We report calculations of QED corrections to the $g$ factor of Li-like ions induced by the exchange of two virtual photons between the electrons. The calculations are performed within QED theory to all orders in the nuclear binding strength parameter $Zα$, where $Z$ is the nuclear charge number and $α$ is the fine-structure constant. In the region of low nuclear charges we compare results from three different methods: QED, relativistic many-body perturbation theory, and nonrelativistic QED. All three methods are shown to yield consistent results. With our calculations we improve the accuracy of the theoretical predictions of the $g$ factor of the ground state of Li-like carbon and oxygen by about an order of magnitude. Our theoretical results agree with those from previous calculations but differ by 3-4 standard deviations from the experimental results available for silicon and calcium.
Charge exchange collisions between ultracold fermionic 6Li atoms and 40Ca+ ions are observed in the mK temperature range. The reaction product of the charge exchange collision is identified via mass spectrometry during which the motion of the ions is excited parametrically. The cross-sections of the charge exchange collisions between 6Li atoms in the ground state and 40Ca+ ions in the ground and metastable excited states are determined. Investigation of the inelastic collision characteristics in the atom-ion mixture is an important step toward ultracold chemistry based on ultracold atoms and i…
We investigate theoretically the possibility for robust and fast cooling of a trapped atomic ion by transient interaction with a pre-cooled ion. The transient coupling is achieved through dynamical control of the ions' equilibrium positions. To achieve short cooling times we make use of shortcuts to adiabaticity by applying invariant-based engineering. We design these to take account of imperfections such as stray fields, and trap frequency offsets. For settings appropriate to a currently operational trap in our laboratory, we find that robust performance could be achieved down to $6.3$ motion…
In this paper we present a simple model for computing single electron exchange between light nuclei. The electronic capture is pictured as a tunnelling process in a model potential. This allows to analytically compute the transmission probability. Some comparisons with data from existing literature are given.
We present ab initio calculations of the complete gauge-invariant set of two-photon exchange graphs for the $(1s)^2 2p_{3/2}$ electron configuration in Li-like ions. These calculations are an important step towards the precise theoretical determination of the $2p_{3/2}$-$2s$ transition energy in the framework of QED.
The influence of hypothetical new interactions beyond the Standard Model on atomic spectra has attracted recent interest. In the present work, interelectronic photon-exchange corrections and radiative quantum electrodynamic corrections to the hypothetical contribution to the energy levels of few-electron ions from a new interaction are calculated. The $1s$, $2s$ and $2p_{1/2}$ ground states of H-like, Li-like and B-like ions are considered, as motivated by proposals to use isotope shift spectroscopy of few-electron ions in order to set stringent constraints on hypothetical new interactions. It…
We have employed x-ray spectroscopy to probe the charge changing process only in the bulk of the foil when swift heavy ions pass through it. In contrast, the electromagnetic methods take into account integral effect of the charge changing process in the bulk as well as the charge exchange phenomenon at the surface of the foil. Thus, the difference between the mean charge states so measured from the two methods disentangles the charge exchange phenomenon at the surface from the charge changing process in the bulk and, provides opportunities to refine the understanding of ion-surface interaction…
The two most widely used ion cooling methods are laser cooling and sympathetic cooling by elastic collisions (ECs). Here we demonstrate another method of cooling ions that is based on resonant charge exchange (RCE) between the trapped ion and the ultracold parent atom. Specifically, trapped Cs$^{+}$ ions are cooled by collisions with co-trapped, ultracold Cs atoms and, separately, by collisions with co-trapped, ultracold Rb atoms. We observe that the cooling of Cs$^{+}$ ions by Cs atoms is more efficient than cooling of Cs$^{+}$ ions by Rb atoms. This signals the presence of a cooling mechanis…
The screened QED corrections to the g factor of Li-like ions are evaluated utilizing an effective potential approach. The evaluation is performed within the range of nuclear charge numbers Z=32-92. The results obtained serve for improving the theoretical predictions for the g factor of heavy Li-like ions.
