ACR CAPT DESCRIBED NMAC/TCAS RA EVENT WHILE ON DESCENT TO BNA WITH TRACON. NO TFC INFO PROVIDED BY CTLR.

Narrative

WE WERE DSNDING UNDER BNA APCH CTL. THE CTLR HAD TURNED US TO A HDG OF 080 DEGS WITH A DSCNT TO 4000 FT MSL. IT WAS A VECTOR TO RWY 2R LOC. PASSING 9000 FT THE CTLR ISSUED US DIRECTIONS TO SLOW TO 210 KIAS. PASSING APPROX 8700 FT WITH THE ACFT DSNDING AT 600-1000 FPM; THE TCAS GAVE US A 1-2 SECOND TFC ALERT. TARGET WAS ON THE NOSE; 5 NM; SAME ALT! CTLR WAS TALKING...I QUICKLY CHANGED SCREEN TO 5 NM SCALE. ABOUT THAT TIME; THE TCAS GAVE US ANOTHER MOMENTARY TARGET ON THE NOSE; 2 NM; SAME ALT! I IMMEDIATELY DISCONNECTED THE AUTOPLT AND INITIATED EVASIVE MANEUVER WITH 30 DEGS OF BANK WHILE SIMULTANEOUSLY INCREASING THE DSCNT RATE. CTLR STILL TALKING...WE PICKED UP THE ACFT VISUALLY; PASSING JUST TO THE L SIDE OF OUR ACFT. IT WAS A C172 WNWBOUND. AS THE CESSNA PASSED TO OUR L THE TCAS GAVE US AN RA! IT INITIALLY TOLD US TO CLB BUT QUICKLY REVERSED ITS DIRECTIVE TO DSND. IT NEVER GAVE US A TURN DIRECTIVE. THE RA WAS TOO LATE TO AVOID A CATASTROPHIC ACFT ACCIDENT. THE NEXT THING WE HEARD FROM OUR CTLR WAS 'UNDERSTAND YOU ARE IN A R TURN.' WE ADVISED HIM OF THE RA. WE LANDED AT BNA WITHOUT FURTHER INCIDENT. UPON GATE ARR; I CALLED BNA TRACON AND TALKED TO THE SUPVR. HE APOLOGIZED STATING THE CTLR HAD JUST MISSED THE TFC ON HIS SCREEN. HE HAD ALREADY ANNOTATED THE INCIDENT IN THE LOG...I'VE BEEN FLYING A LONG TIME. ALTHOUGH USED TO MEETING OTHER FIGHTER ACFT CANOPY TO CANOPY; I BELIEVE HAD WE NOT TAKEN PREEMPTIVE ACTION BEFORE THE TCAS ISSUED THE RA; I WOULD NOT BE WRITING THIS NARRATIVE.