Embodiments of the invention relate generally to rotor cooling and, more particularly, to a stator member having at least one passage for the delivery of cooling steam to a bucket root. In one embodiment, the invention provides a turbine comprising: a rotor including a first bucket root; and a stator member having: a rotor bore within which at least a portion of the rotor is disposed; a facing end adjacent to the first bucket root of the rotor; a plurality of seals within the rotor bore for sealing against the rotor, the plurality of seals including a first seal nearest the facing end and a second seal adjacent to the first seal; and a plurality of passages, each extending from a surface of the rotor bore at a point between the first seal and the second seal and extending through the facing end.