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Abstract

The development of precision atomic spectroscopy experiments and theoretical advancements plays a crucial role in measuring fundamental physical constants and testing quantum electrodynamics (QED) theories. It also provides a significant platform for studying the internal structure of atomic nuclei and developing high-precision nuclear structure theories. Nuclear structure effects such as charge distribution, magnetic moment distribution, and nuclear polarizability have been accurately determined in many atomic spectroscopy experiments, significantly enhancing the precision of nuclear structure detection. This paper systematically reviews the theoretical research and developments on the corrections of two-photon exchange (TPE) effects on the Lamb shift and hyperfine structure (HFS) in light ordinary and muonic atoms. Advanced nuclear force models and ab initio methods are employed to analyze the TPE nuclear structure corrections to the Lamb shift in a series of light muonic atoms. The paper compares the calculation of TPE effects from various nuclear models and evaluates the model dependencies and theoretical uncertainties of TPE effect predictions. Furthermore, the paper discusses the significant impact of TPE theory on explaining the discrepancies between experimental measurements and QED theoretical predictions in atomic hyperfine structures, resolving the accuracy difficulties in traditional theories. Detailed analyses of TPE effects on HFS in electronic and muonic deuterium using pionless effective field theory show good agreement with experimental measurements, validating the accuracy of theoretical predictions. The theoretical studies of TPE effects in light atoms are instrumental for determining nuclear charge radii and Zemach radii from spectroscopy measurements. These results not only enhance the understanding of nuclear structure and nuclear interactions but also offer crucial theoretical guidance for future experiments, thereby advancing the understanding of the proton radius puzzle and related studies.

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Ji Chen^1,2

Corresponding author:Ji Chen,jichen@ccnu.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant Nos. 12175083, 12335002, 11805078).

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	$ \delta^{N}_{\rm el} $	$ \delta^{N}_{\rm pol} $	$ \delta^{A}_{\rm el} $	$ \delta^{A}_{\rm pol} $	$ \delta_{\rm TPE} $
$ \text{µ}^2{\rm H} $	–0.030(02)	–0.020(10)	–0.423(04)	–1.245(13)	–1.718(17)
$ \text{µ}^3{\rm H} $	–0.033(02)	–0.031(17)	–0.227(06)	–0.480(11)	–0.771(22)
$ \text{µ}^3 {\rm He}^{+} $	–0.52(03)	–0.25(13)	–10.49(23)	–4.23(18)	–15.49(33)
$ \text{µ}^4 {\rm He}^{+} $	–0.54(03)	–0.34(20)	–6.14(31)	–2.35(13)	–9.37(44)

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	²H (1S)/kHz	µ²H (1S)/meV	µ²H (2S)/meV
$ E_{\rm el} $	–42.1(2.1)	–0.984(46)	–0.123(6)
$ E_{\rm pol} $	109.8(4.5)	2.86(12)	0.358(14)
$ E_{\rm nucl}=E_{\rm el}+E_{\rm pol} $	67.7(4.2)	1.878(88)	0.235(11)
$ E_{\rm 1 p} $^[71]	–35.54(8)	–1.018(2)	–0.1272(2)
$ E_{\rm 1 n} $^[72]	9.6(1.0)	0.079(32)	0.010(4)
$ \varDelta_{3\gamma} $	±0.49	±0.052	±0.0065
$ E_{\rm TPE} $	41.7(4.4)	0.94(11)	0.117(13)
Ref. [64,65]	43
Ref. [26,69] mod	64.5
Ref. [70]		0.304(68)	0.0383(86)
$ \nu_{\rm exp}-\nu_\text{QED} $^[25,68]	45.2		0.0966(73)
注: “mod”对原文献修正核子反冲与极化效应; TPE效应在µ²H的1S和2S态中相差8倍.

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Vol. 73, Issue 20 - 2024-10-20

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