QED Effect on the Nuclear Magnetic Shielding of

The leading quantum electrodynamic corrections to the nuclear magnetic shielding in one- and two-electron atomic systems are obtained in a complete form, and the shielding constants of ^{1}H, ^{3}He^{+}, and ^{3}He are calculated to be 17.735 436(3)×10^{-6}, 35.507 434(9)×10^{-6}, and 59.967 029(23)×10^{-6}, respectively. These results are orders of magnitude more accurate than previous ones, and, with the ongoing measurement of the nuclear magnetic moment of ^{3}He^{+} and planned ^{3}He^{2+}, they open the window for high-precision absolute magnetometry using ^{3}He NMR probes. The presented theoretical approach is applicable to all other light atomic and molecular systems, which facilitates the improved determination of magnetic moments of any light nuclei.

Hyperfine Structure of the First Rotational Level in H_{2}, D_{2} and HD Molecules and the Deuteron Quadrupole Moment.

We perform the four-body calculation of the hyperfine structure in the first rotational state J=1 of the H_{2}, D_{2}, and HD molecules and determine the accurate value for the deuteron electric quadrupole moment Q_{d}=0.285 699(15)(18) fm^{2} in significant disagreement with former spectroscopic determinations. Our results for the hyperfine parameters agree very well with the currently most accurate molecular-beam magnetic resonance measurement performed several decades ago by N.F. Ramsey and coworkers. They also indicate the significance of previously neglected nonadiabatic effects. Moreover, a very good agreement with the recent calculation of Q_{d} based on the chiral effective field theory, although much less accurate, indicates the importance of the spin dependence of nucleon interactions in the accurate description of nuclei.

Nonadiabatic QED Correction to the Dissociation Energy of the Hydrogen Molecule.

The quantum electrodynamic correction to the energy of the hydrogen molecule has been evaluated without expansion in the electron-proton mass ratio. The obtained results significantly improve the accuracy of theoretical predictions reaching the level of 1 MHz for the dissociation energy, in very good agreement with the parallel measurement [Hölsch et al., Phys. Rev. Lett. 122, 103002 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103002]. Molecular hydrogen has thus become a cornerstone of ultraprecise quantum chemistry, which opens perspectives for determination of fundamental physical constants from its spectra.

Nuclear Charge Radii of

The first laser spectroscopic determination of the change in the nuclear charge radius for a five-electron system is reported. This is achieved by combining high-accuracy ab initio mass-shift calculations and a high-accuracy measurement of the isotope shift in the 2s^{2}2p ^{2}P_{1/2}→2s^{2}3s ^{2}S_{1/2} ground state transition in boron atoms. Accuracy is increased by orders of magnitude for the stable isotopes ^{10,11}B and the results are used to extract their difference in the mean-square charge radius ⟨r_{c}^{2}⟩^{11}-⟨r_{c}^{2}⟩^{10}=-0.49(12) fm^{2}. The result is qualitatively explained by a possible cluster structure of the boron nuclei and quantitatively used to benchmark new ab initio nuclear structure calculations using the no-core shell model and Green's function Monte Carlo approaches. These results are the foundation for a laser spectroscopic determination of the charge radius of the proton-halo candidate ^{8}B.

Nuclear Spin-Spin Coupling in HD, HT, and DT.

The interaction between nuclear spins in a molecule is exceptionally sensitive to the physics beyond the standard model. However, all present calculations of the nuclear spin-spin coupling constant J are burdened by computational difficulties, which hinders the comparison to experimental results. Here, we present a variational approach and calculate the constant J in the hydrogen molecule with the controlled numerical precision, using the adiabatic approximation. The apparent discrepancy with experimental result is removed by an analysis of nonadiabatic effects based on the experimental values of the J constant for HD, HT, and DT molecules. This study significantly improves the reliability of the NMR theory for searching new physics in the spin-spin coupling.

Nonadiabatic Relativistic Correction to the Dissociation Energy of H_{2}, D_{2}, and HD.

The relativistic correction to the dissociation energy of H_{2}, D_{2}, and HD molecules has been accurately calculated without expansion in the small electron-nucleus mass ratio. The obtained results indicate the significance of nonadiabatic effects and resolve the discrepancy of theoretical predictions with recent experimental values for H_{2} and D_{2}. While the theoretical accuracy is now significantly improved and is higher than the experimental one, we observe about 3σ discrepancy for the dissociation energy of HD, which requires further investigation.

Complete α

We perform the calculation of all relativistic and quantum electrodynamic corrections of the order of α^{6} m to the ground electronic state of a hydrogen molecule and present improved results for the dissociation and the fundamental transition energies. These results open the window for the high-precision spectroscopy of H_{2} and related low-energy tests of fundamental interactions.

Frequency-dependent polarizability of helium including relativistic effects with nuclear recoil terms.