We investigate the energy dependence and the internal-state dependence of the charge-exchange collision cross sections in a mixture of $^6$Li atoms and $^{40}$Ca$^+$ ions in the collision energy range from 0.2 mK to 1 K. Deliberately excited ion micromotion is used to control the collision energy of atoms and ions. The energy dependence of the charge-exchange collision cross section obeys the Langevin model in the temperature range of the current experiment, and the measured magnitude of the cross section is correlated to the internal state of the $^{40}$Ca$^+$ ions. Revealing the relationship…
A detailed description of the numerical procedure is presented for the evaluation of the one-loop self-energy correction to the $g$-factor of an electron in the $1s$ and $2s$ states in H-like ions to all orders in $Zα$.
The one-loop self-energy correction to the hyperfine structure splitting of the 1s and 2s states of hydrogenlike ions is calculated both for the point and finite nucleus. The results of the calculation are combined with other corrections to find the ground state hyperfine splitting in lithiumlike ^{209}Bi^{80+} and ^{165}Ho^{64+}.
The influence of nuclear polarization on the bound-electron $g$ factor in heavy hydrogenlike ions is investigated. Numerical calculations are performed for the K- and L-shell electrons taking into account the dominant virtual nuclear excitations. This determines the ultimate limit for tests of QED utilizing measurements of the bound-electron $g$ factor in highly charged ions.
The finite nuclear size corrections to the relativistic recoil effect in H-like ions are calculated within the Breit approximation. The calculations are performed for the $1s$, $2s$, and $2p_{1/2}$ states in the range $Z =$ 1-110. The obtained results are compared with previous evaluations of this effect. It is found that for heavy ions the previously neglected corrections amount to about 20% of the total nuclear size contribution to the recoil effect calculated within the Breit approximation.
The static dipole polarizability for the hydrogen molecular ions H$_2^+$, HD$^+$, and D$_2^+$ are calculated. These new data for polarizability takes into account the leading order relativistic corrections to the wave function of the three-body system resulted from the Breit-Pauli Hamiltonian of $mα^4$ order. Our study covers a wide range of rotational ($L=0-5$) and vibrational ($v=0-10$) states, which are of practical interest for precision spectroscopy of the hydrogen molecular ions.
We present an ab initio calculation of the screened self-energy correction for (1s)^2 2p3/2 and (1s)^2 2s states of Li-like ions with nuclear charge numbers in the range Z = 12-100. The evaluation is carried out to all orders in the nuclear-strength parameter Z α. This investigation concludes our calculations of all two-electron QED corrections for the 2p3/2-2s transition energy in Li-like ions and thus considerably improves theoretical predictions for this transition for high-Z ions.
Mass-dependent and field shift components of the isotopic shift are determined to high accuracy for the ground $1^1S-$states of some light two-electron Li$^{+}$, Be$^{2+}$, B$^{3+}$ and C$^{4+}$ ions. To determine the field components of these isotopic shifts we apply the Racah-Rosental-Breit formula. We also determine the lowest order QED corrections to the isotopic shifts for each of these two-electron ions.
We present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields,also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H$^{-}$, H$^{2-}$, He, He$^{-}$, He$^{2-}$, He$^{3-}$ within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through th…
The one-electron quantum-electrodynamic corrections to the magnetic-dipole transition amplitude between the fine-structure levels (1s^2 2s^2 2p) ^2P_3/2 - ^2P_1/2 in boronlike ions are calculated to all orders in (αZ). The results obtained serve for improving the theoretical accuracy of the lifetime of the (1s^2 2s^2 2p) ^2P_3/2 level in boronlike argon.
Results of a calculation valid to all orders in the nuclear-strength parameter Zαare presented for the two-loop Lamb shift, notably for the two-loop self-energy correction, for the ground and first excited states of ions with the nuclear charge numbers Z=60-100. A detailed comparison of the all-order calculation with earlier investigations based on an expansion in the parameter Zαis given. The calculation removes the largest theoretical uncertainty for the 2p_j-2s transition energies in heavy Li-like ions and is important for interpretation of experimental data.
