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.
Nuclear-size correction to the one-loop self-energy in hydrogenlike ions
Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新院）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Physics, St. Petersburg State University（圣彼得堡国立大学物理系）
Extraction of the electron mass from $g$ factor measurements on light hydrogenlike ions
从潘宁陷阱测量与$^{12}$ C $^{5+}$离子和从理论结果的束缚电子$g$因素的电子质量的测定进行了详细描述。一些最近计算的贡献稍微移动提取的质量值。从实验和理论两方面讨论了进一步提高电子质量的前景。用$^4$ He $^+$离子进行的测量将使电子质量值的一致性检查成为可能，并且在将来改进$^4$ He核质量和确定精细结构常数。
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）
In this paper we study the influence of electron screening on the Bohr-Weisskopf (BW) effect in many-electron atoms. The BW effect gives the finite-nucleus magnetization contribution to the hyperfine structure. Relativistic atomic many-body calculations are performed for s and p_1/2 states of several systems of interest for studies of atomic parity violation and time-reversal-violating electric dipole moments -- Rb, Cs, Fr, Ba+, Ra+, and Tl. For s states, electron screening effects are small, and the relative BW correction for hydrogenlike ions and neutral atoms is approximately the same. We r…
A charged particle in a magnetic field possesses discrete energy levels associated with particle rotation around the field lines. A bound complex of particles with a nonzero net charge possesses an analogous levels associated with its center-of-mass motion and, in addition, the levels associated with internal degrees of freedom, that is with relative motions of its constituent particles. The center-of-mass and internal motions are mutually dependent, which complicates theoretical studies of the binding energies, radiative transitions and other properties of the complex ions moving in quantizin…
A model-operator approach to fully relativistic calculations of the nuclear recoil effect on energy levels in many-electron atomic systems is worked out. The one-electron part of the model operator for treating the normal mass shift beyond the Breit approximation is represented by a sum of semilocal and nonlocal potentials. The latter ones are constructed by employing the diagonal and off-diagonal matrix elements rigorously evaluated for hydrogenlike ions to first order in the electron-to-nucleus mass ratio. The specific mass shift beyond the lowest-order relativistic approximation has a form …
Gauge Invariant Evaluation of Nuclear Polarization with Collective Model
在计算类氢重离子的核极化能时，通常采用的集体模型在只考虑梯形图和十字图的情况下，发现核极化能存在严重的规范破坏.利用电荷电流密度与微观模型的等价性，计算了$^{208}_{~82}$ Pb $^{81+}$和$^{238}_{~92}$ U $^{91+}$中$1s_{1/2}$态的NP能移随集体模型的规范不变.
The influence of the blackbody radiation field on the $g$-factor of light hydrogenlike ions is considered within the framework of quantum electrodynamics at finite temperature for bound states. One-loop thermal corrections are examined for a wide range of temperatures. The numerical results for $1s$, $2s$, $2p_{1/2}$, and $2p_{3/2}$ states are presented. It is shown that for excited states finite temperature corrections to the bound-electron $g$-factor are close to the level of current experimental uncertainty even at room temperatures and can be discerned within the measurements anticipated i…
Fully relativistic approach is applied to evaluation of the nuclear recoil effect on the bound-electron $g$ factor in hydrogenlike ions to first order in the electron-to-nucleus mass ratio $m/M$ and to all orders in $αZ$. The calculations are performed in the range $1 \leqslant Z \leqslant 20$ for the $g$ factors of $1s$, $2s$, $2p_{1/2}$, and $2p_{3/2}$ states. The $αZ$-dependence of the nontrivial QED recoil contribution as a function of $Z$ is studied.
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 shift of atomic energy levels due to hadronic vacuum polarization is evaluated in a semiempirical way for hydrogenlike ions and for muonic hydrogen. A parametric hadronic polarization function obtained from experimental cross sections of $e^-e^+$ annihilation into hadrons is applied to derive an effective relativistic Uehling potential. The energy corrections originating from hadronic vacuum polarization are calculated for low-lying levels using analytical Dirac-Coulomb wave functions, as well as bound wave functions accounting for the finite nuclear size. Closed formulas for the hadronic …
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…
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。
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 …
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…
