Deviations from the Isobaric Multiplet Mass Equation due to threshold states

Abstract

Recent studies have completed the A=16 isospin quintets for states with spin/parity Jπ =0+ and 2+. The dependence of their masses as a function of isospin projection shows evidence for deviations from quadratic behavior indicating isospin violation beyond the expectation from two- body forces. The deviation is most pronounced for the 2+ states. Predictions from the Shell Model Embedded in the Continuum (SMEC) allow us to explain that this isospin violation is associated with a modification of the nuclear structure due to the open-quantum-system nature of the proton- rich members of the quintet. In particular, the 0+ and 2+ states in 16Ne and the 2+ state in 16F are threshold resonances located just above a proton-decay threshold where s-wave coupling to the continuum is expected. The measured deviations of these threshold states from the quadratic behavior of the remaining members of the multiplets makes it possible to obtain information on the magnitude and the energy dependence of the continuum-coupling energy correction. Continuum coupling is also indicated for the ground state of 8C, but this time through p-wave coupling.

Figures (3)

• Figure 1: Energy $E_{p}$ above the indicated threshold for the $A$=16 and $A$=8 quintet states as a function of their isospin projection.
• Figure 2: Residuals of quadratic fits to the mass excesses of the (a) 2$^+$ and (b) 0$^+$ quintets for $A$=16 and the (c) 0$^+$ quintet for $A$=8. The solid blue curve shows a quadratic extrapolation using the masses of neutron-rich members to estimate the values of the proton-rich masses when threshold effects are absent. The hatched area show the $\pm$1$\sigma$ region of these extrapolated values. The stars indicate the values extracted using the new masses presented in the companion paper CharityLong:2025.
• Figure 3: Magenta curves shows the predicted continuum-coupling correlation energy as a function of the energy above the appropriate threshold for the (a) 2$^+$ resonances in $^{16}$Ne and $^{16}$F, (b) 0$^+$ ground state of $^{16}$Ne, and (c) 0$^+$ ground state of ${^8}$C. The data points give the experimental values, and SMEC predictions for each data point are shown as the green squares.