Precision Tests of Isospin Symmetry through Coulomb excitation of A = 62 Nuclei

Abstract

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.

Figures (4)

• Figure 1: Doppler-corrected $\gamma$-ray energy spectra for inelastic scattering on the $^{197}$Au target for (a) $^{62}$Zn, (b) $^{62}$Ga, and (c) $^{62}$Ge. The spectra were constructed using the forward-most DALI$2^+$ detectors ($\theta_\gamma < 60^{\circ}$) for background suppression. Add-back of neighboring crystals is applied. The inset shows the high-energy region of the $^{62}$Zn spectrum around the $2^+_2\rightarrow 0^+_1$ transition.
• Figure 2: $M_p(T_z)$ linearity in the $A=62$ isospin triplet. The error bars indicate statistical uncertainties, while the additional caps show the total uncertainties including statistical, systematical, and uncertainties arising from the reaction theory calculations. Large-scale shell-model calculations were performed in the $fp$ model space using the KB3GR interaction with two sets of effective charges: $e_p = 1.31$, $e_n = 0.46$ (SM1) and $e_p = 1.50$, $e_n = 0.50$ (SM2). The beyond-mean-field EXVAM calculations were done with effective charges $e_p = 1.50$, $e_n = 0.50$mihai22.
• Figure 3: Linearity of $M_p(T_z) / \langle M_p \rangle$ in $A=42 - 70$ mass triplets. The results of the present study are compared to values from the literature hadynska16boso19giles19wimmer21pritychenko16. The bands indicate the corresponding uncertainties. The linearity test is performed relatively within each mass triplet. For $A=62$, the error band represents statistical uncertainties including the small transmission correction. For all other triplets, total uncertainties (statistical and systematic) are used in the comparison.
• Figure 4: Metric quantifying the linearity of $M_p$ and the data quality. (a) $c$ coefficient from a quadratic fit $M_p=a+b\cdot T_z+c\cdot T_z^2$ for $T=1$ triplets. (b) Information content for the same triplets. The results from the present study are highlighted in red.