IFR C310 EXPERIENCED NMAC WITH UNRPTED TFC WHILE UNDER ZLA CTL.

Narrative

THIS 'NEAR MISS' WOULD ABSOLUTELY AND POSITIVELY BEEN A CRASH WITH THE LOSS OF OUR PLANE AND PEOPLE; HAD I NOT HAD THE TCASII SYS INSTALLED IN OUR PLANE. WE WERE NOT GIVEN ANY WARNING OF OTHER TFC BY OUR FAA CTLR AT ANY TIME. I WAS IN THE R SEAT; MY WIFE (ALSO AN ATP RATED PLT) IN THE L SEAT. IFR FLT PLAN FROM SNA TO BJC. TALKING TO ZLA CTLR IN THE VICINITY OF GOFFS VOR AT 11000 FT ROUGHLY ON V8. ON AUTOPLT; OUR TCASII SYS GAVE US AURAL AND VISUAL (YELLOW THREAT SYMBOLS) WARNING. WE LOOKED AT THE MULTI-FUNCTION DISPLAY SCREEN AND THE TFC WAS SHOWN TO BE APPROX -100 FT BELOW US; CLBING. THAT WAS THE FIRST AND ONLY WARNING. NO WARNING OR TFC CALL BY OUR ATC CTLR AT ANY TIME. WE LOOKED UP TO SEE ANOTHER PLANE DIRECTLY IN FRONT OF US WITH ITS L WING TO US; AT OUR ALT AND APPROX 30 FT IN DISTANCE. I COULD SEE THE PLT AND THE PAINT COLOR. I PUT OUR AIRPLANE INTO A 45-60 DEG R BANK AND GUESS THAT WE MISSED THAT PLANE BY LESS THAN 30 FT. AS WE ROLLED INTO OUR BANK WE RECEIVED 2 SHARP 'BUMPS' FROM THE OTHER AIRPLANE'S WAKE. IF WE HAD NOT HAD THE TCASII SYS ONBOARD; AND NOT IMMEDIATELY ROLLED AWAY FROM THE OTHER PLANE; BOTH PLANES WOULD CERTAINLY HAVE CRASHED. I AM ABSOLUTELY SURE OF THIS. WHEN WE WERE BACK IN CTL OF THE SIT (EMOTIONALLY AND PHYSICALLY); I ASKED THE CTLR WHY SHE DID NOT CALL OUT THE TFC AND SHE SAID 'I DID NOT THINK HE WOULD CLB THAT FAST;' SHE SAID NOTHING ELSE. I AM ASSUMING SHE GAVE THE OTHER PLANE A CLRNC THROUGH OUR ALT BASED ON WHAT SHE THOUGHT HIS CLB CAPABILITY WAS. SHE WAS APPARENTLY IN RADIO CONTACT WITH THE OTHER PLANE. PERHAPS I AM WRONG IN ASSUMING THAT THE OTHER PLANE WAS UNDER ATC CTL AT ALL. BUT; BY THE CTLR'S OWN COMMENT; THAT AT LEAST TELLS ME THAT SHE DID SEE THE OTHER PLANE AND COULD HAVE POINTED IT OUT TO US.