We investigate the resonant process of nuclear excitation by electron capture, in which a continuum electron is captured into a bound state of an ion with the simultaneous excitation of the nucleus. In order to derive the cross section a Feshbach projection operator formalism is introduced. Nuclear states and transitions are described by a nuclear collective model and making use of experimental data. Transition rates and total cross sections for NEEC followed by the radiative decay of the excited nucleus are calculated for various heavy ion collision systems.
In heavy atoms and ions, nuclear structure effects are significantly enhanced due to the overlap of the electron wave functions with the nucleus. This overlap rapidly increases with the nuclear charge $Z$. We study the energy level shifts induced by the electric dipole and electric quadrupole nuclear polarization effects in atoms and ions with $Z \geq 20$. The electric dipole polarization effect is enhanced by the nuclear giant dipole resonance. The electric quadrupole polarization effect is enhanced because the electrons in a heavy atom or ion move faster than the rotation of the deformed nuc…
Ionization of light atoms and ions during the nuclear $β^{-}$-decay is considered. To determine the final state probabilities of electron ionization we have developed a procedure based on the natural orbital expansions for the bound state wave functions of all atoms/ions involved in this process.
The extraction of nuclear charge radii from spectroscopy experiments in muonic atoms is currently limited by the large uncertainties associated with the theoretical evaluation of the nuclear polarizability effects. To facilitate calculations, these polarizability corrections are conventionally expressed as an expansion in a dimensionless parameter $η$, which has been argued in previous literature to hold an approximate value of 0.33 in light-nuclear systems. In this work, we check this claim by doing a Bayesian analysis of the nuclear-polarizability corrections to the Lamb shift in $μ^2$H and …
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 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 nuclear recoil effect on the ground-state $g$ factor of highly charged boronlike ions is considered within the relativistic framework. The interelectronic-interaction contribution is evaluated within the Breit approximation employing two independent approaches: the second-order perturbation theory and the configuration-interaction Dirac-Fock-Sturm method. The uncertainty of the nuclear recoil $g$-factor contributions is significantly reduced, especially for low- and middle-$Z$ ions.
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…
According to the Schiff theorem the nuclear electric dipole moment (EDM) is screened in neutral atoms. In ions this screening is incomplete. We extend a derivation of the Schiff theorem to ions and molecules. The finite nuclear size effects are considered including Z^2 alpha^2 corrections to the nuclear Schiff moment which are significant in all atoms and molecules of experimental interest. We show that in majority of ionized atoms the nuclear EDM contribution to the atomic EDM dominates while in molecules the contribution of the Schiff moment dominates. We also consider the screening of elect…
The nuclear magnetic shielding is considered within the fully relativistic approach for the ground state of H-, Li-, and B-like ions in the range Z=32-92. The interelectronic interaction is evaluated to the first order of the perturbation theory in Li- and B-like ions. The calculations are based on the finite-field method. The numerical solution of the Dirac equation with the magnetic-field and hyperfine interactions included within the dual-kinetic-balance method is employed. The nuclear magnetic shielding constant is an important ingredient for accurate determination of the nuclear magnetic …
A systematic investigation of the nuclear-polarization effects in one- and few-electron heavy ions is presented. The nuclear-polarization corrections in the zeroth and first orders in $1/Z$ are evaluated to the binding energies, the hyperfine splitting, and the bound-electron g factor. It is shown, that the nuclear-polarization contributions can be substantially canceled simultaneously with the rigid nuclear corrections. This allows for new prospects for probing the QED effects in strong electromagnetic field and the determination of fundamental constants.
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 process of internal conversion from excited electronic states is investigated theoretically for the case of the vacuum-ultraviolet nuclear transition of $^{229}{\mathrm Th}$. Due to the very low transition energy, the $^{229}{\mathrm Th}$ nucleus offers the unique possibility to open the otherwise forbidden internal conversion nuclear decay channel for thorium ions via optical laser excitation of the electronic shell. We show that this feature can be exploited to investigate the isomeric state properties via observation of internal conversion from excited electronic configurations of ${\ma…
Nuclear-spin-dependent (NSD) parity violating (PV) effects can be strongly enhanced in diatomic molecules containing heavy atoms. Future measurements are anticipated to provide nuclear anapole moments and strength constants for PV nuclear forces. In light molecules, the NSD electroweak electron-nucleus interaction may also be detected. Here we calculate NSD PV effects for molecular ions. Our calculations are motivated by rapid developments in trapping techniques for such systems at low temperatures.
