Charge radii of Cl isotopes from x-ray spectroscopy of muonic atoms

TL;DR

This study precisely measured the charge radii of stable chlorine isotopes using muonic x-ray spectroscopy, significantly improving accuracy and resolving previous discrepancies in nuclear charge radius data.

Contribution

It provides the most precise charge radii for $^{35}$Cl and $^{37}$Cl, using muonic atom spectroscopy combined with advanced theoretical analysis.

Findings

Charge radii of $^{35}$Cl and $^{37}$Cl determined with 18 ppm uncertainty.

Charge radius difference $ ext{delta} raket{r^2}$ is 25 times more precise than previous data.

Results resolve previous discrepancies and align with global nuclear trends.

Abstract

Nuclear charge radii are vital for nuclear and atomic physics, the determination of fundamental constants, and searches for new physics. Muonic atoms, where a single negative muon orbits a nucleus, are sensitive tools for determining nuclear radii due to the large wavefunction overlap of the muon and nucleus. Here we report on a new measurement of the $2, 3, 4p\to1s$ x-ray energies in muonic $^{35,37}$Cl with uncertainties reaching 18 ppm. By employing a large-scale germanium detector array, it was possible to extract these energies from a high statistics dataset using highly enriched samples of only a few tens of milligrams. Combining these results with state-of-the-art atomic and nuclear theory input, the charge radii of the stable chlorine isotopes were determined to be $R(^{35}\text{Cl}) = 3.3333(23)~fm$ and $R(^{37}\text{Cl}) = 3.3444(23)~fm$. This is an order of magnitude more precise and significantly different from previously tabulated values. Our new values solve a discrepancy observed for the charge radius difference in mirror nuclei, agreeing with the overall global trend. The charge radius difference $\delta \langle r^2 \rangle (^{37}\text{Cl} - {^{35}\text{Cl}}) = -0.0776(64)~fm^2$ we extract is 25 times more precise than the previous values. This precision is crucial for establishing reference values for future laser spectroscopy measurements of radioactive isotopes.