ACR X DSCNT THROUGH OCCUPIED ALT HAD LTSS FROM SMT Y. SYS ERROR.

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ACR X ENTERED MY AIRSPACE FROM 30 MI N AT 12000 FT. I ALSO HAD AN SMT Y OVERFLYING AUSTIN 30 MI N; SWBOUND AT 10000 FT. I ASSIGNED ACR X 11000 FT AND A HDG OF 110 DEGS. THE NORMAL HDG ASSIGNMENT SHOULD HAVE BEEN 190 DEGS; BUT I HAD '110' ON MY MIND. I ASSIGNED A HDG OF 190 DEGS TO THE SMT Y AND TOLD HIM TFC WOULD BE AN ACR X '3 O'CLOCK AND 5 MI DSNDING THROUGH YOUR ALT.' I DSNDED ACR X TO 3000 FT AND ISSUED TFC 'AN SMT Y; 9 O'CLOCK AND 5 MI LEVEL AT 10000 FT;' ASSUMING I HAD ALSO GIVEN HIM A HDG OF 190 DEGS INSTEAD OF THE NOW CONVERGING HDG OF 110 DEGS. ACR X ACKNOWLEDGED THE DSCNT AND 'QUESTIONINGLY' REPEATED THE HDG 190. I REALIZED ACR X HAD TURNED EBOUND TOWARD SMT Y AND SO I TURNED HIM FURTHER TO A 210 DEG HDG AND ASSIGNED HIM 11000 FT. ACR X ONLY ACKNOWLEDGED THE NEW HDG; NOT THE ALT; 11000 FT. I RE-ISSUED TFC TO THE SMT Y. 'ACR X 2 MI NW OF YOU; STOPPED AT 11000.' I THOUGHT I HAD SAVED THE SIT. I THEN ASKED ACR X IF HE HAD SIMPLY MISUNDERSTOOD MY FIRST XMISSION. HE RESPONDED AND ENDED WITH 'WE WERE STILL CLRED TO 3000 FT; CORRECT?' I SAID; 'AFFIRMATIVE; WHEN YOU WERE ON A 190 DEG HDG.' UNFORTUNATELY; HE WAS ASKING IN THE PRESENT AND I WAS RESPONDING TO A SIT RECENTLY PASSED. ACR X SAID; 'OK; WE'RE TURNING BACK L HDG 190 DEGS; DOWN TO 3000 FT.' I SAID; 'NEGATIVE; NEGATIVE; MAINTAIN 11000 FT HDG 210 DEGS; YOU'RE HDG RIGHT FOR THE TFC I JUST ISSUED YOU.' IT WAS A COMEDY OF MISCOM. VERT AND LATERAL SEPARATION WAS REDUCED TO 800 FT AND 2.2 MI. ACR X WAS TCASII EQUIPPED AND I WONDER WHY THE EQUIP DIDN'T ALERT THE PLT TO THE SMT Y. SUPPLEMENTAL INFO FROM ACN 253502: AFTER CONTACTING APCH CTL; WE WERE GIVEN A HDG OF 090 DEGS AND A DSCNT TO 3000 FT. THERE WERE SEVERAL BLOCKED RADIO CALLS AND THEN A SOMEWHAT URGENT CALL TELLING US TO TURN TO 190 DEGS AND THEN FURTHER R TO 210 DEGS. WE WERE THEN TOLD TO EXPECT LOWER SHORTLY. SINCE WE WERE STILL ABOVE 10000 CLRED TO 3000; THIS CALL PROMPTED US TO RECONFIRM OUR DSCNT TO 3000. WE WERE THEN GIVEN 5000 FT. AFTER LNDG WE WERE TOLD TO CONTACT APCH BY TELEPHONE. OVER THE PHONE WE WERE TOLD THAT THE CTLR STATED HE NEVER GAVE US A TURN TO 090 DEGS AND THAT WE HAD A CONFLICT WITH ANOTHER ACFT. WE WERE TOTALLY UNAWARE OF THE CONFLICT WITH THE OTHER ACFT SINCE WE WERE NEVER GIVEN ANY TFC CALLS. I SUSPECT THERE WAS A MISCOM THAT TOOK TOO LONG TO CORRECT; BECAUSE OF BLOCKED RADIO CALLS.