Muonic X-Ray Measurement for the Nuclear Charge Distribution: the Case of Stable Palladium Isotopes

TL;DR

This study measures muonic X-ray transition energies for palladium isotopes to determine their nuclear charge radii and discuss charge distribution, introducing a new method to analyze nuclear charge distribution from muonic transitions.

Contribution

The paper presents a novel approach to deduce nuclear charge distribution from muonic transition energies, specifically applying it to stable palladium isotopes.

Findings

Muonic transition energies for five palladium isotopes were measured.

Root-mean-square charge radii were deduced assuming a two-parameter Fermi distribution.

Charge distribution analysis employed the Barrett model, highlighting the importance of $3d$-$2p$ transitions.

Abstract

Background: The nuclear charge radius and distribution are the most fundamental quantities of the atomic nucleus. From the muonic transition energies, the absolute charge radius has been experimentally obtained, while there have been no established methods to discuss the distribution. Purpose: The muonic transition energies for five palladium isotopes with the mass number $A = 104$, $105$, $106$, $108$ and $110$ were measured. The procedure to deduce the charge radii and the method to discuss the charge distribution from the muonic transition energies are proposed. Method: The experiment was performed at the MuSIC-M1 beamline at Research Center for Nuclear Physics, Osaka University. A continuous muon beam impinged on the enriched palladium targets. Muonic X rays were measured by high-purity germanium detectors. Results: The muonic transition energies up to $4f$-$3d$ transitions were determined for five palladium isotopes. Discussion and conclusion: The root-mean-square charge radii are deduced assuming the two-parameter Fermi distribution. The charge distribution of the nucleus is discussed employing the Barrett model. The muonic transition energies of the $3d$-$2p$ transitions are crucial to discuss both the charge radius and the charge distribution.