We consider higher-order corrections to hyperfine coefficients related to the spin-orbit and spin-spin tensor interactions in hydrogen molecular ions. The $mα^7 \ln(α)$-order radiative correction is derived in the NRQED framework. We present complete numerical calculations, including as well the $mα^6$-order relativistic correction, for the case of H$_2^+$. The theoretical uncertainty is reduced by more than one order of magnitude with respect to the Breit-Pauli level, down to a few ppm. We also compare our results with available rf spectroscopy data.
Calculations of various corrections to the g factor of Li-like ions are presented, which result in a significant improvement of the theoretical accuracy in the region Z = 6-92. The configuration-interaction Dirac-Fock method is employed for the evaluation of the interelectronic-interaction correction of order 1/Z^2 and higher. This correction is combined with the 1/Z interelectronic-interaction term derived within a rigorous QED approach. The one-electron QED corrections of first in αare calculated to all orders in the parameter αZ. The screening of QED corrections is taken into account to the…
A rigorous evaluation of the complete gauge-invariant set of the screened one-loop QED corrections to the hyperfine structure and g factor in lithiumlike heavy ions is presented. The calculations are performed in both Feynman and Coulomb gauges for the virtual photon mediating the interelectronic interaction. As a result, the most accurate theoretical predictions for the specific difference between the hyperfine splitting values of H- and Li-like Bi ions as well as for the g factor of Li-like Pb ion are obtained.
QED corrections to the $g$ factor of Li-like and B-like ions in a wide range of nuclear charges are presented. Many-electron contributions as well as radiative effects on the one-loop level are calculated. Contributions resulting from the interelectronic interaction, the self-energy effect, and most of the terms of the vacuum-polarization effect are evaluated to all orders in the nuclear coupling strength $Zα$. Uncertainties resulting from nuclear size effects, numerical computations, and uncalculated effects are discussed.
The major goal of the high-precision studies of ro-vibrational states in the hydrogen molecular ions is to provide an alternative way for improving the electron-to-proton mass ratio, or the atomic mass of electron. By now the complete set of relativistic and radiative corrections have been obtained for a wide range of ro-vibrational states of H_2^+ and HD^+ up to order R_\inftyα^4. In this work we complete calculations of various contributions to the R_\inftyα^4 order by computing the relativistic corrections to the binding energy of electron.
A rigorous QED evaluation of the two-photon exchange corrections to the g factor of lithiumlike ions is presented. The screened self-energy corrections are calculated for the intermediate-$Z$ region and its accuracy for the high-$Z$ region is essentially improved in comparison with that of previous calculations. As a result, the theoretical accuracy of the g factor of lithiumlike ions is significantly increased. The theoretical prediction obtained for the g factor of $^{28}$Si$^{11+}$ ${\rm g}_{\rm th} = 2.000\,889\,892(8)$ is in an excellent agreement with the corresponding experimental value…
In this paper we study theoretically the process of electron capture between one-optical-electron atoms (e.g. hydrogenlike or alkali atoms) and ions at low-to-medium impact velocities (v/v_e <= 1) working on a modification of an already developed classical Over Barrier Model (OBM) [V. Ostrovsky, J. Phys. B: At. Mol. Opt. Phys. {\bf 28} 3901 (1995)], which allows to give a semianalytical formula for the cross sections. The model is discussed and then applied to a number of test cases including experimental data as well as data coming from other sophisticated numerical simulations. It is found t…
Formulas and expectation values which are need to determine the lowest-order QED corrections ($\sim α^3$) and corresponding recoil (or finite mass) corrections in the two-electron helium-like ions are presented. Other important properties of the two-electron ions are also determined to high accuracy, including the expectation values of the qausi-singular Vinti operator and $\langle r^{-2}_{eN} \rangle$ and $\langle r^{-2}_{ee} \rangle$ expectation values. Elastic scattering of fast electrons by the two-electron ions in the Born approximation is considered. Interpolation formulas are derived fo…
A critical set of two-loop QED corrections to the $g$ factor of hydrogenlike ions is calculated without expansion in the nuclear binding field. These corrections are due to the polarization of the external magnetic field by the quantum vacuum, which is dressed by the binding field. The result obtained for the self-energy--magnetic-loop diagrams is compared with the current state-of-the-art result, derived through a perturbative expansion in the binding strength parameter $Zα$, with $Z$ the atomic number and $α$ the fine-structure constant. Agreement is found in the $Z\rightarrow0$ limit. Howev…
A rigorous QED theory of the spectral line profiles is applied to transition probabilities in few-electron highly charged ions. Interelectron interaction corrections are included as well as radiative corrections. Parity nonconserving (PNC) amplitudes with effective weak interactions between the electrons and nucleus are also considered. QED and interelectron interaction corrections to the PNC amplitudes are derived.
