AN ACR MDT STOPPED ITS IFR CLB TO AVOID A 'POP-UP' VFR SMA.

Narrative

WE WERE CLBING TO 6000 FT ENRTE FROM BQK TO JAX. SINCE THE FLT WAS RELATIVELY SHORT; I HAD BEEN MONITORING ATIS. MY FO WAS MONITORING ATC. AFTER FINISHING COPYING THE ATIS; I RETURNED TO THE ATC FREQ AND MY NORMAL PATTERN OF SCANNING FOR OTHER TFC. I VERY QUICKLY DISCOVERED AN SMA AT OUR 12 O'CLOCK POS AND 3 TO 4 MI AHEAD. I GLANCED DOWN AT TCASII; WHICH SHOWED THE TFC LEVEL AT 6000 FT; SAME DIRECTION; WHICH SUBSEQUENTLY ISSUED A TA. I ASKED MY FO IF ATC HAD ISSUED THE TFC; AND HE SAID NO; AND CONTINUED TO CLB. I IMMEDIATELY LEVELED THE ACFT AT 5500 AND QUERIED ATC OF THE TFC. THE CTLR SAID THE TFC HAD JUST POPPED UP ON HER SCREEN; AND ISSUED A 30 DEG R TURN TO AVOID THE TFC. AT THAT TIME; I TOLD ATC THAT WE HAD THE TFC IN SIGHT; AND COULD MAINTAIN A VISUAL SEPARATION AT 5500 FT UNTIL WE CLRED THE TFC. THE CTLR AGREED AND WE PASSED THE TFC TO THE E AT 5500 FT; UNTIL WE CLRED AND HAD SEPARATION; THEN CONTINUED OUR CLB TO 6000 FT. THE FLT CONTINUED UNEVENTFULLY AND LANDED AT JAX. I THEN HAD A 'TALK' WITH MY FO AND MADE SURE THAT HE UNDERSTOOD THAT JUST BECAUSE WE WERE ON AN IFR FLT PLAN; IT IS STILL OUR RESPONSIBILITY TO SEE AND AVOID TFC.