利用 Dirac 方程，我们研究了原子氢和类氢离子中由有限核尺寸（FNS）效应、相对论 QED 辐射修正以及核反冲修正引起的电子结合能和超精细分裂修正。文中考虑了核内电荷分布与磁矩分布的三种模型。计算针对轻原子（H、He 和 K）以及重原子（Rb、Cs、Pb、Bi、U）进行。结果表明，对于轻核，基态能量的 FNS 修正小于电子–核约化质量修正，并且与相对论 QED 辐射修正相当；但对于重核，FNS 修正远大于这两类修正。文中还将结果与氢的 1s–2s 跃迁频率实验进行了比较。对于基态超精细分裂，轻核的 FNS 修正在量级上与相对论 QED 辐射修正相当，而在重核中则更大。
英文摘要：
Using the Dirac equation, we study corrections to electron binding energies and hyperfine splittings of atomic hydrogen and hydrogen-like ions due to finite nuclear size (FNS) effects, relativistic QED radiative corrections and nuclear recoil corrections. Three models for the charge distribution and the magnetic moment distribution within the nucleus are considered. Calculations are carried for light atoms (H, He and K) and heavy atoms (Rb, Cs, Pb, Bi, U). The FNS corrections to the ground-state energy are shown to be smaller than the electron-nucleus reduced mass corrections, and comparable to the relativistic QED radiative corrections for the light nuclei, but much larger than both these corrections for heavy nuclei. Comparison is made with an experiment on the $1s$-$2s$ transition frequency for hydrogen. FNS corrections to the ground state hyperfine splitting are comparable in size to the relativistic QED radiative corrections for light nuclei, but are larger for heavy nuclei.
Hyperfine structure splitting of the positron-helium ions $e^{+}[^3$He$(2^3S)]$ and $e^{+}[^4$He$(2^3S)]$
测定了正电子氦离子$e^{+}[^3$ He $(2^3S)]$和$e^{+}[^4$ He $(2^3S)]$最低束缚态的超精细结构分裂。特别地，我们发现对于$e^{+}[{}^3$ He $(2^3S)]$离子，可以观察到以下三个超精细结构分裂：5824.3986 $MHz$、76466.5308 $MHz$和5824.4019 $MHz$。在$e^{+}[{}^4$ He $(2^3S)]$离子中，只能观察到一个超精细结构分裂82963.0427 $MHz$。所有这些值都可以在现代实验中测量。
In this work, we consider the thermal correction to the hyperfine interaction in hydrogen, deuterium, and the $^3$He$^+$ ion. This correction is effectively described by one-loop Feynman graphs in the framework of the quantum electrodynamics theory for bound states at a finite temperature. A simple analysis shows the importance of the obtained results for future prospects for measuring hyperfine splitting. In addition, the application for testing the time variation of fundamental constants is briefly discussed.
We perform accurate calculations of energy levels as well as fine and hyperfine splittings of the lowest $^{1,3}\!P_J$, $^{3}\!S_1$, $^{3}\!P^e_J$, and $^{1,3}\!D_J$ excited states of the $^9$Be atom using explicitly correlated Gaussian functions and report on the breakdown of the standard hyperfine structure theory. Because of the strong hyperfine mixing, which prevents the use of common hyperfine constants, we formulate a description of the fine and hyperfine structure that is valid for an arbitrary coupling strength and may have wide applications in many other atomic systems.
The measurement of Cesium (Cs) 7D5/2 excited state's hyperfine splitting intervals and hyperfine-interaction constants has been experimentally investigated based on ladder-type (852 nm + 698 nm) three-level Cs system (6S1/2 - 6P3/2 - 7D5/2) with room-temperature Cs atomic vapor cell. By scanning the 698-nm coupling laser's frequency, the Doppler-free high-resolution electromagnetically-induced transparency (EIT) assisted double-resonance optical pumping (DROP) spectra have been demonstrated via transmission enhancement of the locked 852-nm probe laser. The EIT-assisted DROP spectra are employe…
Nuclear structure corrections of orders $Zα\, E_F$ and $(Zα)^2 E_F$ are calculated for the hyperfine splitting of the muonic deuterium. The obtained results disagree with previous calculations and lead to a $5\,σ$ disagreement with the current experimental value of the $2S$ hyperfine splitting in $μ$D.