High-precision variational calculations of the operators for the relativistic corrections in the leading $mα^4$ order are presented. The ro-vibrational states in the range of the total orbital angular momentum $L\!=\!0\!-\!4$ and vibrational quantum number $v\!=\!0\!-\!10$ for the $\mbox{H}_2^+$ and $\mbox{HD}^+$ molecular ions are considered. We estimate that about ten significant digits are obtained. This high precision is required for making theoretical predictions for transition frequencies at the level of $10^{-12}$ relative uncertainty.
Total electronic correlation correction to the binding energies of the isoelectronic series of Beryllium, Neon, Magnesium and Argon, are calculated in the framework of relativistic multiconfiguration Dirac-Fock method. Convergence of the correlation energies is studied as the active set of orbitals is increased. The Breit interaction is treated fully self-consistently. The final results can be used in the accurately determination of atomic masses from highly charged ions data obtained in Penning-trap experiments.
We present experimental evidence of charge exchange between laser-cooled potassium $^{39}$K atoms and calcium $^{40}$Ca$^+$ ions in a hybrid atom-ion trap and give quantitative theoretical explanations for the observations. The $^{39}$K atoms and $^{40}$Ca$^+$ ions are held in a magneto-optical (MOT) and a linear Paul trap, respectively. Fluorescence detection and high resolution time of flight mass spectra for both species are used to determine the remaining number of $^{40}$Ca$^+$ ions, the increasing number of $^{39}$K$^+$ ions, and $^{39}$K number density as functions of time. Simultaneous…
Ab initio calculations of QED radiative corrections to the $^2P_{1/2}$ - $^2P_{3/2}$ fine-structure transition energy are performed for selected F-like ions. These calculations are nonperturbative in $αZ$ and include all first-order and many-electron second-order effects in $α$. When compared to approximate QED computations, a notable discrepancy is found especially for F-like uranium for which the predicted self-energy contributions even differ in sign. Moreover, all deviations between theory and experiment for the $^2P_{1/2}$ - $^2P_{3/2}$ fine-structure energies of F-like ions, reported rec…
The ground-state hyperfine splitting values of high-Z boronlike ions are calculated. Calculation of the interelectronic-interaction contribution is based on a combination of the 1/Z perturbation theory and the large-scale configuration-interaction Dirac-Fock-Sturm method. The screened QED corrections are evaluated utilizing an effective screening potential approach. Total hyperfine splitting energies are presented for several B-like ions of particular interest: {}^{45}Sc{}^{16+}, {}^{57}Fe{}^{21+}, {}^{207}Pb{}^{77+}, and {}^{209}Bi{}^{78+}. For lead and bismuth the experimental values of the …
The mass corrections to the bound state energies of the three-body muonic molecular ions $ppμ, pdμ, ptμ, ddμ, dtμ$ and $ttμ$ are determined numerically from the results of highly accurate computations. The total energies and some other bound state properties of these ions are evaluated to very high accuracy for the bound $S(L = 0)-, P(L = 1)-$ and $D(L = 2)-$states. In these highly accurate calculations we used the most recent and accurate masses of particles $m_p, m_d, m_t$ and $m_μ$ known from high energy experiments.
A part of the two-loop self-energy correction, the so-called P term, is evaluated numerically for the 1s state to all orders in Zα. Our calculation, combined with the previous investigation [S. Mallampalli and J. Sapirstein, Phys. Rev. A 57, 1548 (1998)], yields the total answer for the two-loop self-energy correction in H-like uranium and bismuth. As a result, the major uncertainty is eliminated from the theoretical prediction for the Lamb shift in these systems. The total value of the ground-state Lamb shift in H-like uranium is found to be 463.93(50) eV.
