High-Precision Mass Measurements of 52Ni and 51Co Reveal Breakdown of the Isobaric Multiplet Mass Equation in the f p Shell

Technical Summary: High-Precision Mass Measurements of 52Ni and 51Co

Problem and Motivation
The Isobaric Multiplet Mass Equation (IMME) serves as a fundamental framework for predicting the masses of exotic nuclei and testing isospin symmetry in nuclear physics. The IMME posits that the binding energies of isobaric analog states (IAS) within a multiplet follow a quadratic dependence on the isospin projection $T_z$. Deviations from this quadratic form, particularly the emergence of significant cubic ($d$) or quartic ($e$) terms, signal isospin-symmetry-breaking effects or deficiencies in theoretical treatments of the Coulomb interaction. While previous studies have identified breakdowns in the IMME for specific mass numbers, high-precision data in the proton-rich $fp$-shell remains scarce. This work addresses the need for stringent benchmarks to test theoretical descriptions of Coulomb-exchange terms and isospin non-conserving forces in this region.

Methodology
The authors performed high-precision mass measurements of the proton-rich nuclei $^{51}\text{Co}$ and $^{52}\text{Ni}$ using the Low Energy Beam and Ion Trap (LEBIT) Penning trap at the Facility for Rare Isotope Beams (FRIB).

• Beam Production: A radioactive beam was generated via projectile fragmentation of a 250 MeV/u $^{58}\text{Ni}$ primary beam on a natural carbon target. The resulting ions were separated using the Advanced Rare Isotope Separator (ARIS) and stopped in the Advanced Cryogenic Gas Stopper (ACGS).
• Ion Manipulation: Ions were extracted, mass-separated, and accumulated in a linear Paul-trap cooler-buncher before being injected into a 9.4 T hyperbolic Penning trap.
• Measurement Techniques:
  • $^{51}\text{Co}$: Due to its relatively high production rate and short half-life ($T_{1/2} = 68.8$ ms), the Time-of-Flight Ion-Cyclotron-Resonance (ToF-ICR) technique was employed. An excitation time of 50 ms was used to accommodate the decay, with the cyclotron frequency determined by minimizing the time-of-flight to a microchannel-plate detector.
  • $^{52}\text{Ni}$: Given the substantially lower yield and short half-life ($T_{1/2} = 41.4$ ms), the Phase-Imaging Ion-Cyclotron-Resonance (PI-ICR) technique was utilized. This method measures the phase accumulation of the ion's motion over specific accumulation times (up to 31 ms) on a position-sensitive detector.
• Reference Standards: Measurements were interleaved with stable reference ions ($N_2^+$ for $^{51}\text{Co}$ and $C_2H_2^+$ for $^{52}\text{Ni}$) to cancel magnetic field drifts. Systematic uncertainties were minimized by using low ion bunches (< 5 ions/bunch) and averaging over magnetron periods.

Key Results

• Mass Excess Values:
  • $^{52}\text{Ni}$: A mass excess of $-22474.8(2.2)$ keV was determined. This result is consistent with a recent storage-ring measurement at CSRe but improves the precision by a factor of 37.
  • $^{51}\text{Co}$: A mass excess of $-27375.1(5.7)$ keV was obtained, agreeing with recent CSRe results while reducing the uncertainty by a factor of 2.
• Derived Mass of $^{54}\text{Zn}$: By combining the new $^{52}\text{Ni}$ mass with the two-proton decay energy of $^{54}\text{Zn}$ ($Q_{2p} = 1344(41)$ keV, a weighted average of GANIL and RIKEN measurements), the authors derived a mass excess for $^{54}\text{Zn}$ of $-6463(42)$ keV. This value differs significantly from the extrapolated value in the AME2020 evaluation.
• IMME Analysis:
  • $b$-coefficients: Comparisons with global nuclear models (e.g., UNEDF0, FRDM12, BSkG4) indicate that models omitting the Coulomb-exchange term (or using specific approximations like the Slater approximation without exchange) generally reproduce the experimental $b$-coefficients better than those including the exact exchange term.
  • $d$-coefficients (Breakdown of IMME): The new high-precision data reveals substantial deviations from the quadratic IMME form:
    • For the $A=52, T=2$ multiplet, the cubic coefficient $d$ is determined to be $-15.4(1.5)$ keV (quartic fit yields $d = -17.9(1.6)$ keV), representing a $10.3\sigma$ deviation from zero. This is the second-largest known deviation among all multiplets.
    • For the $A=54, T=3$ multiplet, the $d$ coefficient is $18.2(2.6)$ keV, a $7\sigma$ deviation from zero.
  • Potential Origins: The authors note that while these deviations suggest a breakdown of the quadratic IMME, they could also stem from experimental issues, such as the misidentification of Isobaric Analog States (IAS) or inaccurate binding energies of specific members (e.g., $^{52}\text{Co}$ or $^{54}\text{Fe}$).

Significance and Claims
The paper claims that these measurements provide the most stringent benchmarks to date for isospin-symmetry-breaking effects in the proton-rich $fp$-shell. The primary significance lies in the revelation of a "substantial breakdown" of the IMME for $A=52$ and $A=54$. The results favor theoretical descriptions that omit the Coulomb-exchange term, challenging standard Energy Density Functional (EDF) approaches that include it. Furthermore, the work highlights the necessity for future high-precision mass measurements and a reevaluation of IAS assignments to clarify whether the observed IMME breakdowns are due to new physics or unresolved experimental uncertainties. The authors explicitly state that a direct mass measurement of $^{54}\text{Zn}$ is required to resolve the discrepancy between their derived value and the AME2020 extrapolation, though they acknowledge such a measurement remains experimentally challenging.