Three-body Thomas-Ehrman shifts of analog states of ${}^{17}$Ne and ${}^{17}$N

Abstract

The lowest-lying states of the Borromean nucleus ${}^{17}$Ne (${}^{15}$O+$p$ + $p$) and its mirror nucleus ${}^{17}$N (${}^{15}$N+$n$ + $n$) are compared by using the hyperspheric adiabatic expansion. Three-body resonances are computed by use of the complex scaling method. The measured size of ${}^{15}$O and the low-lying resonances of ${}^{16}$F (${}^{15}$O+$p$) 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.

Comments: 9 pages, 3 postscript figures, revtex style. To be published in Phys. Rev. C