Excited states in Xe137 have been studied by using the near-barrier single-neutron transfer reactions C13(Xe136,C12γ)Xe137 and Be9(Xe136,Be8γ)Xe137 in inverse kinematics. Particle-γ and particle-γγ coincidence measurements have been performed with the Phoswich Wall and Digital Gammasphere detector arrays. Evidence is found for a 13/22+ level (E=3137keV) and for additional high-lying 3/2- and 5/2- states. The results are discussed in the framework of realistic shell-model calculations. These calculations are also extended to the 13/21+ and 13/22+ levels in the N=83 isotonic chain. They indicate that there is a need for a value of the neutron 0i13/2 single-particle energy (ESPE=2366keV) lower than the one proposed in the literature. It is also demonstrated that the population patterns of the j=±1/2 single-particle states in Xe137 are different for the two targets used in these measurements and the implications of this effect are addressed