The nuclear recoil correction to the g factor of boronlike ions is evaluated within the lowest-order relativistic (Breit) approximation. The interelectronic-interaction effects are taken into account to the first order of the perturbation theory in 1/Z. Higher orders in 1/Z are partly accounted for by means of the effective screening potential. The most accurate up-to-date values of this contribution are presented for the ions in the range Z=10-20.
The shielding of the nuclear magnetic moment by the bound electron in hydrogen-like ions is calculated ab initio with inclusion of relativistic, nuclear, and quantum electrodynamics (QED) effects. The QED correction is evaluated to all orders in the nuclear binding strength parameter and, independently, to the first order in the expansion in this parameter. The results obtained lay the basis for the high-precision determination of nuclear magnetic dipole moments from measurements of the g-factor of hydrogen-like ions.
A method is proposed to determine the $M1$ nuclear transition amplitude and hence the lifetime of the "nuclear clock transition" between the low-lying ($\sim 8$ eV) first isomeric state and the ground state of $^{229}$Th from a measurement of the ground-state $g$ factor of few-electron $^{229}$Th ions. As a tool, the effect of nuclear hyperfine mixing (NHM) in highly charged $^{229}$Th-ions such as $^{229}$Th$^{89+}$ or $^{229}$Th$^{87+}$ is utilized. The ground-state-only $g$-factor measurement would also provide first experimental evidence of NHM in atomic ions. Combining the measurements fo…
The quantum electrodynamical theory of the three-photon transitions in hydrogen-like ions is presented. Emission probabilities of various three-photon decay channels for $ 2p_{3/2} $, $ 2p_{1/2} $ and $ 2s_{1/2} $ states are calculated for the nuclear charge $Z$ values $1\leqslant Z \leqslant 95$. The results are given in two different gauges. The fully relativistic three-photon decay rates of hydrogen-like ions with half-integer nuclear spin are given for transitions between fine structure components. The results can be applied to the tests of the Bose-Einstein statistics for the multiphoton …
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.
We report an ab initio calculation of the shielding of the nuclear magnetic moment by the bound electron in hydrogen-like ions. This investigation takes into account several effects that have not been calculated before (electron self-energy, vacuum polarization, nuclear magnetization distribution), thus bringing the theory to the point where further progress is impeded by the uncertainty due to nuclear-structure effects. The QED corrections are calculated to all orders in the nuclear binding strength parameter and, independently, to the leading order in the expansion in this parameter. The res…
The nuclear recoil effect on the g factor of highly charged Li-like ions is evaluated in the range Z=10-92. The calculations are performed using the 1/Z perturbation theory. The one-electron recoil contribution is evaluated within the fully relativistic approach with the wave functions which account for the screening effects approximately. The two-electron recoil contributions of the first and higher orders in 1/Z are calculated within the Breit approximation using a four-component approach.
We consider excitation of highly charged hydrogen-like ions by the impact of equivelocity electrons and protons. The kinetic energy of the protons is more than three orders of magnitude larger than that of the equivelocity electrons. It is shown, however, that despite this fact, the electrons can be much more effective in inducing excitation at collision velocities (slightly) above the threshold for electron impact excitation. The basic reason for this is the strong distortion of the motion of the electron by the attractive field of the nucleus of the highly charged ion.
The nuclear recoil effect on the $g$ factor of the ground state of highly charged B-like ions is studied to first order in the electron-to-nucleus mass ratio $m/M$. The leading one-electron and two-electron recoil contributions are calculated nonperturbatively in the parameter $αZ$ within the rigorous QED formalism. The interelectronic-interaction correction to the nuclear recoil effect is evaluated in the Breit approximation by means of perturbation theory to the first order in $1/Z$. The higher-order interelectronic-interaction corrections are taken into account partially by performing the c…
The alignment of nuclear states resonantly formed in nuclear excitation by electron capture (NEEC) is studied by means of a density matrix technique. The vibrational excitations of the nucleus are described by a collective model and the electrons are treated in a relativistic framework. Formulas for the angular distribution of photons emitted in the nuclear relaxation are derived. We present numerical results for alignment parameters and photon angular distributions for a number of heavy elements in the case of E2 nuclear transitions. Our results are intended to help future experimental attemp…
In sudden perturbation approximation, the probability of the shake-up process accompanying inner-shell ionization is calculated for the isoelectronic sequences of Li-, Na- and K-like ions in the ground and excited $n$p and $n$d states. Numerical solutions of Hartree-Fock equations and hydrogen-like radial orbitals are used. Very large differences between the results of both approximations for all ions and strong dependences on ion charge are obtained at the beginning of the isoelectronic sequences.