We present a method for generating cold neutral atoms via charge exchange reactions between trapped ions and Rydberg positronium. The high charge exchange reaction cross section leads to efficient neutralisation of the ions and since the positronium-ion mass ratio is small, the neutrals do not gain appreciable kinetic energy in the process. When the original ions are cold the reaction produces neutrals that can be trapped or further manipulated with electromagnetic fields. Because a wide range of species can be targeted we envisage that our scheme may enable experiments at low temperature that…
We compute the ground-state electric dipole polarizability of group-IIIA ions using the perturbed relativistic coupled-cluster (PRCC) theory. To account for the relativistic effects and QED corrections, we use the Dirac-Coulomb-Breit Hamiltonian with the corrections from the Uehling potential and the self-energy. The effects of triple excitations are considered perturbatively in the PRCC. Our PRCC results for $α$ are good in agreement with the previous theoretical results for all the ions. From our computations we find that the nonlinear terms in PRCC have significant contributions and must be…
The screened QED corrections of the first orders in αand 1/Z to the g factor and the hyperfine splitting of lithiumlike ions are evaluated within ab initio quantum electrodynamical approach. The complete gauge-invariant set of the two-electron self-energy diagrams in the presence of the magnetic field and a dominant part of the two-electron vacuum-polarization diagrams are calculated. The most accurate values of the g factor of Li-like lead and uranium are presented. The theoretical prediction for the specific difference of the hyperfine splittings of H- and Li-like bismuth is improved.
Absolute total cross sections for electron capture between slow, highly charged ions and alkali targets have been recently measured. It is found that these cross sections follow a scaling law with the projectile charge which is different from the one previously proposed basing on a classical over-barrier model (OBM) and verified using rare gases and molecules as targets. In this paper we develop a "semi-classical" (i.e. including some quantal features) OBM attempting to recover experimental results. The method is then applied to ion-hydrogen collisions and compared with the result of a sophist…
A rigorous evaluation of the two-photon exchange corrections to the hyperfine structure in lithiumlike heavy ions is presented. As a result, the theoretical accuracy of the specific difference between the hyperfine splitting values of H- and Li-like Bi ions is significantly improved. This opens a possibility for the stringent test of the many-electron QED effects on a few percent level in the strongest electromagnetic field presently available in experiments.
We have investigated the correction to the hyperfine structure of heavy multicharged ions, which is connected with the nuclear-polarization effect caused by the unpaired bound electron. Numerical calculations are performed for hydrogenlike ions taking into account the dominant collective nuclear excitations. The correction defines the ultimate limit of precision in accurate theoretical predictions of the hyperfine-structure splittings.
The nuclear shape correction to the g factor of a bound electron in 1S-state is calculated for a number of nuclei in the range of charge numbers from Z=6 up to Z=92. The leading relativistic deformation correction has been derived analytically and also its influence on one-loop quantum electrodynamic terms has been evaluated. We show the leading corrections to become significant for mid-Z ions and for very heavy elements to even reach the 10^(-6) level.