The ASACUSA collaboration is developing a polarized beam of antihydrogen atoms to precisely determine the ground-state hyperfine structure for studies of CPT and Lorentz invariance. Using a beam of ordinary hydrogen, measurements of both the $σ$ and $π$-transition have been performed, investigating orientation-dependent SME coefficients. Furthermore a first hyperfine experiment with a beam of deuterium is being prepared.
Toward the measurement of the hyperfine structure of muonic hydrogen in the FAMU experiment. Multi-pass cavity optimization for experiments with pulsed sources
Radiative and interelectronic-interaction corrections to the hyperfine splitting in highly charged B-like ions
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 …
NRQED approach to the fine and hyperfine structure corrections of order m$α$ 6 and m$α$ 6 (m/M)-Application to the hydrogen atom The NRQED approach is applied to the calculation of relativistic corrections to the fine and hyperfine structure of hydrogenlike atoms at orders m$α$ 6 and m$α$ 6 (m/M). Results are found to be in agreement with those of the relativistic theory. This confirms that the derived NRQED effective potentials are correct, and may be used for studying more complex atoms or molecules. Furthermore, we verify the equivalence between different forms of the NRQED Lagrangian used …
The hyperfine structure of the ground states in the helium muonic atoms
本文用高精度变分波函数研究了${}^{3}$ He $^{2+} μ^{-} e^{-}$和${}^{4}$ He $^{2+} μ^{-} e^{-}$的超精细基态结构。超精细结构（即超精细分裂）的相应水平之间的差异被确定为非常高的数值精度。特别地，我们发现${}^{4}$ He $^{2+} μ^{-} e^{-}$原子基态的超精细结构分裂是$Δν\approx 4464.55454(3)$ $MHz$，而${}^{3}$ He $^{2+}μ^{-}e^{-}$原子的类似分裂是$Δν\approx 4166.43547(3)$。
The prospects of tests of CPT symmetry using precision spectroscopy of antihydrogen are discussed with special emphasis on the ground-state hyperfine structure, a measurement of which is the aim of the ASACUSA collaboration at the AD/ELENA facility of CERN. Ongoing parallel experiments using hyperfine spectroscopy of hydrogen and deuterium aiming at studying Lorentz invariance by determining coefficients of the Standard Model Extension framework are described.
The antihydrogen programme of the ASACUSA collaboration at the antiproton decelerator of CERN focuses on Rabi-type measurements of the ground-state hyperfine splitting of antihydrogen for a test of the combined Charge-Parity-Time symmetry. The spectroscopy apparatus consists of a microwave cavity to drive hyperfine transitions and a superconducting sextupole magnet for quantum state analysis via Stern-Gerlach separation. However, the small production rates of antihydrogen forestall comprehensive performance studies on the spectroscopy apparatus. For this purpose a hydrogen source and detector …
The rigorous QED evaluation of the one- and two-photon exchange corrections to the ground-state hyperfine splitting in Li-like ions is presented for the wide range of nuclear charge number $Z= 7 - 82$. The calculations are carried out in the framework of the extended Furry picture, i.e., with inclusion of the effective local screening potential in the zeroth-order approximation. The interelectronic-interaction contributions of the third and higher orders are taken into account in the framework of the Breit approximation employing the recursive perturbation theory. In comparison to the previous…
We present a high-precision calculation of the recoil--finite-size correction to the hyperfine splitting (HFS) in muonic and electronic hydrogen based on nucleon electromagnetic form factors obtained from dispersion theory. This will help guide the upcoming searches of the HFS transition in muonic hydrogen, and will allow a precise determination of the polarizability and Zemach radius contributions when this transition is found.