Ionization of helium-like ions with simultaneous excitation of the ns-states due to photon scattering is considered. The differential and total cross sections of the process are calculated to leading order of perturbation theory with respect to the interelectron interaction. The formulas obtained are applicable in the nonrelativistic energy range far beyond the ionization threshold.
Nuclear deformation effects on the binding energies in heavy ions are investigated. Approximate formulas for the nuclear-size correction and the isotope shift for deformed nuclei are derived. Combined with direct numerical evaluations, these formulas are employed to reanalyse experimental data on the nuclear-charge-distribution parameters in $^{238}\textrm{U}$ and to revise the nuclear-size corrections to the binding energies in H- and Li-like $^{238}\textrm{U}$. As a result, the theoretical uncertainties for the ground-state Lamb shift in $^{238}\textrm{U}^{91+}$ and for the $2p_{1/2}-2s$ tra…
We study a method for mass-selective removal of ions from a Paul trap by parametric excitation. This can be achieved by applying an oscillating electric quadrupole field at twice the secular frequency $ω_{\text{sec}}$ using pairs of opposing electrodes. While excitation near the resonance with the frequency $ω_{\text{sec}}$ only leads to a linear increase of the amplitude with excitation duration, parametric excitation near $2\, ω_{\text{sec}}$ results in an exponential increase of the amplitude. This enables efficient removal of ions from the trap with modest excitation voltages and narrow ba…
Optical atomic clocks using highly-charged ions hold an intriguing promise of metrology at the 19th significant figure. Here we study transitions within the $4f^{12}$ ground-state electronic configuration of highly charged ions. We consider isotopes lacking hyperfine structure and show that the detrimental effects of coupling of electronic quadrupole moments to gradients of trapping electric field can be effectively reduced by using specially chosen virtual clock transitions. The estimated systematic fractional clock accuracy is shown to be below $10^{-19}$.
A new mechanism of nuclear excitation via two-photon electron transitions (NETP) is proposed and studied theoretically. As a generic example, detailed calculations are performed for the $E1E1$ $1s2s\,^1S_0 \rightarrow 1s^2\,^1S_0$ two-photon decay of He-like $^{225}$Ac$^{87+}$ ion with the resonant excitation of the $3/2+$ nuclear state with the energy 40.09(5) keV. The probability for such a two-photon decay via the nuclear excitation is found to be $P_{\rm NETP} = 3.5 \times 10^{-9}$ and, thus, is comparable with other mechanisms, such as nuclear excitation by electron transition and by elec…
The hyperfine splitting in hydrogenlike $^{209}$Bi, $^{203}$Tl, and $^{205}$Tl is calculated with the nuclear magnetization determined from experimental data on the hyperfine splitting in the corresponding muonic atoms. The single-particle and configuration-mixing nuclear models are considered. The QED corrections are taken into account for both electronic and muonic atoms. The obtained results are compared with other calculations and with experiment.
We use correlation potential and many-body perturbation theory techniques to calculate spin-independent and nuclear spin-dependent parts of the parity nonconserving amplitudes of the transitions between the $6s_{1/2}$ ground state and the $5d_{3/2}$ excited state of Ba$^+$ and Yb$^+$ and between the $7s_{1/2}$ ground state and the $6d_{3/2}$ excited state of Ra$^+$. The results are presented in a form convenient for extracting of the constants of nuclear-spin-dependent interaction (such as, e.g., anapole moment) from the measurements.
The quantum electrodynamical theory of the two-photon transitions in hydrogenlike ions is presented. The emission probability for 2s1/2 -> 2E1+1s1/2 transitions is calculated and compared to the results of the previous calculations. The emission probabilities 2p12 -> E1E2+1s1/2 and 2p1/2 -> E1M1+1s1/2 are also calculated for the nuclear charge Z values 1-100. This is the first calculation of the two latter probabilities. The results are given in two different gauges.
