Light Atomic Systems Research Articles

Diamagnetic corrections to low-excited electronic states of light molecular systems

Compact astrophysical objects like white dwarfs and neutron stars generate very strong magnetic fields. In their atmosphere, accretion disks, and the interstellar medium surrounding them, the predominant matter consists of hydrogen, helium and few-particle atoms and molecules. In this work, we have studied the effects of strong magnetic fields on light atomic and molecular systems like hydrogen molecular ions and antiprotonic helium. The full energy of the investigated systems is calculated in the Born-Oppenheimer approximation for a few low-lying electronic states. We investigate the case where the leading effect comes from the quadratic magnetic field term in the interaction Hamiltonian. The electronic energies and wavefunctions are computed in spheroidal coordinates by a finite difference method on a nonequidistant grid. The diamagnetic contributions to the total energy for an arbitrary value of the magnetic field strength are also calculated in perturbation theory. Then they are compared with the exact results, and where possible - with previous calculations. The electronic energy terms could be used for precise computations of the spectral lines of the hydrogen molecular ion and antiprotonic helium. This will allow searching for objects, like neutron stars and white dwarfs with strong magnetic fields, containing such molecular systems in their atmospheres or accretion discs. When the effects from the approximations are taken into account, the tabulated results presented in this work could also find an application in studies for much weaker magnetic field strengths existing in laboratory environments.

Nuclear polarizability effects in He+3 hyperfine splitting

The nuclear polarizability effects in hyperfine splitting of light atomic systems are not well known. The only system for which they were previously calculated is the hydrogen atom, where these effects were shown to contribute about 5\% of the total nuclear correction. One generally expects the polarizability effects to become more pronounced for composite nuclei. In the present work we determine the nuclear polarizability correction to the hyperfine splitting in He$^+$ by comparing the effective Zemach radius deduced from the experimental hyperfine splitting with the Zemach radius obtained from the electron scattering. We obtain a surprising result that the nuclear polarizability of the helion yields just 3\% of the total nuclear correction, which is smaller than for the proton.

Variational vs perturbative relativistic energies for small and light atomic and molecular systems.

Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called non-radiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac-Coulomb-Breit (DCB) equation to all orders of the α fine-structure constant. The analysis of the polynomial α dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the non-relativistic energy to high precision without regularization. Contributions from the Breit-Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The α dependence of the no-pair DCB energy shows that the higher-order (α4Eh) non-radiative QED correction is 5% of the leading-order (α3Eh) non-radiative QED correction for Z = 2 (He), but it is 40% already for Z = 4 (Be2+), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers.

Nuclear recoil correction to the hyperfine splitting in atomic systems

We consider leading $O(m/M)$ nuclear recoil corrections to the hyperfine splitting in light atomic systems. Due to the singularity of hyperfine interactions, the electromagnetic form factors of the nucleus have to be introduced as a function of the four-momentum square, which goes beyond the Hamiltonian description of the system. We present a compact formula for $O(Z\phantom{\rule{0.16em}{0ex}}\ensuremath{\alpha})$ recoil corrections and indicate the importance, especially for light atoms, of a more realistic description of the nuclear structure effects.

QED theory of the nuclear magnetic shielding in H and He3

The derivation of leading quantum electrodynamic corrections to the nuclear magnetic shielding in light hydrogen- and helium-like atomic systems is described in detail. The presented theoretical approach applies to any light atomic and molecular systems, enabling the determination of the magnetic moment of light nuclei with much higher precision than known presently.

QED Effect on the Nuclear Magnetic Shielding of ^{3}He.

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.

Precision measurements of the charge radii of potassium isotopes

Precision nuclear charge radii measurements in the light-mass region are essential for understanding the evolution of nuclear structure, but their measurement represents a great challenge for experimental techniques. At the Collinear Resonance Ionization Spectroscopy (CRIS) setup at ISOLDE-CERN, a laser frequency calibration and monitoring system was installed and commissioned through the hyperfine spectra measurement of $^{38--47}\mathrm{K}$. It allowed for the extraction of the hyperfine parameters and isotope shifts with better than 1 MHz precision. These results are in excellent agreement with available literature values and they demonstrate the suitability of the CRIS technique for the study of nuclear observables in light atomic systems. In addition, the spectral line shapes obtained under different conditions were systematically investigated, highlighting the importance of finding optimal conditions, under which the extracted nuclear properties remain unaffected by laser-atom interactions.

