## SciPost Submission Page

# Muonic Lithium atoms: nuclear structure corrections to the Lamb shift

### by S. Li Muli, A. Poggialini, S. Bacca

#### This is not the current version.

### Submission summary

As Contributors: | Simone Salvatore Li Muli |

Arxiv Link: | https://arxiv.org/abs/1910.14370v1 |

Date submitted: | 2019-11-01 |

Submitted by: | Li Muli, Simone Salvatore |

Submitted to: | SciPost Physics Proceedings |

Proceedings issue: | 24th European Few Body Conference (University of Surrey, U.K.) |

Discipline: | Physics |

Subject area: | Nuclear Physics - Theory |

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.

###### Current status:

### Submission & Refereeing History

## Reports on this Submission

### Report 1 by Krzysztof Pachucki on 2019-12-3 Invited Report

### Report

This is a valuable work. The calculation of the leading nuclear

structure corrections to the Lamb shift in muonic lithium atoms

is crucial for the interpretation of the planned measurements.

However, several specific comments or questions shall be addressed

before approving this work for the publication, namely:

### Requested changes

1: the proton radius puzzle is merely the disagreement between

Paris measurements in hydrogen with all the rest.

CODATA 2014, H world data 2014 are all based on Paris measurements,

so they are not independent, as Figure 1 would suggest.

Moreover, the recent PRAD value (published in NATURE)

of the proton charge radius is also in agreement with muH rp.

CODATA 2018 also assumed smaller proton radius.

So to my opinion, there is no basis for heating this proton radius puzzle.

2: Authors should clarify the meaning of Lamb shift in \delta_{LS},

it is not 2S-2P but 2S - 2P_{1/2} energy difference.

3: It is not clear what Authors mean by discovery of the deuteron radius puzzle,

since r_d^2 - r_p^2 agrees between electronic and muonic measurements.

Do Authors consider it to be an independent puzzle ?

4: Authors define \delta_{TPE} as a nuclear structure corrections of order (Z alpha)^5,

however \delta_C^{(0)} in Eq. (6) is of higher order in Z alpha.

What is the basis to call it a two-photon exchange TPE correction ?

5: \delta^N in Eq. (1) is not defined anywhere.

6: After Eq. (8) Authors claim the \phi^2(0) is a squared wave function,

define \beta and \lambda which have not yet been used so far. Moreover,

if r_n is defined to be the neutron charge radius, how come r_n^2 is negative.

7: Authors elaborate on page 6 the calculations of \delta_{Z1}^{(1)} and \delta_{Z3}^{(1)}

which obviously cancel out in the sum in Eq. (1), explanations are needed.

8: A better representation of works by others on nuclear structure effects would be in place.