OPERROR BTWN UGA X AND ACR Y.

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AT THE ABOVE TIME I WAS WORKING THE APE HIGH RADAR POS TFC WAS BUILDING AND GETTING VERY COMPLEX. (THE PIT ARR PUSH WAS IN PROGRESS AND I WAS GETTING NO HELP FROM ADJACENT SECTORS OR TMU RELEASES. THE JETS WERE HIGH; FAST; AND SIDE BY SIDE. I AM REQUIRED TO PROVIDE 20 MI IN TRAIL TO THE NEXT LOW ALT CTLR ON THIS TFC. THIS MEANT VECTORING ACFT ALL OVER SECTOR. UGA X; A KING AIR; CHKED ON FREQ AT FL280 VIA HVQ APE VWV TOL AND WAS TURNED 15 DEGS L TO AVOID PIT ARR TFC AREA. UGA X WAS THEN CLRED DIRECT UWV AND DSNDED TO FL260. ACR Y CHKED ON FREQ LEAVING FL230 FOR FL250. AS SOON AS UGA X CLRED AN OVERFLT AT FL250; I CLRED UGA X TO FL240. ACR Y WAS TOLD TO REDUCE TO 250 KTS FOR SPACING. TRACKER ADVISED ME OF CONFLICT BTWN UGA X AND ACR Y. I THEN CLRED ACR Y TO EXPEDITE DSCNT TO FL240. UGA X 6 WAS RECLRED TO MAINTAIN FL250; ACFT ADVISED 'STOPPING AT FL250.' ACR Y WAS THEN TURNED TO A HDG OF 180 DEGS NO READBACK OF THIS CLRNC. ACR Y ADVISED OF RA AND CLBING. I THEN VERIFIED THAT ACR Y WAS CLBING AND ISSUED THE KING AIR TFC TO HIM. UGA X WAS RECLRED TO FL240. UPON RECEIVING; THE RA; ACR Y CLBED FROM FL250 TO FL255 IN 1 RADAR UPDATE. IN MY OPINION IF HIS DSCNT WAS THIS GOOD OR THE TURN TAKEN THIS SIT WOULD NOT HAVE BEEN AS BAD OR MIGHT NOT HAVE HAPPENED. SUPPLEMENTAL INFO FROM ACN 281766: AT FL250; ZID ON 132.82 CLRED US TO FL240 AND SAID TO HURRY DOWN. AS WE STARTED TO DSND WE RECEIVED A TCASII RA TO CLB AT 2000 FPM. WE STARTED THE CLB; ADVISED ATC AND AT FL260 WERE CLR OF CONFLICT. ATC THEN TOLD US TO JUST MAINTAIN FL260. SUPPLEMENTAL INFO FROM ACN 282038: ACR Y ORIGINALLY DSNDED TO FL248; MAINTAINED IT; THEN RESPONDED TO THE RA AND CLBED TO FL260. ACR Y NEVER TURNED OR ATTEMPTED TO GET TO FL240. DO NOT KNOW WHEN THE TCASII RA HAPPENED BUT IT TURNED THE SIT INTO A LOSS OF SEPARATION A LOT CLOSER THAN WHAT IT ORIGINALLY WOULD HAVE BEEN.