LR24 FLC IS ISSUED DSCNT CLRNC AND TFC INFO. LR24 ENCOUNTERS AN NMAC WITH AN UNCTLED BE60. LR24 PIC STATES THAT ATC SHOULD HAVE PROVIDED SOME TYPE OF POSITIVE SEPARATION.

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CPR FLT FROM MBS TO 55J (FERNANDINA BEACH ARPT; FL). OUR FLT WAS BEING CTLED BY JAX APCH. WE HAD JUST CROSSED SSI ARPT AT 9000 FT; BEING VECTORED TO OUR DEST ARPT; FERNANDINA BEACH; WE WERE TOLD TO DSND FROM 9000 FT TO 4000 FT AND THAT WE HAD TFC 12 O'CLOCK POS; 3 MI; BELOW US. WE LOOKED FOR THE TFC; NO CONTACT. PASSING THROUGH 8000 FT; WE WERE RECLRED TO LEVEL OFF AT 7000 FT. THE CLRNC WAS ACKNOWLEDGED AND WE LEVELED OFF AT 7000 FT. TO OUR SURPRISE; AN AIRPLANE PASSED RIGHT ABOVE US. THE ONLY THING I SAW FROM THE CORNER OF MY EYE WAS THE BOTTOM SIDE OF THE AIRPLANE AND ELEVATORS. MY QUESTION TO (MY COPLT) WAS; WHAT WAS THAT? HIS ANSWER WAS WE JUST MISSED A BEECH DUKE. JAX APCH WAS ADVISED OF THE NEAR MISS. JAX APCH ACKNOWLEDGED OUR CALL; AS IF NOTHING HAPPENED; AND THEN CLRED US TO DSND TO 4000 FT; SAYING WE WERE CLR OF TFC. I REPLIED THAT THIS TA AND WARNING WAS TOTALLY UNACCEPTABLE. THE RESPONSE WAS THEY WERE NOT TALKING TO THAT TFC; AND ASKED IF WE WERE ALL RIGHT. I WONDER WHY THE CTLR DID NOT VECTOR US AWAY FROM THE TFC. THE TFC WAS SAID TO BE BELOW OUR ALT; THAT WAS THE REASON FOR STOPPING OUR DSCNT TO 4000 FT. I FEEL THE CTLR WAS NOT MONITORING; THE TFC; AS THE DUKE WAS REALLY CLBING. WHAT I LEARNED FROM THE EXPERIENCE IS WHEN I AM UNABLE TO SEE THE TFC I WILL ASK FOR VECTORS FOR TFC AVOIDANCE.