Precision Tests of Isospin Symmetry through Coulomb excitation of A = 62 Nuclei
Isospin symmetry in the $A=62$ mass system was investigated through Coulomb excitation reactions at the RIKEN Radioactive Isotope Beam Factory. Beams of $^{62}$Zn, $^{62}$Ga, and $^{62}$Ge were studied using the BigRIPS-ZeroDegree-DALI2$^+$ setup under identical experimental conditions, allowing for cancellation of systematic uncertainties. Inelastic scattering cross sections measured with two different targets were used to extract nuclear deformation lengths and $E2$ matrix elements. The isospin symmetry of the $A=62$ system was rigorously tested by examining the linearity of the proton matrix elements within the triplet with high precision. The observed linear relationship between the reduced proton matrix elements for the three nuclei holds within experimental uncertainties, providing a stringent test of isospin symmetry. This experiment provides the most accurate test, to date, of isospin symmetry rules using transition matrix elements. These results were interpreted using large-scale shell-model calculations, offering valuable insights into isospin symmetry behavior in this region of the nuclear chart.