Charge radii of $^{11-16}$C, $^{13-17}$N and $^{15-18}$O determined from their charge-changing cross-sections and the mirror-difference charge radii

TL;DR

This study measures charge radii of specific isotopes using charge-changing cross-sections and introduces a correction to the Glauber model, providing new data and insights into mirror nuclei charge radius differences and their relation to isospin asymmetry.

Contribution

First determination of charge radii for several isotopes using a corrected Glauber model and analysis of mirror charge radius differences in relation to isospin asymmetry.

Findings

Charge radii of $^{11}$C, $^{13,16}$N, and $^{15}$O determined for the first time.

Mirror-difference charge radii of certain pairs follow empirical relations predicted by ab initio calculations.

Deviations observed in some mirror pairs suggest complexities beyond current models.

Abstract

Charge-changing cross-sections of $^{11-16}$C, $^{13-17}$N and $^{15-18}$O on a carbon target have been determined at energies around 300 MeV/nucleon. A nucleon separation energy-dependent correction factor has been introduced to the Glauber model calculation for extracting the nuclear charge radii from the experimental CCCSs. The charge radii of $^{11}$C, $^{13,16}$N and $^{15}$O thus were determined for the first time. With the new radii, we studied the experimental mirror-difference charge radii ($\Delta R_{\text {ch}}^{\text {mirror}}$) of $^{11}$B-$^{11}$C, $^{13}$C-$^{13}$N, $^{15}$N-$^{15}$O, $^{17}$N-$^{17}$Ne pairs for the first time. We find that the $\Delta R_{\text {ch}}^{\text {mirror}}$ values of $^{13}$C-$^{13}$N and $^{15}$N-$^{15}$O pairs follow well the empirical relation to the isospin asymmetry predicted by the $ab$ $initio$ calculations, while $\Delta R_{\text {ch}}^{\text {mirror}}$ of $^{11}$B-$^{11}$C and $^{17}$N-$^{17}$Ne pairs deviate from such relation by more than two standard deviations.