Effects of isospin mixing in the $A=32$ quintet

For the $A=32$, $T=2$ quintet we provide a unified theoretical description for three related aspects of isospin mixing: the necessity of more than three terms in the isobaric mass multiplet equation, isospin-forbidden proton decay in ${}^{32}$Cl, and a correction to the allowed Fermi ${\beta }^{+}$ decay of ${}^{32}$Ar. We demonstrate that all three effects observed in experiment can be traced to a common origin related to isospin mixing of the $T=2$ states with $T=1$ states.

Figure 1

Accuracy of the IMME in the $A=32$ quintet with three terms (bottom panel) and with an additional cubic (middle) or quartic (top) term. Circles correspond to experimental data, with error bars from Table . Crosses correspond to theoretical calculations with the USDB interaction. Note the reduction in scale for the middle panel.

Figure 2

0${}^{+}$ levels in ${}^{32}$S given by $T$ vs $E_x$. For ${}^{32}$P and ${}^{32}$Cl, the $T=0$ levels can be ignored to give an approximate distribution of the 0${}^{+}$ states.