Experiments with low-energy kaons at the DAΦNE Collider

The investigations of light kaonic atoms offer the unique opportunity to perform experiments equivalent to scattering at vanishing relative energies, being their atomic binding energies in the keV range. This allows the determination of the hadron-nucleus interaction at threshold without the need of an extrapolation to zero relative energy. The energy shift and broadening of the lowest-lying states of such atoms, induced by the kaon-nucleus strong interaction, can be determined with high precision from atomic X-ray spectroscopy. The lightest atomic systems, kaonic hydrogen and kaonic deuterium, deliver the isospin-dependent kaon-nucleon scattering lengths. The most precise kaonic hydrogen measurement to date, together with an exploratory measurement of kaonic deuterium, were carried out by the SIDDHARTA collaboration at the DAΦNE electron-positron collider of LNF-INFN. The measurement of kaonic deuterium will be realized in the near future by SIDDHARTA-2, a major upgrade of SIDDHARTA. A correlated study of the kaon-nuclei interaction at momenta below 130 MeV/c is carried out by the AMADEUS collaboration, using the KLOE detector and dedicated targets inserted near the collider interaction point. In this paper an overview of the main results obtained by SIDDHARTA together with the future plans, the SIDDHARTA-2 experiment and with the preliminary results of the study of charged antikaons interacting with nuclei by the AMADEUS collaboration, are shown.

The kaonic atoms research program at DAΦNE: overview and perspectives

The interaction of antikaons with nucleons and nuclei in the low-energy regime represents an active research field in hadron physics with still many important open questions. The investigation of light kaonic atoms is, in this context, a unique tool to obtain precise information on this interaction. The energy shift and broadening of the lowest-lying states of such atoms, induced by the kaon-nucleus strong interaction, can be determined with high precision from atomic X-ray spectroscopy. This experimental method provides unique information to understand the low energy kaon-nucleus interaction at threshold. The lightest atomic systems, kaonic hydrogen and kaonic deuterium, deliver the isospin-dependent kaon-nucleon scattering lengths. The most precise kaonic hydrogen measurement to date, together with an exploratory measurement of kaonic deuterium, were carried out by the SIDDHARTA collaboration at the DAΦNE electron-positron collider of LNF-INFN, by combining the excellent quality kaon beam delivered by the collider with new experimental techniques, as fast and precise X-ray detectors: Silicon Drift Detectors. The measurement of kaonic deuterium will be realized in the near future by SIDDHARTA-2, a major upgrade of SIDDHARTA. In this paper an overview of the main results obtained by SIDDHARTA together with the future plans, are given.

The kaonic atoms research program at DAΦNE: from SIDDHARTA to SIDDHARTA-2

The interaction of antikaons with nucleons and nuclei in the low-energy regime represents an active research field in hadron physics with still many important open questions. The investigation of light kaonic atoms, in which one electron is replaced by a negatively charged kaon, is a unique tool to provide precise information on this interaction; the energy shift and the broadening of the low-lying states of such atoms, induced by the kaon-nucleus hadronic interaction, can be determined with high precision from the atomic X-ray spectroscopy, and this experimental method provides unique information to understand the low energy kaon-nucleus interaction at the production threshold. The lightest atomic systems, like the kaonic hydrogen and the kaonic deuterium deliver, in a model-independent way, the isospin-dependent kaon-nucleon scattering lengths. The most precise kaonic hydrogen measurement to-date, together with an exploratory measurement of kaonic deuterium, were carried out in 2009 by the SIDDHARTA collaboration at the DAΦNE electron-positron collider of LNF-INFN, combining the excellent quality kaon beam delivered by the collider with new experimental techniques, as fast and very precise X-ray detectors, like the Silicon Drift Detectors. The SIDDHARTA results triggered new theoretical work, which achieved major progress in the understanding of the low-energy strong interaction with strangeness reflected by the antikaon-nucleon scattering lengths calculated with the antikaon-proton amplitudes constrained by the SIDDHARTA data. The most important open question is the experimental determination of the hadronic energy shift and width of kaonic deuterium; presently, a major upgrade of the setup, SIDDHARTA-2, is being realized to reach this goal. In this paper, the results obtained in 2009 and the proposed SIDDHARTA-2 upgrades are presented.

How Well Can the M06 Suite of Functionals Describe the Electron Densities of Ne, Ne6+, and Ne8+?

The development of better approximations to the exact exchange-correlation functional is essential to the accuracy of density functionals. A recent study suggested that functionals with few parameters provide more accurate electron densities than recently developed many-parameter functionals for light closed-shell atomic systems. In this study, we calculated electron densities, their gradients, and Laplacians of Ne, Ne6+, and Ne8+ using 19 electronic structure methods, and we compared them to the CCSD reference results. Two basis sets, namely, aug-cc-pωCV5Z and aug-cc-pV5Z, are utilized in the calculations. We found that the choice of basis set has a significant impact on the errors and rankings of some of the selected methods. The errors of electron densities, their gradients, and Laplacians calculated with the aug-cc-pV5Z basis set are substantially reduced, especially for Minnesota density functionals, as compared to the results using the aug-cc-pωCV5Z basis set (a larger basis set utilized in earlier work (Medvedev et al. Science 2017, 355, 49-52)). The rankings of the M06 suite of functionals among the 19 methods are greatly improved with the aug-cc-pV5Z basis set. In addition, the performances of the HSE06, BMK, MN12-L, and MN12-SX functionals are also improved with the aug-cc-pV5Z basis set. The M06 suite of functionals is capable of providing accurate electron densities, gradients, and Laplacians using the aug-cc-pV5Z basis set, and thus it is suitable for a wide range of applications in chemistry and physics.

