A320 CREW HAD AN NMAC WITH A SINGLE ENG CESSNA WHILE APCHING RWY 30 AT LGB.

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FLYING UNDER IFR; ON AN RNAV (GPS) APCH TO LGB RWY 30; WE WERE ON LGB TWR FREQ AND HAD BEEN CLRED TO LAND ON RWY 30. AS WE APCHED XING THE BECCA OM AT ABOUT 1600 FT AGL; WHILE DSNDING ON THE APCH WE GOT A POP-UP TCASII TA AT -300 FT BELOW US; AND JUST IN FRONT L OFF OUR NOSE. FO WAS FLYING. WE LOOKED FOR THE TFC AND DID NOT SEE ANY. I INSTRUCTED FO TO DISCONNECT THE AUTOPLT; AND HE DID; AND WE CONTINUED THE APCH; STILL LOOKING FOR THE TFC. NEXT TCASII SHOWED THE TFC AT -100 FT BELOW US; AND JUST IN FRONT OF OUR NOSE APPROX 1/4 MI AWAY. WE STILL DID NOT SEE ANY TFC. IT APPEARED TO ME; THAT BASED ON THE TCASII TA; AND OUR SHALLOW DSCNT RATE AND THE CLOSE PROX OF THE TFC DISPLAYED; THAT IF WE CONTINUED ON OUR APCH PATH; THAT WE WOULD HAVE A MIDAIR COLLISION. THEREFORE; I TOLD THE FO TO LEVELOFF; AND HE DID. A SECOND OR TWO LATER WE GOT A TCASII RA; AND THE FO DID NOT RESPOND. WITHIN A SECOND OR TWO I TOOK CTL OF THE JET AND PERFORMED THE RA CLB; CLB NOW; ESCAPE MANEUVER AS DIRECTED BY TCASII. ACCORDING TO TCASII WE MISSED THE TFC BY NO MORE THAN 100 FT. I NEVER SAW ANY TFC. I NEVER HEARD ANY TA'S FROM TWR. ONE DAY AFTER THE EVENT; THE LGB TWR SUPVR RPTED WE DID HAVE A TFC CONFLICT WITH A CESSNA. THE SUPVR SAID THE TWR TAPES RECORDED THE TWR CTLR RPTED TO US: 'TFC 11 O'CLOCK POS; 2 MI; ON THE DOWNWIND; A CESSNA...YOUR FLT IMMEDIATELY ADVISED YOU WERE GOING AROUND.' THE CTLR THEN ISSUED A SECOND TFC CALL AS YOU WERE EXECUTING THE MISSED APCH OF 'TFC MOVING TO 12 O'CLOCK POS; 1 MI.' I NEVER HEARD ANY TA'S FROM TWR. WHEN I CHKED ON TO TWR ORIGINALLY; WE WERE CLRED TO LAND. NEXT; WITHIN A FEW SECONDS WE GOT THE POP-UP TCASII TA. IF TA'S WERE MADE; WE MUST HAVE MISSED THEM; DUE TO OUR TA AND RA ALERTS GOING OFF. TO CONCLUDE; I BELIEVE OUR FLT (WHICH WAS ON IFR APCH) SHOULD NOT HAVE BEEN ISSUED A LNDG CLRNC UPON INITIAL TWR CONTACT. WE SHOULD HAVE BEEN ISSUED A TA; AND TOLD TO 'CONTINUE' THE APCH TO RWY 30. THE VFR CESSNA APPEARS TO HAVE DRIFTED WELL S OF THE L DOWNWIND PATTERN FOR RWY 25L; AND HE SHOULD HAVE ORDERED OUT OF THE PATTERN BY ATC; WELL PRIOR TO XING THE IFR APCHING TFC (ME) FOR RWY 30. EITHER MY FLT OR THE VFR CESSNA SHOULD NOT HAVE BEEN ALLOWED TO PROCEED AS WE WERE ALLOWED TO; WHICH LED TO A NEAR MIDAIR COLLISION. THE LGB TWR CTLRS MUST NEVER ALLOW A VFR AND AN IFR ACFT TO CROSS EACH OTHERS PATH IN THE CTL ZONE. I BELIEVE SUCH A RESTR SHOULD BE PUT IN FORCE IMMEDIATELY AT LGB; SO AS TO PREVENT A FUTURE MIDAIR COLLISION THERE. SUPPLEMENTAL INFO FROM ACN 631153: THE CAPT WANTED ME TO LEVEL OFF AND DISCONNECT AUTOPLT. I SAW AN AIRPLANE 12-12:30 O'CLOCK POS; A LITTLE LOWER APPROX 1100-1200 FT. IT WAS ON L DOWNWIND RWY 25L. I SAID I THINK THAT IS THE TFC. BECAUSE OF CLOSURE BTWN US AND THE CESSNA; THOUGH IT WAS ACTUALLY DIVERGING; WE GOT AN RA. THE CAPT NEVER ACKNOWLEDGED THE TFC I SPOTTED. THERE IS NO WAY LGB TWR WOULD HAVE OPPOSITE DIRECTION TFC ON OUR GPS FINAL APCH COURSE. REGARDLESS; BECAUSE OF RA THE CAPT SAID HE HAD FLT CTLS AND EXECUTED GAR. WE EXCHANGED DUTIES THEN AND THERE; AND RETURNED AFTER HDOF TO SOCAL APCH AND RADAR VECTORS FOR ANOTHER GPS APCH. THE CAPT RETURNED CTL AFTER CLEAN-UP. HE DID THIS NOT BECAUSE OF MY ABILITIES OR ACTIONS. HE JUST DID IT HIMSELF AS MY FO'S COMPLAIN OF HIS MICRO MGMNT OF EACH CREW MEMBER. WE RETURNED AND LANDED UNEVENTFUL. THE TFC TURNS OUT TO BE THE CESSNA I SAW ON DOWNWIND. THE LEVELOFF AND AUTOPLT DISCONNECT BY THE CAPT EXACERBATED THE POTENTIAL FOR A CONFLICT. HAD WE CONTINUED ON THE GLIDE PATH WE WOULDN'T HAVE HAD THE RA. THE TA'S ON THE APCH ARE QUITE NORMAL AND NEVER HAVE LED TO AN RA AS WE ARE DIVERGING VERTLY. THE CAPT SAID HE DIDN'T HEAR ME POINT OUT THE TFC. THE NOISE OF DISCONNECTING THE AUTOPLT AND TCASII DISTR THE TA BY LGB TWR TO BOTH CAPT AND FO. I FEEL THE CAPT SHOULD HAVE LET ME FLY THE AIRPLANE AS PLANNED AND NOT MICRO-MANAGE AS HE DID. THIS LED TO HIM CALLING FOR AUTOPLT OFF AND THE RESULTING DISTRS AND INDUCED CLOSURE FOR THE TCASII AND MISSED TWR TA'S. IT IS READILY APPARENT WHEN RWY 25L L-HAND TFC CROSSES AHEAD AT 1000 FT AGL WHILE ON APCH TO RWY 30. WE GENERALLY PASS UNDER 500 FT BELOW AND DIVERGING FROM RWY 25L/R TFC.