  The exotic structures in the 2s_{1/2} states of five pairs of mirror nuclei
^{17}O-^{17}F, ^{26}Na-^{26}P, ^{27}Mg-^{27}P, ^{28}Al-^{28}P and
^{29}Si-^{29}P are investigated with the relativistic mean-field (RMF) theory
and the single-particle model (SPM) to explore the role of the Coulomb effects
on the proton halo formation. The present RMF calculations show that the exotic
structure of the valence proton is more obvious than that of the valence
neutron of its mirror nucleus, the difference of exotic size between each
mirror nuclei becomes smaller with the increase of mass number A of the mirror
nuclei and the ratios of the valence proton and valence neutron
root-mean-square (RMS) radius to the matter radius in each pair of mirror
nuclei all decrease linearly with the increase of A. In order to interpret
these results, we analyze two opposite effects of Coulomb interaction on the
exotic structure formation with SPM and find that the contribution of the
energy level shift is more important than that of the Coulomb barrier for light
nuclei. However, the hindrance of the Coulomb barrier becomes more obvious with
the increase of A. When A is larger than 34, Coulomb effects on the exotic
structure formation will almost become zero because its two effects counteract
with each other.
