MD80 CREW HAD AN NMAC WITH A SINGLE ENG CESSNA DEPARTING LGB IN SCT CLASS C AIRSPACE.

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NMAC WITH SINGLE ENG CESSNA. ON DEP FROM LGB; WE HAD MADE OUR INITIAL TURN TO A HDG OF 180 DEGS AND WERE CLBING THROUGH 3000 FT MSL WHEN AT APPROX THE SAME TIME ATC CALLED TFC AND WE RECEIVED A TCASII ALERT. THE ACFT WAS INSIDE THE 2.5 MI RANGE ON THE TCASII DISPLAY. I ACQUIRED THE ACFT VISUALLY AT ABOUT THE SAME TIME THAT WE RECEIVED A TCASII RA. THE AURAL WARNING INSTRUCTED US TO DSND; WHICH DID NOT CORRESPOND TO WHAT I WAS SEEING OUT THE WINDOW. THE CESSNA HAD NOSED OVER INTO A RAPID DSCNT AND WAS GOING TO PASS JUST BELOW THE NOSE BY MAYBE 300 FT IN VERT SEPARATION AND APPROX 300 FT IN LATERAL SEPARATION. THE CAPT; WHO WAS THE PF; DID NOT HAVE THE ACFT VISUALLY AND THEREFORE FOLLOWED THE RA. WHEN I TOLD HIM TO KEEP CLBING; WE BOTH BECAME CONFUSED BECAUSE THE RA/VSI WAS INDICATING THAT WE SHOULD DSND (GREEN BAND) BTWN 0-200 FPM. THE RED BAND WAS FROM 300 FT TO APPROX 2000 FPM DOWN. THERE WAS NO GREEN BAND ABOVE THE 0 VSI MARK. BOTH OF US THOUGHT THAT THERE MUST BE ANOTHER ACFT CAUSING THE RA AND BEGAN TO SEARCH VISUALLY. I BELIEVE THAT I TOLD HIM AT THIS POINT THAT THE ACFT PASSING UNDER OUR NOSE MUST HAVE CAUSED THE RA; AT WHICH POINT HE POINTED TO THE RA/VSI AND TOLD ME TO LOOK AT IT. THERE ARE 2 DISCONCERTING POINTS TO THIS RPT: THE FIRST BEING THE LACK OF SEPARATION PROVIDED BY ATC; AND THE SECOND BEING THE IMPROPER PROMPTS ISSUED BY THE TCASII SYS. LGB APPEARED TO BE A VERY BUSY GA ARPT WITH MANY SINGLE ENG ACFT EXECUTING TOUCH-AND-GOES ON SEVERAL DIFFERENT RWYS AT ONCE. IN MY OPINION; THIS IS A RECIPE FOR DISASTER UNLESS BETTER VERT SEPARATION CAN BE MAINTAINED BY ATC. AS FAR AS THE TCASII PROB; I CAN ONLY ASSUME THAT BECAUSE WE WERE CLBING AND THE OTHER ACFT WAS DSNDING; THAT THE LOGIC IN THE TCASII SYS COULD NOT KEEP UP WITH THE CHANGES THAT BOTH ACFT WERE MAKING VERTLY AND THEREFORE ISSUED IMPROPER PROMPTS. THE RESULT OF FOLLOWING THE IMPROPER PROMPTS PLACED US IN MUCH CLOSER PROX TO THE CESSNA THAT WE SHOULD HAVE BEEN.