INADVERTENTLY USING A ONE HALF BANK TURN WHICH GAVE A WIDER TURN THAN EXPECTED; A GULFSTREAM CREW LOSES SEPARATION FROM TFC UNDER ARTCC CTL.

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WE TOOK OFF FROM FXE AT XA30. THE NORMAL CLRNC IS FT LAUDERDALE 9; THNDR TRANSITION AS FILED; CLB AND MAINTAIN 2000 FT. THE USUAL HDG AFTER TKOF IS 330 DEGS. BOTH SHORT RANGE NAVS (VORS) WERE SET UP FOR THE 335 DEG RADIAL OFF OF DHP VOR. I (THE PF) WAS IN THE L SEAT AND THE CAPT (PNF) WAS IN THE R. AFTER TKOF; WE WERE ASSIGNED A 330 DEG HDG. MIA DEP SAID TO CLB AND MAINTAIN 16000 FT. I TURNED THE AUTOPLT ON AT ABOUT 8000 FT. DEP THEN SAID FLY A 270 DEG HDG TO INTERCEPT THE THNDR TRANSITION. I SELECTED 1/2 BANK FOR PAX COMFORT. AS SOON AS THE LNAV CAPTURED; IT TURNED THE 1/2 BANK OFF. THE CAPT (WHO WAS THE PNF) ASKED IF I WANTED THE FMS (BLUE) DATA. HE ENTERED IT INTO HIS FMS AND XFERRED IT TO MY FMS. I LOOKED AT IT AND THEN SELECTED THE LNAV TO ARM THE INTERCEPT FOR THNDR. WE LEVELED AT 16000 FT. THEN MIA DEP TOLD US TO FLY A 240 DEG HDG FOR TFC. A FREQ SWITCH TO ZMA. THEY TOLD US TO FLY A 290 DEG HDG TO INTERCEPT THNDR AGAIN. I TURNED THE HDG BUG AND ENGAGED LNAV AGAIN. ONCE ON THE 290 DEG HDG; I REACHED INTO MY POCKET TO GET A THROAT LOZENGE FOR I HAD A SORE THROAT. AS I WAS UNWRAPPING THE LOZENGE; MIAMI TOLD US TO FLY A 340 DEG HDG. I ASKED THE CAPT IF HE COULD TURN THE ACFT. HE DESELECTED LNAV AND SELECTED HDG. THE 1/2 BANK WAS STILL ON. I POPPED THE LOZENGES INTO MY MOUTH AND TOOK THE ACFT BACK FROM HIM. MIAMI CLRED US TO FL230 AND TOLD US TO EXPEDITE THE CLB THROUGH 17000 FT. I WAS CLBING AT 2300 FPM. MIAMI POINTED OUT TFC AT 10 O'CLOCK POS AND 6 MI. WE BOTH LOOKED BUT DID NOT HAVE A VISUAL ON THE TFC. WE DID SEE HIM ON TCASII AT ABOUT 5 MI. WE SAW A SOLID DIAMOND BUT NO RA. BY MY ESTIMATION; THE TFC GOT WITHIN ABOUT 4.5 MI FROM US. BOTH THE CAPT AND I LOOKED TO SEE IF WE WERE OFF COURSE. I HAD FMS DATA SELECTED WITH A BEARING POINTER ON THE DHP VOR AND THE CAPT HAD SHORT RANGE DHP VOR ON HIS SIDE. WE LOOKED AT BOTH THE NEEDLES AND THEY SEEMED TO MATCH THE 335 DEG BEARING TO THNDR. ZMA TOLD US TO CALL THEM WHEN WE LANDED. AFTER WE CALLED MIAMI ON THE GND; THEY SAID WE WERE 4.4 MI AND 400 FT FROM THE OTHER TFC WHO WAS ON A DEP OUT OF MIAMI. ALSO; WE WERE 4 MI OFF COURSE. BOTH I AND THE CAPT TALKED ABOUT IT AND WE MAY HAVE HAD THE WRONG RADIAL IN THE FMS. IN REFLECTION; I THINK THE USE OF 1/2 BANK SHOULD ONLY BE USED ABOVE FL180. VIGILANCE FOR THE SAME DEP THAT IS FLOWN DAY IN AND DAY OUT IS VERY IMPORTANT. ALWAYS DOUBLECHK THE OTHER PLT -- EVEN AN EXPERIENCED ONE. ALSO; SINCE THE GIV IS HIGHLY AUTOMATED; THE USE OF SHORT RANGE NAV SHOULD BE USED UNTIL YOU HAVE CAPTURED THE COURSE.