A B737 CAPT RPTED AN NMAC DURING CLBOUT FROM LGB.

Narrative

WE TOOK OFF FROM LGB RWY 30; CLRED TO CLB TO 1500 FT; L TURN TO HDG 180 DEGS; THEN CONTINUE CLB TO 3000 FT. IT WAS THE FO'S LEG. AFTER TURNING TO 180 DEGS; WE WERE SWITCHED TO DEP CTL. THEY CLRED US TO 4000 FT. AT SOME POINT AFTER PASSING AROUND 2500 FT; WE GOT A TA FOR SOME TFC AT APPROX 1230 O'CLOCK AND 800 FT ABOVE US. I TOLD THE FO TO EXPECT AN RA; AND WE IMMEDIATELY GOT ONE; FIRST TO 'MONITOR VERT SPD;' WHICH ALMOST IMMEDIATELY CHANGED TO 'DSND; DSND NOW.' THE RA CALLED FOR A LARGE PITCH CHANGE FROM OUR CLB RATE OF MORE THAN 2000 FPM TO A LARGE RATE OF DSCNT. AS OUR VERT SEPARATION CLOSED TO 100 FT; MY FO SPOTTED THE TFC AT ABOUT 1 O'CLOCK POS. WE HAD STOPPED OUR CLB AND STARTED DSNDING. I DIDN'T SEE THE TFC; BUT IT WAS CLOSE TO US; EVEN ON THE 2 1/2 MI SCALE ON MY NAV DISPLAY. I WOULD ESTIMATE THAT WE GOT TO WITHIN ABOUT 1 MI OF THE TFC. JUST AS WE PASSED THE CLOSEST POINT OF APCH; MY FO SAID HE SAW THE TFC (WHICH HE BELIEVED TO BE A PIPER CHEROKEE) SHARPLY PULL UP AND TO THE L TO PASS BEHIND US. IT WAS AT THIS POINT THAT ATC CALLED US WITH A TA FOR THE FIRST TIME. I ADVISED HIM THAT WE WERE ALREADY RESPONDING TO AN RA AND WOULD RETURN TO ASSIGNED ALT WHEN ABLE. SINCE WE HAD AN ALT DISPLAYED FOR THE TFC THROUGHOUT THIS EVENT; I HAVE TO BELIEVE HE WAS SQUAWKING MODE 3C; SO I CAN'T EXPLAIN ATC'S FAILURE TO CALL THE TFC; MUCH LESS CLRING US TO CLB INTO IT.