Isotope scattering and phonon thermal conductivity in light atom compounds: LiH and LiF

Engineered isotope variation is a pathway toward modulating lattice thermal conductivity (\ensuremath{\kappa}) of a material through changes in phonon-isotope scattering. The effects of isotope variation on intrinsic thermal resistance is little explored, as varying isotopes have relatively small differences in mass and thus do not affect bulk phonon dispersions. However, for light elements, isotope mass variation can be relatively large (e.g., hydrogen and deuterium). Using a first principles Peierls-Boltzmann transport equation approach, the effects of isotope variance on lattice thermal transport in ultra-low-mass compound materials LiH and LiF are characterized. The isotope mass variance modifies the intrinsic thermal resistance via modulation of acoustic and optic phonon frequencies, while phonon-isotope scattering from mass disorder plays only a minor role. This leads to some unusual cases where \ensuremath{\kappa} values of isotopically pure systems (${}^{6}\mathrm{LiH}{,}^{7}\mathrm{L}{\mathrm{i}}^{2}\mathrm{H}$, and ${}^{6}\mathrm{LiF}$) are lower than the values from their counterparts with naturally occurring isotopes and phonon-isotope scattering. However, these \ensuremath{\kappa} differences are relatively small. The effects of temperature-driven lattice expansion on phonon dispersions and calculated \ensuremath{\kappa} are also discussed. This paper provides insight into lattice thermal conductivity modulation with mass variation and the interplay of intrinsic phonon-phonon and phonon-isotope scattering in interesting light atom systems.

Kaonic atoms and strangeness in nuclei: SIDDHARTA-2 and AMADEUS experiments

The dynamics of the strong interaction processes in the non-perturbative regime is currently approached by lattice calculations and effective field theories (ChPT), still lacking several experimental results, fundamental for a good understanding of the strangeness sector. Among these, the information provided by the low-energy kaon nucleon/nuclei interaction, accessible through the study of kaonic atoms and kaonic nuclear processes, plays a key-role. The lightest atomic systems, the kaonic hydrogen and the kaonic deuterium, deliver, in a model-independent way, the isospin-dependent kaon-nucleon scattering lengths, through the X- ray spectroscopy of the exotic atoms de-exciting to the fundamental level. The most precise kaonic hydrogen measurement to-date, together with an exploratory measurement of kaonic deuterium, were carried out in 2009 at the DAΦNE collider, by the SIDDHARTA collaboration. Nowadays, an upgraded setup was built, for a precise measurement of kaonic deuterium and, eventually, of heavier exotic atoms. A correlated study of the kaon-nuclei interaction at momenta below 130 MeV/c is carried out by the AMADEUS collaboration, using the KLOE detector and dedicated targets inserted near the collider interaction point. Preliminary results of the study of charged antikaons interacting with nuclei are shown, including a discussion of the still controversial Λ(1405).

Effects from spin-orbit coupling on electron-nucleus hyperfine coupling calculated at the restricted active space level for Kramers doublets.

Calculations of electron-nucleus hyperfine coupling were implemented at the restricted active space state interaction (RASSI) level to treat spin-orbit (SO) coupling, based on scalar relativistic restricted active space wave functions. The current implementation is suitable for light atomic systems, for light ligand atoms in heavy metal complexes, and for spin-orbit coupling-induced hyperfine coupling of heavy atoms if the unpaired electrons are described by orbitals with high angular momentum. Spin polarization is reasonably well treated by allowing one hole and one electron in a window of active orbitals ('ras1', 'ras3') surrounding the principal active space ('ras2'). A benchmark set of Kramers doublet states of molecules with light and heavy atoms is used to evaluate the approach and verify the implementation. For NpF6, the impact of SO coupling on the Np and F hyperfine coupling tensors is investigated in detail. It is demonstrated that the Np hyperfine coupling is strongly dominated by SO effects, that there is a large SO effect on the F hyperfine tensor components, and that SO coupling causes the fluorine dipolar term to acquire an isotropic component.

