion in the center of the POP structures. Carrier-free ^205/206Bi radioisotopes (as surrogates of α-emitting ²¹³Bi) were incorporated into the POP host-cage for the preparation of ^205/206BiPd₁₂AsL, ^205/206BiPd₁₂AsL_N, ^205/206BiPd₁₂AsL_C, and ^205/206BiPd₁₅PL, respectively. The radiometal incorporation was complete (>99% radiochemical yield) in 10 min according to radio-thin-layer chromatography. The ^205/206BiPd₁₂AsL polyanion was purified by solid-phase extraction. The incubation in rat serum showed the formation of a ^205/206BiPd₁₂AsL-protein aggregate.

Nuclear Magnetic Moments of Francium-207-213 from Precision Hyperfine Comparisons

We report a fourfold improvement in the determination of nuclear magnetic moments for neutron-deficient francium isotopes 207-213, reducing the uncertainties from 2% for most isotopes to 0.5%. These are found by comparing our high-precision calculations of hyperfine structure constants for the ground states with experimental values. In particular, we show the importance of a careful modeling of the Bohr-Weisskopf effect, which arises due to the finite nuclear magnetization distribution. This effect is particularly large in Fr and until now has not been modeled with sufficiently high accuracy. An improved understanding of the nuclear magnetic moments and Bohr-Weisskopf effect are crucial for benchmarking the atomic theory required in precision tests of the standard model, in particular atomic parity violation studies, that are underway in francium.

NMR absolute shielding scales and nuclear magnetic dipole moments of transition metal nuclei

This work reports new, accurate nuclear magnetic dipole moments for transition metal nuclei where the long-standing systematic error due to obsolete diamagnetic correction has been eliminated by ab initio calculations of NMR shielding constants.

g Factor of Lithiumlike Silicon: New Challenge to Bound-State QED

The recently established agreement between experiment and theory for the g factors of lithiumlike silicon and calcium ions manifests the most stringent test of the many-electron bound-state quantum electrodynamics (QED) effects in the presence of a magnetic field. In this Letter, we present a significant simultaneous improvement of both theoretical g_{th}=2.000 889 894 4 (34) and experimental g_{exp}=2.000 889 888 45 (14) values of the g factor of lithiumlike silicon ^{28}Si^{11+}. The theoretical precision now is limited by the many-electron two-loop contributions of the bound-state QED. The experimental value is accurate enough to test these contributions on a few percent level.

Weak Pnictogen Bond with Bismuth: Experimental Evidence Based on Bi-P Through-Space Coupling

To study pnictogen bonding involving bismuth, flexible accordion-like molecular complexes of the composition [P(C6 H4 -o-CH2 SCH3 )3 BiX3 ], (X=Cl, Br, I) have been synthesised and characterised. The strength of the weak and mainly electrostatic interaction between the Bi and P centres strongly depends on the character of the halogen substituent on bismuth, which is confirmed by single-crystal X-ray diffraction analyses, DFT and ab initio computations. Significantly, 209 Bi-31 P through-space coupling (J=2560 Hz) is observed in solid-state 31 P NMR spectra, which is so far unprecedented in the literature, delivering direct information on the magnitude of this pnictogen interaction.