The structure of the low-lying levels in the mirror nuclei Ni-57 and C
u-57 is described within the extended unified model. The problem of si
ngle-particle energies in Ni-56 is treated in detail. ''Bare'' single-
particle energies are extracted from existing experimental data for th
e energy levels in Ni-57 and Cu-57 by carefully considering the influe
nce of the coupling to excitations of the core. Important contribution
s arise, influencing especially the results on the spin-orbit splittin
g. The differences between the Coulomb energy shifts of various orbita
ls in Ni-56 are discussed and compared with those resulting from Hartr
ee-Fock calculations carried out using a broad range of Skyrme interac
tions. The parameters of the Woods-Saxon potential reproducing these n
eutron ''bare'' single-particle energies and the charge root-mean-squa
re radius of Ni-56 are extracted. It is demonstrated that the contribu
tions associated with the Thomas-Ehrman effect and the electromagnetic
spin-orbit interaction are important and large enough to account for
the differences between the Coulomb energy shifts of the single-partic
le levels in Ni-56.