Calculation of the Thomas-Ehrman shift in $^{16}$F and $^{15}$O(p,p) cross section with the Gamow shell model

The $^{16}$F nucleus is situated at the proton drip-line and is unbound by proton emission by only about 500 keV. Continuum coupling is then prominent in this nucleus. Added to that, its low-lying spectrum consists of narrow proton resonances as well. It is then a very good candidate to study nuclear structure and reactions at proton drip-line. The low-lying spectrum and scattering proton-proton cross section of $^{16}$F have then been calculated with the coupled-channel Gamow shell model framework for that matter using an effective Hamiltonian. Experimental data are very well reproduced, as well as in its mirror nucleus $^{16}$N. Isospin-symmetry breaking generated by the Coulomb interaction and continuum coupling explicitly appears in our calculations. In particular, the different continuum couplings in $^{16}$F and $^{16}$N involving $s_{1/2}$ partial waves allow to explain the different ordering of low-lying states in their spectrum.