  The unbound proton-rich nuclei $^{16}$F and $^{15}$F are investigated
experimentally and theoretically. Several experiments using the resonant
elastic scattering method were performed at GANIL with radioactive beams to
determine the properties of the low lying states of these nuclei. Strong
asymmetry between $^{16}$F-$^{16}$N and $^{15}$F-$^{15}$C mirror nuclei is
observed. The strength of the $nucleon-nucleon$ effective interaction involving
the loosely bound proton in the $s_{1/2}$ orbit is significantly modified with
respect to their mirror nuclei $^{16}$N and $^{15}$C. The reduction of the
effective interaction is estimated by calculating the interaction energies with
a schematic zero-range force. It is found that, after correcting for the
effects due to changes in the radial distribution of the single-particle wave
functions, the mirror symmetry of the $n-p$ interaction is preserved between
$^{16}$F and $^{16}$N, while a difference of 63\% is measured between the $p-p$
versus $n-n$ interactions in the second excited state of $^{15}$F and $^{15}$C
nuclei. Several explanations are proposed.
