Air carrier being vectored into SDF experienced a TCAS TA/RA at 3000; while on base outside the Class C. Traffic was not issued by ATC.

Narrative

We were being vectored to the final approach course for 17R by Louisville Approach. We were at 3000ft on a right base and assigned a 140 heading to intercept; maintain 3000 feet until intercept; and maintain 180 knots to FAF. We made the turn to 140 degrees. As we were about to intercept the localizer at 3000 feet (near BLGRS intersection); the TCAS announced 'Traffic; traffic.' It was at this time that we spotted a Single-Engine Low-Wing Aircraft at 12 o'clock and at our altitude (3000ft). It crossed the final approach moving from East to West. We were probably within 100 yards away from the aircraft as it passed by our right side and continued Westbound. After it had passed; the TCAS announced a 'Descend; Descend Now' RA. I called approach to inform them of the aircraft. Until that time; they had mentioned nothing about the traffic. He seemed a little stunned that something was there. He responded a little later and said that the traffic was just outside the Class C Airspace. No excessive maneuvers were required and the flight terminated normally. The traffic 'popped up' suddenly on our TCAS display (I had my TCAS display already up on my MFD at a 12nm scale). There was no RA until the traffic had already passed by our right side.