Exploring Isospin Symmetry Breaking in Exotic Nuclei: High-Precision Mass Measurement of 23Si and Shell-Model Calculations of T = 5/2 Nuclei

TL;DR

The paper addresses how isospin symmetry breaking manifests in exotic sd-shell nuclei at high isospin, focusing on the $T_z=-5/2$ system $^{23}$Si. It employs high-precision mass measurements via TOF-ICR in a 9.4 T Penning trap at FRIB/LEBIT, interleaved with a stable reference to optimize the cyclotron-frequency ratio and extract masses with $M(^{23}\mathrm{Si}) = 23362.9(5.8)$ keV. The results, compared with USDC/USDCm sd-shell shell-model calculations of binding-energy differences and Thomas–Ehrman shifts up to $T=5/2$, show overall good agreement and indicate Coulomb interaction as the dominant isospin-breaking mechanism, refining IMME-based predictions. This work provides a stringent benchmark for isospin-symmetry breaking in sd-shell nuclei and strengthens confidence in shell-model treatments of high-$T$ systems, with implications for nuclear structure and astrophysical modeling.

Abstract

We present a high-precision mass measurement of the proton-rich nucleus 23Si, performed with the LEBIT Penning trap at the Facility for Rare Isotope Beams (FRIB) utilizing the time-of-flight ion cyclotron resonance (TOF-ICR) technique. We determined a mass excess of 23362.9(5.8) keV, which agrees with a recent storage-ring measurement from CSRe but has a factor 20 improved precision. 23Si is hence the nucleus with the most precisely known mass of all nuclei with an isospin projection of Tz =-5/2. We performed shell-model calculations with the USDC and USDCm Hamiltonians to study binding energy differences and Thomas-Ehrmann shifts in mirror systems with an isospin up to T = 5/2. Our experimental result and other recently reported masses of neutron-deficient sd-shell nuclei agree well with the theoretical predictions, demonstrating that isospin symmetry breaking in sd-shell nuclei, even at high isospin values, is well described by modern shell-model calculations.

Figures (7)

• Figure 1: The nuclear landscape in the region of $^{23}$Si. Individual nuclei are colored based on their respective isospin $T$. A black dashed border refers to an unmeasured mass, a black dotted border to a stable nucleus, no border to a mass measurement reported in AME2020 AME2020 and a red full border to a recent mass measurement as reported in this work for $^{23}$Si and references PhysRevC.110.L031301PhysRevLett.133.222501PhysRevLett.131.092501PhysRevLett.132.152501PhysRevC.110.L031302.
• Figure 2: A summed ToF-ICR spectrum of the last two cyclotron frequency measurements (number 4 and 5) taken for 23Si+ with a quadrupole excitation time of 25 ms. The spectrum is formed by 1598 ions. The full red line shows a $\chi^{2}$-minimization fit to the data points depicted in black as described in KONIG199595. The cyclotron frequency $\nu_{c}$ is obtained from $\nu_{RF}$ at the minimum time-of-flight of the fit.
• Figure 3: Cyclotron frequency ratios $R$ with respect to the average ratio $\bar{R} = 0.99846634(27)$. The gray bar shows the $\pm 1 \sigma$ uncertainty in $\bar{R}$.
• Figure 4: Mass excess for $^{23}$Si compared with the extrapolated value from AME2020 AME2020 and the recent measurement by CSRe PhysRevLett.133.222501.
• Figure 5: Nuclei with isospin $T=5/2$ in the $sd$ shell: The mass excess values are taken from AME2020 AME2020 except for $^{21}$Al PhysRevC.110.L031301, $^{23}$Si (this work), $^{27}$S PhysRevLett.133.222501, $^{31}$Ar PhysRevLett.133.222501 and $^{35}$Ca PhysRevLett.131.092501. A black dashed border around a nuclide refers to an unmeasured mass, a full red border to a recent mass measurement and no border to a mass measurement as reported in AME2020 AME2020.