NMAC BETWEEN ACR-MDT ON APCH AND GA-SMA IN PATTERN.

Narrative

AFTER BEING CLRED FOR THE VOR 27 APCH INTO OSH; CHICAGO CENTER HANDED US OFF TO OSH TWR. AT THIS POINT ON OUR FLT WE WERE IN IMC CONDITIONS AT 2800' MSL 8 DME E OF OSH VOR ON THE CENTERLINE OF THE VOR 27 APCH. IN RESPONSE TO OUR INITIAL CALL THE OSH TWR CLRED US TO LAND AND ADVISED US OF A VFR SMA E OF THE ARPT; EBND; AND THAT THE SMA WAS TOLD TO STAY WELL CLR OF THE APCH COURSE. IN RESPONSE TO THAT INFO I DOUBLE CHKED THAT ALL OF OUR ANTICOLLISION; LNDG AND TAXI LIGHTS WERE ON. SHORTLY AFTER BREAKING OUT OF THE CLOUDS THE F/O STATED HE HAD THE SMA AND BEGAN A HARD LEFT TURN TO AVOID THE OTHER PLANE. AT THAT POINT I SAW THE OTHER ACFT COMING AT US IN A LEFT BANK; TRYING TO AVOID US. AFTER PASSING THE SMA WE CONTINUED THE APCH AND LANDED NORMALLY. THE PROB AROSE DUE TO THE MIXING OF IFR AND VFR TFC IN MARGINAL VFR CONDITIONS. LISTENING TO THE OTHER PLT ON THE RADIO SHE SOUNDED INEXPERIENCED AND CONFUSED. SO; EVEN THOUGH SHE WAS TOLD TO STAY CLR OF THE APCH COURSE; I CAN'T HELP BUT WONDER IF SHE EVEN KNEW WHAT AND WHERE THAT WAS. OSH TWR IS ONLY A VFR FAC AND THEREFORE HAS LIMITED CAPABILITIES; BUT GIVING A SUGGESTED HDG FOR A GIVEN DISTANCE TO ENSURE SEP COULD HAVE AVOIDED THE WHOLE SITUATION. IF THE SMA HAD MAINTAINED 500' BELOW THE CEILING; WE WOULD HAVE HAD MORE TIME TO SEE AND AVOID.