ZTL CTLR EXPERIENCED OPERROR AT APPROX FL280 WHEN FAILING TO SEPARATE OPPOSITE DIRECTION TFC COMPLICATED BY ONE TCAS AND ONE NON TCAS ACFT.

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THE B737 WAS A DEP FROM RDU. HE WAS CLBING OUT OF ABOUT FL280; WHEN HE WAS GIVEN A CLRNC TO DEVIATE L AND TO FLM WHEN ABLE. HE WAS CLBING TO FL340 AT ABOUT 1200-1500 FPM. THE LEARJET WAS OPPOSITE DIRECTION AND LNDG GRAND STRAND; SC. EVEN THOUGH I KNEW THE POTENTIAL CONFLICT WAS GOING TO OCCUR IF THE B737 DEVIATED FAR ENOUGH W; I KNEW THAT I COULD SWAP THE LEARJET AND THE B737 IN TIME VERTICALLY. I WAS VERY BUSY WITH OTHER ACFT AND PROBABLY SHOULD HAVE APPLIED MORE POSITIVE SEPARATION TO THE SITUATION BY STOPPING THE CLB OF THE B737 AND THE DSCNT OF THE LEARJET. WHEN I EXPEDITED THE LR35 THROUGH FL310 FOR THE B737 I HAD ENOUGH LATERAL DISTANCE TO ACCOMPLISH A VERT SWAP (ACFT WERE HEAD-ON AT ABOUT 15 DME) BUT THE B737 HAD ALREADY DECREASED HIS CLB IN RESPONSE TO HIS TCAS; AND INFORMED ME THAT HE WAS NOW DSNDING. REALIZING THAT VERT WOULD NOT BE ACHIEVED I SIMULTANEOUSLY TURNED BOTH ACFT 30 DEGS R. THE B737 WAS UNABLE TO TURN (DUE TO HIS RATE OF DSCNT) THE NON TCAS EQUIPPED LR35 EXECUTED MY TURN AND 2 MI AND 100 FT VERT WAS ACHIEVED. THE B737; IN HIS MANEUVER WAS ABLE TO ACQUIRE THE LR35 VISUALLY AS THEY PASSED. IN MY OPINION; TCAS/NON-TCAS COMBINATIONS HAVE A GREAT POTENTIAL FOR CTLR-AIDED DISASTERS WHEN THE FREQ IS TOO BUSY/OR PLTS FAIL TO ADVISE OF DEVS IN RESPONSE TO TCAS COMMANDS IN A TIMELY MANNER.