The reduced-mass dependence of relativistic and radiative effects in simple muonic bound systems is investigated. The spin-dependent nuclear recoil correction of order (Zalpha)^4 mu^3/m_N^2 is evaluated for muonic hydrogen and deuterium, and muonic helium ions (mu is the reduced mass and m_N is the nuclear mass). Relativistic corrections to vacuum polarization of order alpha (Zalpha)^4 mu are calculated, with a full account of the reduced-mass dependence. The results shift theoretical predictions. The radiative-recoil correction to vacuum polarization of order alpha (Zα)^5 ln^2(Zalpha) mu^2/m_…
We calculate isotope mass shift for several light ions using Dirac wave functions and mass shift operator with relativistic corrections of the order of $(αZ)^2$. Calculated relativistic corrections to the specific mass shift vary from a fraction of a percent for Carbon, to 2% for Magnesium. Relativistic corrections to the normal mass shift are typically smaller. Interestingly, the final relativistic mass shifts for the levels of one multiplet appear to be even closer than for non-relativistic operator. That can be important for the astrophysical search for possible $α$-variation, where isotope…
The fully relativistic theory of the g factor of Li-like ions with nonzero nuclear spin is considered for the (1s)^2 2s state. The magnetic-dipole hyperfine-interaction correction to the atomic g factor is calculated including the one-electron contributions as well as the interelectronic-interaction effects of order 1/Z. This correction is combined with the interelectronic-interaction, QED, nuclear recoil, and nuclear size corrections to obtain high-precision theoretical values for the g factor of Li-like ions with nonzero nuclear spin. The results can be used for a precise determination of nu…
A complete effective Hamiltonian for relativistic corrections at orders $mα^6$ and $mα^6(m/M)$ in a one-electron molecular system is derived from the NRQED Lagrangian. It includes spin-independent corrections to the energy levels and spin-spin scalar interactions contributing to the hyperfine splitting, both of which had been studied previously. In addition, corrections to electron spin-orbit and spin-spin tensor interactions are newly obtained. This allows improving the hyperfine structure theory in the hydrogen molecular ions. Improved values of the spin-orbit hyperfine coefficient are calcu…
The introduction of gases like nitrogen or neon for cooling the edge region of magnetically confined fusion plasmas has triggered a renewed interest in state selective cross sections necessary for plasma diagnostics by means of charge exchange recombination spectroscopy. To improve the quality of spectroscopic data analysis, charge exchange and ionisation cross sections for N$^{7+}$ + H($n=1,2$) have been calculated using two different theoretical approaches, namely the atomic-orbital close-coupling method and the classical trajectory Monte Carlo method. Total and state resolved charge exchang…
The hyperfine structure (hfs) and the g factor of a bound electron are caused by external magnetic fields. For the hfs, the magnetic field is due to the nuclear spin. A uniform-in-space and constant-in-time magnetic field is used to probe the bound-electron g factor. The self-energy corrections to these effects are more difficult to evaluate than those to the Lamb shift. Here, we describe a numerical approach for both effects in the notoriously problematic regime of hydrogen-like bound systems with low nuclear charge numbers. The calculation is nonperturbative in the binding Coulomb field. Acc…
Motivated by recent claims of a compelling ~3.5 keV emission line from nearby galaxies and galaxy clusters, we investigate a novel plasma model incorporating a charge exchange component obtained from theoretical scattering calculations. Fitting this kind of component with a standard thermal model yields positive residuals around 3.5 keV, produced mostly by S XVI transitions from principal quantum numbers n > 8 to the ground. Such high-n states can only be populated by the charge exchange process. In this scenario, the observed 3.5 keV line flux in clusters can be naturally explained by an inte…
The fully relativistic theory of the Zeeman splitting of the $(1s)^2 2s$ hyperfine-structure levels in lithiumlike ions with $Z=6 - 32$ is considered for the magnetic field magnitude in the range from 1 to 10 T. The second-order corrections to the Breit -- Rabi formula are calculated and discussed including the one-electron contributions as well as the interelectronic-interaction effects of order 1/Z. The 1/Z corrections are evaluated within a rigorous QED approach. These corrections are combined with other interelectronic-interaction, QED, nuclear recoil, and nuclear size corrections to obtai…
The hyperfine structure (HFS) of a bound electron is modified by the self-interaction of the electron with its own radiation field. This effect is known as the self-energy correction. In this work, we discuss the evaluation of higher-order self-energy corrections to the HFS of bound P states. These are expressed in a semi-analytic expansion involving powers of Zalpha and ln(Zalpha), where Z is the nuclear charge number and alpha is the fine-structure constant. We find that the correction of relative order alpha (Zalpha)^2 involves only a single logarithm ln(Zalpha) for P_1/2 states [but no ter…
The ground state hyperfine splitting of light muon-electron ions of lithium, beryllium, boron and helium is calculated on the basis of analytical perturbation theory in terms of small parameters of the fine structure constant and electron-muon mass ratio. The corrections of vacuum polarization, nuclear structure and recoil effects and electron vertex corrections are taken into account. The dependence of the corrections on the nucleus charge Z is studied. The obtained total values of hyperfine splitting intervals can be used for comparison with future experimental data.
