DAY TRACON CTLR EXPERIENCED LOSS OF SEPARATION WITH CLBING B767 AND PA28 OVER FLT AT APPROX 3000 FT BECAUSE OF A READBACK WITHOUT USE OF A CALL SIGN.

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WHILE WORKING THE S ARR/DEP POS; ACFT X; A B767; DEPARTED ILN CLBING TO 3000 FT. I RADAR IDENTED HIM AND ISSUED TFC ON A PA28 OVERFLT AT 4000 FT AT HIS 2 O'CLOCK POS; AND 4 MI XING HIS FLT PATH; AND TOLD HIM TO EXPECT HIGHER PASSING THE TFC. TFC WAS ALSO ISSUED TO THE PA28. ACFT Z; ANOTHER B767; THAT DEPARTED ILN PRIOR TO ACFT X; WAS ALSO ON FREQ LEVEL AT 8000 FT AND AWAITING CLB TO 10000 FT. I XMITTED TO ACFT Z TO CLB AND MAINTAIN 10000 FT AND CONTACT CTR. I RECEIVED A READBACK ACKNOWLEDGING THE CLB AND FREQ CHANGE. I THEN ANSWERED A LANDLINE AND WHILE ON THE LINE; HEARD ACFT Z ASK IF THAT XMISSION WAS FOR HIM. I IMMEDIATELY CAME OFF THE LANDLINE AND XMITTED FOR ACFT X TO MAINTAIN 3000 FT AND THAT XMISSION WAS NOT FOR HIM. I THEN REISSUED THE TFC TO THE PA28 WHO ADVISED THE H/B767 IN SIGHT AND WAS INSTRUCTED TO MAINTAIN VISUAL SEPARATION. ACFT X HAD ALREADY SWITCHED TO CTR. THE CTR CTLR ADVISED HIM TO RETURN TO APCH FREQ AND THE CTR CTLR ALSO ADVISED THAT HE HAD A TA. I TOLD HIM I THOUGHT HE HAD TAKEN INSTRUCTIONS FOR ANOTHER ACFT. HE STATED THAT BOTH HE AND THE OTHER PLT THOUGHT THE CALL WAS FOR THEM. AT THE TIME; I WASN'T SURE IF I HAD USED THE WRONG CALL SIGN OR NOT. AFTER LISTENING TO THE TAPE; THE PROPER CALL SIGN ACFT Z WAS USED; BUT IN THE HEAT OF THE BATTLE; I DIDN'T NOTICE THAT THE READBACK DID NOT INCLUDE THE USE OF ANY CALL SIGN; AND I ASSUMED IT WAS FROM ACFT Z UNTIL ACFT Z CALLED BACK FOR CONFIRMATION. I WAS LUCKY TO HEAR THIS SINCE I WAS ON A LANDLINE TRYING TO LISTEN TO ANOTHER CTLR. A COUPLE THINGS I FEEL I COULD'VE DONE TO POSSIBLY AVOID THIS: 1) ENSURE OR CONFIRM THAT THE CORRECT ACFT ACKNOWLEDGES USING A CALL SIGN IF NONE IS USED IN A READBACK OF CRITICAL INSTRUCTIONS AND; 2) USE CAUTION WHEN ISSUING AN ALT CHANGE AND FREQ CHANGE IN SAME XMISSION. AS FAR AS THE FLT CREW; IF THE PLTS WOULD'VE USED THEIR CALL SIGN WHEN READING BACK THE CLRNC; IT WOULD'VE GIVEN ME A CHANCE TO CATCH AND CORRECT THE ERROR. ALSO; THE PLT; WITH THE VERBAL PICTURE AND INFO ON THE TFC ALONG WITH TCASII INFO IN THE COCKPIT; COULD'VE AND SHOULD'VE QUESTIONED THE CLB THROUGH TFC THAT WAS NEVER CALLED IN SIGHT BY HIM OR ADVISED NO LONGER A FACTOR BY ME. THANK GOODNESS IT WAS VMC.