MD88 PIC TAKES COMMAND OF ACFT FROM FO WHEN ENCOUNTERING TCASII RA FROM UNSEEN; CONFLICTING ACFT.

Narrative

CLBING OUT OF BTR WITH ZHU ON A 080 DEG HDG CLBING THROUGH 4000 FT MSL; CTR ASKED US TO MAINTAIN 4000 FT. AS HE NOTICED WE WERE THROUGH 4000 FT ALREADY; HE THEN AMENDED OUR CLRNC TO 5000 FT MSL. WE NOTICED A TCASII TARGET S OF US AT ABOUT 1-2 O'CLOCK. AT ABOUT THE SAME TIME WE GOT A TA 'TFC' AND A TURN TO 360 DEGS FROM CTR. WE THEN GOT AN RA 'MONITOR VERT SPD.' I NOTICED THE TCASII RED TARGET AT 100 FT ABOVE AND THE VSI GREEN BAND AT LEVEL TO 300 FPM DOWN. OUR ALT WAS 4800 FT MSL; CLBING. VSI RATE IN THE RED AT 1000 FPM UP. I TOOK THE ACFT FROM MY FO AND AGGRESSIVELY PUT THE ACFT IN A SHALLOW DSCNT LOOKING FOR THE GREEN BAND RATE ON MY VSI. I ACTUALLY PUT THE ACFT INITIALLY IN A SLIGHTLY GREATER THAN NECESSARY RATE OF DSCNT. BECAUSE OF THE TRANSITION FROM A CLB TO A DSCNT IT SEEMED LIKE A LARGE MOVE. I ALLOWED THE DSCNT TO CONTINUE TO ABOUT 4000 FT MSL GIVING ME WHAT I THOUGHT TO BE A SAFE MARGIN OF VERT SEPARATION OF 1000 FT. WITH THE HAIR STANDING UP ON THE BACK OF MY NECK WE RPTED THE RA AND EVASIVE MANEUVER TO CTR. THEY CLRED US IMMEDIATELY TO A HIGHER ALT AND ASKED IF WE WOULD CALL THEM WHEN ON THE GND. WE NEVER SAW THE OTHER ACFT. I TALKED WITH ZHU AFTER LNDG AND THEY TOLD ME THE TFC WAS A POP-UP HDOF FROM SOMEWHERE ELSE AND THEY DIDN'T HAVE ENOUGH TIME TO GET THINGS TURNED AROUND TO PREVENT THE RA AND THAT THEY HAD US WITHIN 2 MI AND ALMOST THE SAME ALT.