Constraints on energies of ${}^{15}\mathrm{F}$(g.s.), ${}^{15}\mathrm{O}$(${\frac{1}{2}}^{+},T=\frac{3}{2}$), and ${}^{16}\mathrm{F}$($0^{+},T=2$)

Coulomb energy calculations for the lowest $0^{+},T=2$ state in $A=16$ nuclei allow tight constraints on the masses of the lowest $1/2^{+},T=3/2$ state in ${}^{15}\mathrm{O}$ and ${}^{15}\mathrm{F}$, and of the $0^{+},T=2$ state in ${}^{16}\mathrm{F}$.

Figure 1

Steeper upward sloping lines exhibit the IMME relationship between masses of ${}^{15}\mathrm{F}$(g.s.) and ${}^{15}\mathrm{O}$($1/2^{+},T=3/2$) for $d=0$ and $d=10$ keV. Horizontal lines are at the ${}^{15}\mathrm{F}$ values of Ref. [3] for $\delta =\pi /2$ (solid) and wave-function maximum (dashed). Shallower sloping solid line gives the relationship between the ${}^{15}\mathrm{F}$ and ${}^{15}\mathrm{O}{}^{*}$ masses if ${}^{16}\mathrm{C}$, ${}^{16}\mathrm{O}{}^{*}$, and ${}^{16}\mathrm{Ne}$ all have the same $s^2$ fraction. Dashed lines with this slope represent a 40 keV model uncertainty.

Figure 2

Schematic representation of the energy of ${}^{15}\mathrm{F}$(g.s.) calculated in Ref. [1], measured in Ref. [3], and from present analysis.