PCT CTLR DESCRIBED CONFLICT EVENT WHEN UTILIZING DIVERGING SEPARATION RULE; LAST MINUTE CTLR INTERVENTION WAS REQUIRED TO SAVE SEPARATION.

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LJ35 WAS ON AN OVERFLT OF MY SECTOR AT 9000 FT MSL NW TO SE. P180 WAS HANDED OFF BY THE CTR AT 10000 FT MSL ON THE COATT4 ARR; SW TO NE. I DETERMINED THAT ALTHOUGH THE ACFT WERE ON CONVERGING COURSES A DSCNT WAS POSSIBLE BECAUSE THE DIVERGING COURSE RULE WOULD APPLY AS SOON AS THE LJ35 CROSSED THE PATH OF THE P180. THUS I INSTRUCTED ZDC TO DSND THE P180 TO 6000 FT MSL AND SWITCH HIM TO ME. THE P180 CHKED IN AND I ACKNOWLEDGED WITH THE RICHMOND ALTIMETER. NO TFC WAS ISSUED AT THIS TIME. I WAS VERY BUSY AT THE TIME AND FALLING BEHIND IN MY WORK. ILLNESS WAS A FACTOR. I DEALT WITH SEVERAL OTHER ISSUES AND RETURNED MY ATTN TO THE P180 TO AFFECT A HDOF TO THE NEXT SECTOR. AT THAT TIME I SAW THAT ALTHOUGH THE DIVERGENCE RULE HAD WORKED THE ACFT WERE IN VERY CLOSE PROX. I INSTRUCTED THE LJ35 TO TURN L IMMEDIATELY FOR TFC. HIS RESPONSE WAS WE HAVE THE TFC AND ARE MAINTAINING VISUAL SEPARATION. NO EVASIVE MANEUVERS WERE TAKEN BY EITHER ACFT. I ASKED IF EITHER ACFT HAD A PROB AND THEY BOTH REPLIED NEGATIVE. I ADVISED THAT IT WAS CLOSER THAN I LIKE BUT NO HARM NO FOUL. I THEN INFORMED MY SUPVR THAT I NEEDED TO BE RELIEVED FROM POS AS I WAS NOT ABLE TO KEEP UP WITH THE WORKLOAD AND WAS MAKING MISTAKES. HE HAD ME RELIEVED AND I ADVISED HIM OF THE SITUATION WITH THE LJ35 AND THE P180. I FULLY DESCRIBED THE TFC SITUATION AND THE RULES THAT I HAD APPLIED. MY LAST STATEMENT TO HIM WAS; THE 15 DEG DIVERGENCE RULE AND NO MERGING TARGET RULE MAY BE LEGAL; BUT I WAS GOING TO REFRAIN FROM USING IT IN THE FUTURE BECAUSE IT CAN ALLOW ACFT TO GET SCARY CLOSE. THE SUPVR AGREED WITH THAT ASSESSMENT. NO FURTHER ACTION TAKEN AT THIS TIME.