FLC OF B727 CLBED FROM STAR ARR ALT IN RESPONSE TO A TCASII RA AND OBSERVED AN SMA SEL ACFT PASSING UNDER THEIR R WING. ATC HAD NOT ISSUED ANY TA.

Narrative

WHILE FLYING THE VOLLS 5 ARR INTO BNA AT 10000 FT MSL; 250 KIAS; WE RECEIVED A TCASII TFC ALERT. THE TARGET APPEARED ON THE TCASII DISPLAY AT APPROX 5 MI; STRAIGHT AHEAD; 100 FT BELOW OUR ALT. I DISCONNECTED THE AUTOPLT AND INSTRUCTED THE FO TO ASK APCH CTL IF HE HAD ANY TARGETS AT OUR 12 O'CLOCK POS. THE CTLR RESPONDED THAT HE DID NOT AND THAT IT WAS PROBABLY AN ACFT FROM A LCL ARPT THAT HAD JUST TAKEN OFF. APPROX 2-3 SECONDS LATER WE RECEIVED AN RA COMMANDING A 2000 FPM CLB; WHICH WE IMMEDIATELY ESTABLISHED. AT 10600 FT MSL; THE FO OBSERVED A SMALL SINGLE ENG AIRPLANE PASSING APPROX 100 FT UNDER OUR R WING. AT 10800 FT MSL; I PUSHED THE NOSE BACK DOWN AND DSNDED BACK TO 10000 FT MSL. THE FO RPTED THE NEAR MISS AND OUR ALTDEV TO ATC AND THE FLT PROCEEDED UNEVENTFULLY TO BNA. WE COULD NOT IDENT THE REGISTRATION NUMBER OF THE OTHER ACFT. RECOMMENDATIONS: GA PLTS SHOULD BE ADVISED TO AVOID FLYING ON TERMINAL SIDS/STARS WHILE OPERATING VFR. AIR TFC CTLRS SHOULD BE ADVISED TO BE CAREFUL IN ADVISING ACFT UNDER THEIR CTL ABOUT POTENTIAL TFC CONFLICTS.