The lowest-lying states of the Borromean nucleus ${}^{17}\mathrm{Ne}\left({}^{15}\mathrm{O}+p+p\right)$ and its mirror nucleus ${}^{17}\mathrm{N}\left({}^{15}\mathrm{N}+n+n\right)$ are compared by using the hyperspheric adiabatic expansion. Three-body resonances are computed by use of the complex scaling method. The measured size of ${}^{15}\mathrm{O}$ and the low-lying resonances of ${}^{16}\mathrm{F}\left({}^{15}\mathrm{O}+p\right)$ are first used as constraints to determine both central and spin-dependent two-body interactions. The interaction obtained reproduces relatively accurately both experimental three-body spectra. The Thomas-Ehrman shifts, involving excitation energy differences, are computed and found to be less than $3\%$ of the total Coulomb energy shift for all states.

• Received 10 June 2003

DOI:https://doi.org/10.1103/PhysRevC.69.024002