B737-300 CREW HAD LESS THAN LEGAL SEPARATION DEPARTING SJC IN O90 CLASS C.

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WE DEPARTED SJC FOR BUR ON TIME. WE WERE CLRED AND FLEW THE SJ8 DEP AS DEPICTED. WITH A TURN AT 18 NM AND A CLIMB TO 5000 FT. AS WE WERE JOINING THE A OAK 121 DEG RADIAL AND LEVELING AT 5000 FT THE TCAS ALERTED US TO 3 O'CLOCK TFC WITH A TA. BOTH PLTS LOOKED RIGHT AND SAW A LARGE AIRLINER APPROX 1.5 NM AND 3 O'CLOCK AND 1000 TO 1500 FT LOW; WITH NOSE POSITION IN PURE PURSUIT TO SLIGHTLY LAG POSITION. THE FOLLOWING EVENTS HAPPENED NEARLY SIMULTANEOUSLY: BAY APCH ALERTED US OF 3 O'CLOCK TFC SOON AFTER TA ALERT AND DIRECTED A TURN TO 090 DEG (FROM 120 DEG); FO CALLED TFC IN SIGHT; ATC ADVISED US TO MAINTAIN VISUAL FROM ACR Y WHO THEY DID NOT HAVE RADIO CONTACT WITH. CAPT (ME) ALREADY IN CLIMB FOR RA AND VISUAL SIGHTING. ACR Y FLT CONTINUED PURE PURSUIT AND CLOSURE INDICATING HE DID NOT HAVE US IN SIGHT AND PREPARED TO TAKE EVASIVE ACTION AT APPROX HALF NM AND APPROX 500 TO 600 FT OR LESS. THIS EARLY TURNOUT AND APPARENT LACK OF VISUAL RESULTED IN TOO CLOSE OF A CALL. I THEN ASKED HOW ACR Y GOT SO CLOSE TO US AND WAS ADVISED BY BAY APCH THAT HEY MADE AN EARLY TURN OUT OF TFC LIKE A TURN AT 1.8 NM AS DEPICTION SJ8 DEP. AFTER BEING SENT TO OAKLAND CENTER I RETURNED TO BAY APCH TO ASK IF AN ALERT HAD BEEN GIVEN. ATC ADVISED ALERT WARNING SOUNDED AFTER ACR X WAS TOLD TO MAINTAIN VISUAL SEPARATION AND ALSO THAT ATC HAD NO RADIO CONTACT WITH ACR Y. SUBSEQUENT TELECON BETWEEN COMPANY REPS AN ATC REVEALED ACR Y MADE EARLY TURNOUT IMMEDIATELY AFTER LIFTOFF WITH NO WARNING ABOUT EARLY TURN FROM TWR. IT IS MY OPINION THAT THE EVASIVE ACTION BY MYSELF; THE ALERT FROM TCAS AND THE QUICK THINKING BY MY FIRST OFFICER STATING 'WE HAD ACR Y IN SIGHT' CLEARLY PREVENTED A DISASTER! I HAVE NO DOUBT; NONE! LATE EVASIVE ACTION BY ACR Y HELPED; BUT I WONDER WHEN THEY FINALLY LOOKED OUT THE WINDOWS PROVIDED BY BOEING! NOTE: INITIAL CALL BY ATC TO TURN LEFT WOULD HAVE PUT ACR Y AT 5 O'CLOCK TO US WITH A PURE PURSUIT COURSE. WE WERE THE ONLY ONE WITH SA AND DID NOT WANT TO GIVE IT UP BY PUTTING THREAT ACFT AT OUR SIX O'CLOCK. IT ALSO WOULD HAVE GUARANTEED PURE PURSUIT CURVE UNTIL ACR Y TOOK EVASIVE ACTION WHICH ON THEIR OWN OR TO LATE MAY HAVE GUARANTEED IMPACT.