CPR CREW EXPERIENCED TCAS RA WHILE DSNDING.

Narrative

I WAS CRUISING AT FL280 WHEN ZTL ISSUED A DSCNT CLRNC TO CROSS DEHAN AT 8000 FT ON THE AWSON ARR. DURING THE DSCNT WE WERE HANDED OFF TO ATL APCH AND GIVEN FURTHER CLRNC TO CONTINUE DSCNT TO 4000 FT. AT APPROX 9000 FT; ATL INFORMED US OF UNIDENTED VFR TFC AND GAVE US A HDG CHANGE TO AVOID IT DURING THE DSCNT. AS WE PASSED 6500 FT ON THE WAY TO 4000 FT; ATL INFORMED US TO CLB TO 7000 FT. AT THIS POINT WE RECEIVED A TCAS RA TO CLB. I INITIATED AN IMMEDIATE CLB; HOWEVER; ATL STILL WANTED US AT 7000 FT. AS I WAS CLBING; MY FO AND I SPOTTED ADDITIONAL TFC AT THE 10 O'CLOCK HIGH POS WHICH PREVENTED ME FROM CLBING MUCH ABOVE 7500 FT. IN THE MEANTIME; THE RA WAS CLOSING ON US FROM BELOW AND CAME WITHIN 100 FT OF MY ACFT AS I WAS PASSING THROUGH 7200 FT. THE ODD THING IS THAT THE RA DISAPPEARED AT THIS POINT NEVER TO BE SEEN AGAIN. ATL DID NOT SEE THE RA 'TARGET;' NOR DID THEY KNOW ABOUT THE ACFT AT THE 10 O'CLOCK POS. IN ADDITION; THE 10 O'CLOCK POS ACFT WAS NOT ON OUR TCAS. WE WERE FORTUNATE TO HAVE VISUALLY SPOTTED THIS ACFT IN TIME SO WE DIDN'T CREATE A COLLISION HAZARD DURING THE CLB ESCAPE MANEUVER.