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 nucleus, thus experiencing significant corrections to the conventional approximation in which they `see' an averaged nuclear charge density. The electric nuclear polarization effects are computed numerically for $1s$, $2s$, $2p_{1/2}$ and high $ns$ electrons. The results are fitted with elementary functions of nuclear parameters (nuclear charge, mass number, nuclear radius and deformation). We construct an effective potential which models the energy level shifts due to nuclear polarization. This effective potential, when added to the nuclear Coulomb interaction, may be used to find energy level shifts in multi-electron ions, atoms and molecules. The fitting functions and effective potentials of the nuclear polarization effects are important for the studies of isotope shifts and nonlinearity in the King plot which are now used to search for new interactions and particles.
Finite-nuclear-size effect for hydrogenlike ions under high external pressure
College of Physics, Jilin University（吉林大学物理学院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）；Department of Nuclear Engineering and Management, Graduate School of Engineering, The University of Tokyo（东京大学工学研究科核工程与管理系）；Department of Physics, Graduate School of Science, The University of Tokyo（东京大学理学研究科物理系）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所跨学科理论与数学科学中心）
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 …
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 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 …
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…
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.
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 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.
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…
We present a theoretical investigation of the radiative recombination of twisted Bessel electrons with initially hydrogen-like (finally helium-like) heavy ions. In our study, we focus especially on the linear polarization of x-ray photons emitted in the electron capture into the ground $1s^2_{1/2}$ ionic state. Particular emphasis is placed on the question of how this polarization is affected if incident hydrogen-like ions are themselves spin-polarized. To explore such a "polarization transfer" we apply the density matrix theory and derive the Stokes parameters of recombination x-rays for the …
We present a theoretical study of bound-free electron-positron pair production in the interaction of $γ$-rays with bare ions. Special attention is paid to the longitudinal polarization of both the emitted positrons and the produced hydrogen-like ions. To evaluate this polarization we employed exact solutions of the relativistic Dirac equation and treat the electron-photon coupling within the framework of first-order perturbation theory. Detailed calculations have been performed for both, low- and high-Z ions and for a wide range of photon energies. The results of these calculations suggest tha…
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…
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 …
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 implement three-dimensional polarization gradient cooling of trapped ions. Counter-propagating laser beams near $393\,$nm impinge in lin$\,\perp\,$lin configuration, at a frequency below the S$_{1/2}$ to P$_{3/2}$ resonance in $^{40}$Ca$^+$. We demonstrate mean phonon numbers of $5.4(4)$ at a trap frequency of $2π\times 285\,$kHz and $3.3(4)$ at $2π\times480\,$kHz, in the axial and radial directions, respectively. Our measurements demonstrate that cooling with laser beams detuned to lower frequencies from the resonance is robust against an elevated phonon occupation number, and thus works w…
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.
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 …
Parametrization of the angular correlation and degree of linear polarization in two-photon decays of hydrogen-like ions
在二阶微扰理论和狄拉克相对论方程的框架下，研究了类氢离子的双光子衰变。特别注意的角度相关的发射的光子，以及两个光子之一的线性偏振的程度，如果第二个是刚刚观察到给定的角度。角相关和线性偏振度的表达式展开的$\cosθ$ -多项式，其系数取决于原子序数和能量共享的发射光子。包括更高的（电和磁）多极后，超出电偶极子近似的发射光子对的影响进行了讨论。沿着整个氢等电子序列（$1\le Z \le 100$），对跃迁$2s_{1/2}\rightarrow1s_{1/2}$、$3d_{3/2}\rightarrow1s_{1/2}$和$3d_{5/2}\rightarrow1s_{1/2}$进行系数计算。
