Understanding the proton radius puzzle: Nuclear structure effects in light muonic atoms

Chen, Ji; Hernandez, Oscar Javier; Dinur, Nir Nevo; Bacca, Sonia; Barnea, Nir

doi:10.1051/epjconf/201611303006

Cited by 6 publications

(3 citation statements)

References 25 publications

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“…(the individual terms are provided in footnote e ). This value agrees with the result reported in [80]. The total Friar moment contribution according to option a is then given by the sum of Eqs.…”

Section: Two-photon Exchangesupporting

confidence: 91%

Theory of the Lamb Shift and fine structure in muonic 4He ions and the muonic 3He– 4He Isotope Shift

et al. 2018

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We provide an up to date summary of the theory contributions to the 2S → 2P Lamb shift and the fine structure of the 2P state in the muonic helium ion (µ 4 He) + . This summary serves as the basis for the extraction of the alpha particle charge radius from the muonic helium Lamb shift measurements at the Paul Scherrer Institute, Switzerland. Individual theory contributions needed for a charge radius extraction are compared and compiled into a consistent summary. The influence of the alpha particle charge distribution on the elastic two-photon exchange is studied to take into account possible model-dependencies of the energy levels on the electric form factor of the nucleus. We also discuss the theory uncertainty which enters the extraction of the 3 He-4 He isotope shift from the muonic measurements. The theory uncertainty of the extraction is much smaller than a present discrepancy between previous isotope shift measurements. This work completes our series of n = 2 theory compilations in light muonic atoms which we have performed already for muonic hydrogen, deuterium, and helium-3 ions.

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Section: Two-photon Exchangesupporting

confidence: 91%

Theory of the Lamb Shift and fine structure in muonic 4He ions and the muonic 3He– 4He Isotope Shift

et al. 2018

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“…Hiyama and Kamimura used the Gaussian expansion method for ab-initio variational calculations of ground and excited state observables of 4 He trimer and tetramer few-body systems with the LM2M2 potential [21]. Ji et al 2016 implemented the Effective Interaction Hyperspherical Harmonics (EIHH) Expansion method to expand the nuclear Hamiltonians and wave functions in the hyperspherical basis to study nuclear structure effects in μ 4 He + , μ 3 He + and μ 3 H [22]. In the year 2010, Hogaasen, Richard, and Sorba reviewed the quantum mechanics of two-electron atoms (helium atom and helium-like ions with central charge Z) with the application of perturbation theory and variational method [23].…”

Section: Introductionmentioning

confidence: 99%

Few-body model approach to the lowest bound S-state of non-symmetric exotic atoms and ions

Khan

Hasan

2023

Phys. Scr.

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Lowest bound S-state energy of Coulombic three-body systems ($N^{Z+}\mu^-e^-$) consisting of a positively charged nucleus of charge number $Z$ ($N^{Z+}$), a negatively charged muon ($\mu^-$) and an electron ($e^-$), is investigated in the framework of few-body (i.e., two- and three-body) cluster model approach. For the three-body cluster model, we adopted the hyperspherical harmonics expansion (HHE) method. An approximated two-body model calculation is also performed for all the three-body systems considered here. A Yukawa-type screened Coulomb potential with an arbitrary screening parameter ($\lambda$) is chosen for the two-body subsystems of the three-body system. In the resulting Schr"{o}dinger equation (SE), the three-body relative wave function is expanded in the complete set of hyperspherical harmonics (HH). The use of the orthonormality of HH in the SE leads to a set of coupled differential equations (CDEs) which are solved numerically for a manageable basis size to get the energy (E). The pattern of convergence in energy relative to increasing basis size is also investigated. Results are compared with some of those found in the literature.

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“…The current experimental program to study the fine and hyperfine structure of the simplest muonic atoms is successfully measured in muonic hydrogen. The studies of the nucleon and nuclear structure based on light muonic atoms offer a new leap in precise determinations of the charge radii of the proton (Ji et al, 2016;Antognini et al, 2021) which disagreed with the previous determinations from the conventional methods of hydrogen spectroscopy and electron-proton scattering (Lensky et al, 2022). The understanding of this strong dependence of the muonic atoms ISSN: 2811-2881 on nuclear parameters, and the information about atomic nuclei that they can deliver, has triggered interest in the precise knowledge of the level structure of muonic atoms (Oreshkina, 2022).…”

Section: Introductionmentioning

confidence: 99%

An Analytical Formula for 1s 2s2p 3s3p3d Energy Shifts of Finite-Size Nuclei due to Fluctuating Vacuum Fields

Adamu¹,

Ngadda²

2022

AJBAR

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In quantum electrodynamics, the vacuum is not empty but has fluctuating fields which cause an orbiting lepton (electron or muon) to deviate from its quantum orbit and as a result, weaken its coupling with the nucleus, thus causing small changes in lepton energy states. Therefore, in this study, the quantum electrodynamics theory is then applied to determine qualitatively the mean square positions of an oscillating lepton by taking into account the vacuum fields and nuclear size effects. The first-order time-independent perturbation theory as an approximation method is applied to solve for the small changes in the nuclear lepton interaction caused by the two effects. The general expression that can be applied to calculate the changes in lepton energy states is deduced and then applied to calculate numerically these effects on the energy states of single-electron and single muonic atoms. The results showed the dependence of these effects on the principal quantum number n, the orbital quantum number l, the azimuthal quantum number m and the proton number Z. A more significant effect on s (l = 0) states of the large atomic nucleus and muonic atoms is observed. The obtained energy level corrections can be considered as additional energy level corrections that have to be investigated for reanalyzing the existing measured nuclear structure effects and for comparison with future spectroscopic investigations. Moreover, the new proposed formula would be suitable for calculating the energy level corrections in both muonic and electronic atoms caused by the fluctuating vacuum fields.

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Understanding the proton radius puzzle: Nuclear structure effects in light muonic atoms

Cited by 6 publications

References 25 publications

Theory of the Lamb Shift and fine structure in muonic 4He ions and the muonic 3He– 4He Isotope Shift

Theory of the Lamb Shift and fine structure in muonic 4He ions and the muonic 3He– 4He Isotope Shift

Few-body model approach to the lowest bound S-state of non-symmetric exotic atoms and ions

An Analytical Formula for 1s 2s2p 3s3p3d Energy Shifts of Finite-Size Nuclei due to Fluctuating Vacuum Fields

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