ZME CTLR'S EXPERIENCE LOSS OF SEPARATION AT FL310; BTWN 2 ACR'S ON VECTORS.

Narrative

I WAS WORKING WITH SEVERAL ACFT ON FREQ; MANY OF WHOM ARE COMPLAINING OF CHOP. ACFT X WAS SWBOUND ON J-29; ABOUT 45 MI SW OF PXV. ACFT Y WAS NNWBOUND TO ALO; ABOUT 70 MI SSW OF PXV. ACFT X HAD BEEN HANDED OFF TO R-26 WHO CALLED AND REQUESTED CTL FOR A L TURN. AFTER MY TFC SEARCH; IT APPEARED TO ME THERE WERE NO POTENTIAL CONFLICTIONS; SO I RELEASED ACFT X FOR TURNS. WHEN I NOTICED THE SIT; I TURNED ACFT Y TO A 030 DEG HDG. THEY PASSED 4.6 MI APART. SUPPLEMENTAL INFO FROM ACN 611041: THE SECTOR WAS BUSY WITH BAD RIDES DUE TO CHOP. I WAS MAKING A POINT OUT TO FARMINGTON. SECTOR K-14 WHEN THE R-63 CTLR RELEASED ACFT X FOR A L TURN. I DID NOT HEAR THIS DUE TO BEING ON A LANDLINE MAKING A POINTOUT TO K-14 (FARMINGTON). I DID NOT SEE THE DEVELOPING SIT UNTIL THE CONFLICT ALERT ACTIVATED. WHEN THE CONFLICT ALERT ACTIVATED; R-63 TOOK APPROPRIATE ACTION AND TURNED ACFT X R TO A HDG OF 030 DEGS. SUPPLEMENTAL INFO FROM ACN 611042: REQUESTED CTL OF ACFT X. TURNED ACFT X TO A 190 DEG HDG. A FEW MINS LATER; THE CONFLICT ALERT WENT OFF. I TURNED THE ACFT 20 DEGS L AND DSNDED ACFT TO FL280.