Progress and perspectives in the low-energy kaon-nucleon/nuclei interaction studies at the DAΦNE collider

Low-energy QCD is still lacking experimental results, fundamental for reaching a good understanding of the strangeness sector. The information provided by the low energy kaon- nucleon/nuclei interaction is accessible through the study of kaonic atoms and kaonic nuclear processes. The lightest atomic systems, namely the kaonic hydrogen and the kaonic deuterium, provide the isospin dependent kaon-nucleon scattering lengths by measuring the X-rays emitted during their de-excitation to the 1s level. The most precise kaonic hydrogen measurement to date, together with an exploratory measurement of kaonic deuterium and of upper-level transitions in kaonic helium 3 and kaonic helium 4 were carried out at the DAΦNE collider by the SIDDHARTA collaboration. Presently, a significantly upgraded setup developped by the SIDDHARTA-2 collaboration is ready to perform a precise measurement of kaonic deuterium and, afterwards, of heavier exotic atoms. In parallel, the kaon-nuclei interaction at momenta below 130 MeV/c is studied by the AMADEUS collaboration, using the KLOE detector and a dedicated setup inserted in the central region, near the interaction point. Preliminary results of the study of charged antikaons interacting with nuclei are shown, including an analysis of the controversial Λ(1405).

Vacuum polarization in light two-electron atoms and ions

A general theory of the vacuum polarization in light atomic and muon-atomic systems is considered. We derive the closed analytical expression for the Uehling potential and evaluate corrections on vacuum polarization for the 11S-state of the two-electron 3He and 4He atoms and for some two-electron ions, including the Li+, Be2+, B3+ and C4+ ions. The correction for vacuum polarization in two-electron He atoms has been evaluated as ΔEueh≈7.253±0.0025×10−7a.u. The analogous corrections in the two-electron He-like ions rapidly increase with the nuclear charge Q (ΔEueh≈2.7061×10−6a.u. for the Li+ ion and ΔEueh≈2.3495×10−5a.u. for the C4+ ion). The corresponding corrections have also been evaluated for the electron–nucleus and electron–electron interactions.

Analytical formula for the Uehling potential

The closed analytical expression for the Uehling potential is derived. The Uehling potential describes the lowest-order correction on vacuum polarisation in atomic and muon-atomic systems. We also derive the analytical formula for the interaction potential between two electrically charged point particles which includes correction to the vacuum polarisation, but has correct asymptotic behaviour at larger r. Our three-term analytical formula for the Uehling potential opens a new avenue in the study of the vacuum polarisation in light atomic systems.

Quantum effect on thermally activated glide of dislocations

Crystal plasticity involves the motion of dislocations under stress. So far, atomistic simulations of this process have predicted Peierls stresses, the stress needed to overcome the crystal resistance in the absence of thermal fluctuations, of more than twice the experimental values, a discrepancy best-known in body-centred cubic crystals. Here we show that a large contribution arises from the crystal zero-point vibrations, which ease dislocation motion below typically half the Debye temperature. Using Wigner's quantum transition state theory in atomistic models of crystals, we found a large decrease of the kink-pair formation enthalpy due to the quantization of the crystal vibrational modes. Consequently, the flow stress predicted by Orowan's law is strongly reduced when compared with its classical approximation and in much closer agreement with experiments. This work advocates that quantum mechanics should be accounted for in simulations of materials and not only at very low temperatures or in light-atom systems.

The quantum normal form approach to reactive scattering: The cumulative reaction probability for collinear exchange reactions

The quantum normal form approach to quantum transition state theory is used to compute the cumulative reaction probability for collinear exchange reactions. It is shown that for heavy-atom systems such as the nitrogen-exchange reaction, the quantum normal form approach gives excellent results and has major computational benefits over full reactive scattering approaches. For light atom systems such as the hydrogen-exchange reaction however, the quantum normal approach is shown to give only poor results. This failure is attributed to the importance of tunneling trajectories in light atom reactions that are not captured by the quantum normal form as indicated by the only very slow convergence of the quantum normal form for such systems.

High-precision spectroscopy as a test of quantum electrodynamics in light atomic systems

This paper presents a review of recent progress in high-precision calculations for the ground state and low-lying excited states of helium, including the nonrelativistic energy, relativistic corrections of α2 Ry, and quantum electrodynamic (QED) corrections of lowest order α3 Ry and next-to-leading-order α4 Ry, where α is the fine-structure constant. The calculations include the terms of order α4 Ry recently obtained by Pachucki (Phys. Rev. A, 74, 062510 (2006)). Estimates of the terms of order α5 Ry, including two-loop binding corrections, are included. Comparisons with experimental ionization energies indicate reasonably good agreement for the 1s2 1S0, 1s2s 1S0, 1s2s 3S1, and 1s2p 3Pcm states, but there is a significant discrepancy for the 1s2p 1P1 state of 5.6± 3.2 MHz. An asymptotic formula for the calculation of the Bethe logarithm for Rydberg states with large angular momentum L is presented in an Appendix. PACS Nos.: 31.30.Gs, 31.30.Jv