Dielectronic recombination (DR) of few-electron ions has evolved into a sensitive spectroscopic tool for highly charged ions. This is due to technological advances in electron-beam preparation and ion-beam cooling techniques at heavy-ion storage rings. Recent experiments prove unambiguously that DR collision spectroscopy has become sensitive to 2nd order QED and to nuclear effects. This review discusses the most recent developments in high-resolution spectroscopy of low-energy DR resonances, experimental studies of KLL DR of very heavy hydrogenlike ions, isotope shift measurements of DR resona…
The ground state hyperfine splitting values of high Z hydrogenlike ions are calculated. The relativistic, nuclear and QED corrections are taken into account. The nuclear magnetization distribution correction (the Bohr-Weisskopf effect) is evaluated within the single particle model with the g_{S}-factor chosen to yield the observed nuclear moment. An additional contribution caused by the nuclear spin-orbit interaction is included in the calculation of the Bohr-Weisskopf effect. It is found that the theoretical value of the wavelength of the transition between the hyperfine splitting components …
The nuclear recoil effect on the $g$ factor of H- and Li-like heavy ions is evaluated to all orders in $αZ$. The calculations include an approximate treatment of the nuclear size and the electron-electron interaction corrections to the recoil effect. As the result, the second largest contribution to the theoretical uncertainty of the $g$-factor values of $^{208}$Pb$^{79+}$ and $^{238}$U$^{89+}$ is strongly reduced. Special attention is paid to tests of the QED recoil effect on the $g$ factor in experiments with heavy ions. It is found that, while the QED recoil effect on the $g$-factor value i…
The Gamma Factory (GF) initiative aims at the construction of a unique experimental tool exploiting resonant interaction of light with ultra-relativistic partially stripped ions (PSI) stored in circular accelerators at CERN. Resonant excitation of high-energy electronic transitions in the ions is achieved through Doppler-boosting (by twice the Lorentz factor; from hundred to several thousand times) of light energy. In order to efficiently excite the ions, and hence generate intense beams of scattered/fluorescent photons, a detailed knowledge of the ions' electronic energy structure and the dyn…
Electronic bridge excitation of the 76 eV nuclear isomeric state in $^{235}$U is shown to be strongly enhanced in the U$^{7+}$ ion, potentially enabling laser excitation of this nucleus. This is because the electronic spectrum has a very high level density near the nuclear transition energy that ensures the resonance condition is fulfilled. We present a quantum statistical theory based on many-body quantum chaos to demonstrate that typical values for the electronic factor increase the probability of electronic bridge in $^{235}$U$^{7+}$ by many orders of magnitude. We also extract the nuclear …
The total two-photon decay rate of hydrogen-like ions is studied using relativistic quantum electrodynamics. In particular, we analyse how finite nuclear size and QED vacuum polarization corrections affect the decay rate. To calculate these corrections, a finite basis set method based on $B$-splines is used for the generation of quasi-complete atomic spectra and, hence, of the relativistic Green's function. By making use of this $B$-spline approach, high precision calculations have been performed for the $2s_{1/2} \to 1s_{1/2} + 2γ$ and $2p_{1/2} \to 1s_{1/2} + 2γ$ decay of hydrogen-like ions …
Energies, wavelengths, transition probabilities, and oscillator strengths have been calculated for the 4s24p2-4s4p3, 4s24p2-4s24p4d and 4s4p3-4p4 allowed transitions in heavy Ge-like ions with Z=59-63. The fully relativistic Multiconfiguration Dirac-Fock (MCDF) method taking into account both the correlations within the n=4 complex and the quantum electrodynamic (QED) effects have been used in the calculations. MCDFGME code is used to calculate electron impact excitation cross sections for the 4s24p2-4s4p3 and 4s24p2-4s24p4d transitions with plane-wave Born approximation. The results of Pr XXV…
The nuclear recoil effect on the $^2 P_{3/2}$-state $g$ factor of B-like ions is calculated to first order in the electron-to-nucleus mass ratio $m/M$ in the range $Z=18$--$92$. The calculations are performed by means of the $1/Z$ perturbation theory. Within the independent-electron approximation, the one- and two-electron recoil contributions are evaluated to all orders in the parameter $αZ$ by employing a fully relativistic approach. The interelectronic-interaction correction of first order in $1/Z$ is treated within the Breit approximation. Higher orders in $1/Z$ are partially taken into ac…
