  We have performed shell-model calculations for the two one valence-neutron
isotones $^{135}$Te and $^{137}$Xe and the two one valence-proton isotopes
$^{135,137}$Sb. The main aim of our study has been to investigate the evolution
of single-particle states with increasing nucleon number. To this end, we have
focused attention on the spectroscopic factors and the effective
single-particle energies. In our calculations, we have employed a realistic
low-momentum two-body effective interaction derived from the CD-Bonn
nucleon-nucleon potential that has already proved quite successful in
describing the spectroscopic properties of nuclei in the $^{132}$Sn region.
Comparison shows that our results reproduce very well the available
experimental data. This gives confidence in the evolution of the
single-particle states 4 figures predicted by the present study.
