SciPost Submission Page
Muonic Lithium atoms: nuclear structure corrections to the Lamb shift
by S. Li Muli, A. Poggialini, S. Bacca
Submission summary
| Authors (as registered SciPost users): | Simone Salvatore Li Muli |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/1910.14370v2 (pdf) |
| Date accepted: | Dec. 20, 2019 |
| Date submitted: | Dec. 17, 2019, 1 a.m. |
| Submitted by: | Simone Salvatore Li Muli |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | 24th European Few Body Conference (EFB2019) |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
In view of the future plans to measure the Lamb shift in muonic Lithium atoms we address the microscopic theory of the $\mu$-$^6$Li$^{2+}$ and $\mu$-$^7$Li$^{2+}$ systems. The goal of the CREMA collaboration is to measure the Lamb shift to extract the charge radius with high precision and compare it to electron scattering data or atomic spectroscopy to see if interesting puzzles, such as the proton and deuteron radius puzzles, arise. For this experiment to be successful, theoretical information on the nuclear structure corrections to the Lamb shift is needed. For $\mu$-$^6$Li$^{2+}$ and $\mu$-$^7$Li$^{2+}$ there exist only estimates of nuclear structure corrections based on experimental data that suffer from very large uncertainties. We present the first steps towards an ab initio computation of these quantities using few-body techniques.
List of changes
We thank the referee for his valuable comments. We would like to address his points below.
1) In our first paragraphs we describe the history of the proton radius puzzle, not only what it is today. We do not feel that stating that the proton radius puzzle is only a disagreement of the Paris measurement with the rest is fair, because there are electron scattering experiments from Mainz that measured a large radius. As nuclear physicists we want to mention them and we think it is important to understand why they give a large radius. as opposed to the small radius found by PRAD. The PRAD Nature paper was published on Nov 6th, while we submitted the proceedings on Nov 1st. That is why we did not include it in the figure. Of course, we were aware of these data (as preliminary data) but we did not want to include unpublished data, especially when they are from other collaborations. Now that the paper is published, we added the PRAD point to Fig. 1. We also modified the paragraph: "New experiments are also being performed. These account for precise measurements of electron-proton at low momentum transfer, e.g., the Proton Radius (PRad) experiment at JLab [11] and the muon-proton scattering experiment (MUSE) being commissioned at PSI [12]“ to "New experiments were performed or are being performed. These account for precise measurements of electron-proton at low momentum transfer, e.g., muon-proton scattering experiment (MUSE) being commissioned at PSI [11] and the Proton Radius (PRad) experiment at JLab [12], that recently measured a small radius, consistent with the muonic atom results. Furthermore, new ...”
2) We corrected to 2S-2P_1/2.
3) We do not consider the deuteron radius puzzle an independent puzzle, but it has been coined "deuteron radius puzzle" in Ref.[20], so we think we can call it this way. However, to take into account the referee's point we substituted the sentence: " Recent laser spectroscopy experiments in muonic deuterium (μ-2 H ) led to the discovery of the "deuteron radius puzzle" [20], which is rather similar to the proton radius puzzle." => " Recent laser spectroscopy experiments in muonic deuterium (μ-2 H ) led to the discovery of the "deuteron radius puzzle" [20], which is rather similar to, but not independent from, the proton radius puzzle.
4) We want to be consistent with the notation of the our recent JPG review (Ref.[22]), so we call it \delta_TPE. Of course the Coulomb term is not of order (Z\alpha)^5, and the referee is correct in saying that it is not clearly explained. To amend, right after Eq.(4), we have added the following sentence: “ The above terms are all of order $(Z\alpha)^5$, but the Coulomb term (\delta_C^{(0)}) which is logarithmically enhanced to $(Z\alpha)^6\log(Z\alpha$). We include it in our $\delta_{\text{TPE}}$, consistently with Ref. [22], where it is also possible to find a full compilation and derivation of these expressions.”
5) We did not include the expression of \delta_N because it is not the main point of the proceedings. However, to be more clear we added a footnote:\footnote{Expressions of \delta_N can be found in Eq. (3a),(105) and (106) of Ref.[22].}
6) We corrected for that by moving the definitions of \beta and \lambda after Eq. (14). The squared neutron charge radius is negative, even though the neutron is neutral, because it can be pictured as a proton with a negative pion cloud that extends further at larger distance, so that the second moment of the charge distribution is slightly negative.
7) We added the explanation: "From Eq.(1) it is clear that $\delta_{\text{Z1}}^{(1)}$ and $\delta_{\text{Z3}}^{(1)}$ cancel out when considering the total TPE correction, however we still compute them with the purpose of comparing to Ref. [28], who has estimated only the inelastic part of $\delta_{\text{TPE}}$."
8) We have added the following sentence with 4 new citations, before Section 2: “Nuclear structure corrections have been studied by various groups, see, e.g., Refs. [23-26].”
We have performed one other change: * Corrected the value of \eta to 0.33
We hope that now the manuscript can be accepted for publication as a proceedings of the few- body conference 2019 in Surrey.
With best regards, Simone, Anna and Sonia
Published as SciPost Phys. Proc. 3, 028 (2020)