We have developed a novel all-optical broadband scheme for exciting, amplifying and measuring the secular motion of ions in a radio frequency trap. Oscillation induced by optical excitation has been coherently amplified to precisely control and measure the ion's secular motion. Requiring only laser line-of-sight, we have shown that the ion's oscillation amplitude can be precisely controlled. Our excitation scheme can generate coherent motion which is robust against variations in the secular frequency. Therefore, our scheme is ideal to excite the desired level of oscillatory motion under condit…
Relativistic calculations of the isotope shifts of energy levels in highly charged Li-like ions are performed. The nuclear recoil (mass shift) contributions are calculated by merging the perturbative and large-scale configuration-interaction Dirac-Fock-Sturm (CI-DFS) methods. The nuclear size (field shift) contributions are evaluated by the CI-DFS method including the electron-correlation, Breit, and QED corrections. The nuclear deformation and nuclear polarization corrections to the isotope shifts in Li-like neodymium, thorium, and uranium are also considered. The results of the calculations …
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 Dirac Hamiltonian including nuclear recoil and vacuum-polarization operators is considered in a supercritical regime Z > 137. It is found that the nuclear recoil operator derived within the Breit approximation regularizes the Hamiltonian for the point-nucleus model and allows the ground state level to go continuously down and reach the negative energy continuum at a critical value Zcr = 145. If the Hamiltonian contains both the recoil operator and the Uehling potential, the 1s level reaches the negative energy continuum at Zcr = 144. The corresponding calculations for the excited states ha…
Accurate calculations of the nuclear recoil effect to the Lamb shift of hydrogen-like atoms are presented. Numerical results are reported for the $ns$ states with $n \leq 5$ and for the $2p_{1/2}$ and $2p_{3/2}$ states. The calculations are performed to the first order in the electron-nucleus mass ratio and to all orders in the nuclear binding strength parameter $Zα$ (where $Z$ is the nuclear charge number and $α$ is the fine structure constant). The obtained results provide accurate predictions for the higher-order remainder beyond the known $Zα$-expansion terms. In the case of hydrogen, the …
We discuss the results of the calculation of the photoionization with de-excitation of excited He and helium-like ions Li$^{+}$ and B$^{3+}$ at high but non-relativistic photon energies $ω$. Several lower $^{1}S$ and $^{3}S$ states are considered. We present and analyze the ratios $R_{d}^{+\ast}$ of the cross sections of photoionization with de-excitation, $σ_{(d)}^{+\ast}(ω)$, and of the photo-ionization with excitation, $σ^{+\ast}(ω)$. The dependence of $R_{d}^{+\ast}$ on the excitation of the target object and the charge of its nucleus is presented. Apart to theoretical interest, results ob…
We demonstrate the trapping and sympathetic cooling of B$^{+}$ ions in a Coulomb crystal of laser-cooled Ca$^{+}$, We non-destructively confirm the presence of the both B$^+$ isotopes by resonant excitation of the secular motion. The B$^{+}$ ions are loaded by ablation of boron and the secular excitation spectrum also reveals features consistent with ions of the form B$_{n}^{+}$.
The excitation of the 8 eV $^{229m}$Th isomer through the electronic bridge mechanism in highly charged ions is investigated theoretically. By exploiting the rich level scheme of open $4f$ orbitals and the robustness of highly charged ions against photoionization, a pulsed high-intensity optical laser can be used to efficiently drive the nuclear transition by coupling it to the electronic shell. We show how to implement a promising electronic bridge scheme in an electron beam ion trap starting from a metastable electronic state. This setup would avoid the need for a tunable vacuum ultraviolet …
The hyperfine splitting of the ground state of H-, Li-, and B-like ions is investigated in details within the range of nuclear numbers Z = 7-28. The rigorous QED approach together with the large-scale configuration-interaction Dirac-Fock-Sturm method are employed for the evaluation of the interelectronic-interaction contributions of first and higher orders in 1/Z. The screened QED corrections are evaluated to all orders in (αZ) utilizing an effective potential approach. The influence of nuclear magnetization distribution is taken into account within the single-particle nuclear model. The speci…