Future metrology standards will be partly based on physical quantities computed from first principles rather than measured. In particular, a new pressure standard can be established if the dynamic polarizability of helium can be determined from theory with an uncertainty smaller than 0.2 ppm. We present calculations of the frequency-dependent part of this quantity including relativistic effects with full account of leading nuclear recoil terms and using highly optimized explicitly correlated basis sets. A particular emphasis is put on uncertainty estimates. At the He-Ne laser wavelength of 632.9908 nm, the computed polarizability value of 1.39181141 a.u. has uncertainty of 0.1 ppm that is 2 orders of magnitude smaller than those of the most accurate polarizability measurements. We also obtained an accurate expansion of the helium refractive index in powers of density.

Precision Test of Many-Body QED in the Be+ 2p Fine Structure Doublet Using Short-Lived Isotopes.

Absolute transition frequencies of the 2s 2S{1/2}→2p2P{1/2,3/2} transitions in Be^{+} were measured for the isotopes ^{7,9-12}Be. The fine structure splitting of the 2p state and its isotope dependence are extracted and compared to results of ab initio calculations using explicitly correlated basis functions, including relativistic and quantum electrodynamics effects at the order of mα(6) and mα(7) ⁢ln α. Accuracy has been improved in both the theory and experiment by 2 orders of magnitude, and good agreement is observed. This represents one of the most accurate tests of quantum electrodynamics for many-electron systems, being insensitive to nuclear uncertainties.

Quantum electrodynamics corrections to the 2P fine splitting in Li.

We consider quantum electrodynamics (QED) corrections to the fine splitting E(2P_{3/2})-E(2P_{1/2}) in the Li atom. We derive complete formulas for the mα^{6} and mα^{7}lnα contributions and calculate them numerically using highly optimized, explicitly correlated basis functions. The obtained results are in agreement with the most recent measurement, helping to resolve discrepancies between former ones and lay the foundation for the investigation of QED effects in light, many-electron atoms.

Ground state hyperfine splitting in 6,7Li atoms and the nuclear structure.

Relativistic and QED corrections are calculated for a hyperfine splitting of the 2S1/2 ground state in 6,7Li atoms with a numerically exact account for electronic correlations. The resulting theoretical predictions achieve such a precision level that, by comparison with experimental values, they enable determination of the nuclear properties. In particular, the obtained results show that the 7Li nucleus, having a charge radius smaller than 6Li, has about a 40% larger Zemach radius. Together with known differences in the electric quadrupole and magnetic dipole moments, this calls for a deeper understanding of the Li nuclear structure.

Quantum defects at the critical charge.

The quantum defect is an empirically introduced notion that has allowed convenient interpolations of spectral data along atomic isoelectronic sequences and their extrapolation with respect to the principal quantum number. Both yield valuable spectral information, the latter providing estimates of low-energy-electron elastic scattering phase shifts as well. We examine a recently proposed conjecture concerning the extrapolated value of the quantum defect along an isoelectronic sequence: If the binding energy of the outermost electron vanishes in the singly negative ion, then its asymptotic quantum defect is an integer whose value is equal to the number of occupied shells with the same orbital angular momentum. This behavior is associated with the fact, established by means of appropriate electronic structure calculations, that-asymptotically-the outermost orbital becomes an infinitely diffuse hydrogen-like orbital. In most cases explored the asymptotic behavior can be ascertained by analysis of spectral data along the appropriate isoelectronic sequence, but in some cases the approach to the asymptotic value takes place over a very narrow range of nuclear charge in the vicinity of that of the negative ion.

Relativistic, QED, and nuclear mass effects in the magnetic shielding of 3He.

The magnetic shielding sigma of (3)He is studied. The complete relativistic corrections of order O(alpha(2)), leading QED corrections of order O(alpha(3) ln alpha), and finite nuclear mass effects of order O(m/m(N)) are calculated with high numerical precision. The resulting theoretical predictions for sigma = 59.967 43(10)x10(-6) are the most accurate to date among all elements and support the use of (3)He as a NMR standard.

Dipole excitation of the positronium molecule ps2.

The energy interval between the ground and the P-wave excited states of the recently discovered positronium molecule Ps2 is evaluated, including the relativistic and the leading logarithmic radiative corrections, E_{P}-E_{S}=0.181 586 7(8) a.u.. The P state, decaying usually via annihilation, is found to decay into the ground state by an electric dipole transition 19% of the time. Anticipated observation of this transition will provide insight into this exotic system.

Positronium-ion decay.

We present a precise theoretical prediction for the decay width of the bound state of two electrons and a positron (a negative positronium ion), Gamma(Ps-)=2.087 963(12)/ns. We include O(alpha2) effects of hard virtual photons as well as soft corrections to the wave function and the decay amplitude. An outcome of a large-scale variational calculation, this is the first result for second-order corrections to a decay of a three-particle bound state. It will be tested experimentally in the new positronium-ion facility in Garching in Germany.