Correlation between muonic levels and nuclear structure in muonic atoms

TL;DR

This paper explores how muonic atoms can be used to probe nuclear structure, revealing a correlation between muonic levels and nuclear shell effects, especially at neutron magic numbers, with minimal nuclear disturbance.

Contribution

It introduces a unified method to study muonic and nuclear interactions, demonstrating muons as reliable probes for nuclear structure and analyzing muon-induced shifts in muonic levels.

Findings

Identification of a 'kink' in isotope shifts at neutron magic numbers.

Muons minimally alter nuclear structure, serving as clean probes.

Muon-induced shifts in muonic levels are significant, comparable to Lamb shift.

Abstract

A method that deals with the nucleons and the muon unitedly is employed to investigate the muonic lead, with which the correlation between the muon and nucleus can be studied distinctly. A "kink" appears in the muonic isotope shift at a neutron magic number where the nuclear shell structure plays a key role. This behavior may have very important implications for the experimentally probing the shell structure of the nuclei far away from the $\beta$-stable line. We investigate the variations of the nuclear structure due to the interaction with the muon in the muonic atom and find that the nuclear structure remains basically unaltered. Therefore, the muon is a clean and reliable probe for studying the nuclear structure. In addition, a correction that the muon-induced slight change in the proton density distribution in turn shifts the muonic levels is investigated. This correction to muonic level is as important as the Lamb shift and high order vacuum polarization correction, but is larger than anomalous magnetic moment and electron shielding correction.