Recent studies have provided new experimental information on the very neutron-rich nucleus 135 Sb. We have performed a shell-model calculation for this nucleus using a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential. This gives a very good description of the observed properties of 135 Sb. We show that the anomalously low position of the first excited state, J π = 5/2 + , and the strongly hindered M 1 transition to the ground state have their origin in the effective neutron-proton interaction. In the very recent work of Refs. [5,6] the nature of the 5/2 + state in 135 Sb has been further investigated. In particular, at OSIRIS/STUDSVIK the Advanced TimeDelayed βγγ(t) method has been used to measure the lifetime of this state. A very small upper limit for the B(M 1) was found, thus evidencing a strongly hindered transition. This was seen as a confirmation of the singleparticle nature of the 5/2 + state. In this paper we report on a shell-model study of 135 Sb employing matrix elements of the two-body effective interaction derived from a modern nucleon-nucleon (N N ) potential. It is our main aim to verify to what extent a realistic shell-model calculation can account for the properties of 135 Sb, with special attention to the 5/2 + state, and try understand if there is a real need of shell structure modifications to explain the experimental data.We assume that 132 Sn is a closed core and let the valence neutrons occupy the six levels 0h 9/2 , 1f 7/2 , 1f 5/2 , 2p 3/2 , 2p 1/2 , and 0i 13/2 of the 82-126 shell, while for the proton the model space includes the five levels 0g 7/2 , 1d 5/2 , 1d 3/2 , 2s 1/2 , and 0h 11/2 of the 50-82 shell.The two-body matrix elements of the effective interaction are derived from the CD-Bonn N N potential [7]. The strong short-range repulsion of the latter is renormalized by means of the new approach of Ref. [8], which has proved to be an advantageous alternative to the usual G-matrix method [8,9]. In this approach, a smooth potential, V low−k , is constructed by integrating out the high-momentum components, i.e. above a certain cutoff momentum Λ, of the bare N N potential V N N . The V low−k preserves the physics of V N N up to Λ and can be used directly in the calculation of shell-model effective interactions. In the present paper, we have used for Λ the value 2.2 fm −1 . Once the V low−k is obtained, the calculation of the ef-