A320 FOLLOW A TCASII COMMAND DUE TO A C172 XING ITS FLT PATH IN ZOA CLASS E.

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WHILE ON THE JAWWS ARR INTO SJC BTWN PAPEE AND JAWWS; WE FOLLOWED A TCASII RA. THE CTLING AGENCY WAS ZOB. WE WERE AT 250 KTS AND 11000 FT. OAKLAND ADVISED OF VFR TFC AT 10500 FT; 10 O'CLOCK POS; AND 4 MI. WE HAD A WHITE TCASII HIT THERE SHOWING 500 FT BELOW US WITH NO VISUAL. OAKLAND CONTINUED TO DIRECT OTHER TFC. THE TFC BEGAN TO DRIFT L TO R TO 11 O'CLOCK POS; AND THE ALT DIFFERENCE CHANGED TO -400 FT. THE HIT TURNED AMBER WITH THE ASSOCIATED TA AUDIO. STILL NO VISUAL. THERE WERE SCATTERED CUMULUS CLOUDS FROM THE HORIZON AND BELOW; BUT NOT WITH 5 OR 6 MI. ATC QUERIED ABOUT THE TFC AND WE ADVISED THAT WE DID NOT HAVE IT. THE TCASII HIT WAS NOW AT 1-2 MI SHOWING -200 FT; BEARING SLIGHTLY L OF 12 O'CLOCK POS. MY TENDENCY WAS A DESIRE TO TURN L INTO THE TCASII TARGET TO INCREASE THE DRIFT RATE ACROSS THE NOSE. THE CTLR STARTED A CALL FOR US TO TURN; BUT WE NEVER HEARD THE DIRECTION OR HDG AS THE TCASII HIT WENT RED WITH THE RESOLUTION AUDIO AND A COMMAND TO CLB; WHICH WE DID. THE AUTOFLT WAS DISCONNECTED; FOLLOWED BY FAIRLY AGGRESSIVE THROTTLE AND PITCH APPLICATION. WE ADVISED ATC THAT WE WERE CLBING IN RESPONSE TO A TCASII RA TO WHICH HE DID NOT RESPOND. THE TCASII 'CLB' CHANGED TO 'INCREASE CLB;' WHICH WE DID. I ADVISED ATC AGAIN THAT WE HAD MANEUVERED IN RESPONSE TO A TCASII RA. STILL NO RESPONSE FROM ATC. 'MONITOR VERT SPD' FOLLOWED SHORTLY. OUR INITIAL REACTION WAS AS AGGRESSIVE AS ANY PRACTICE TCASII EVENT IN THE SIMULATOR THAT I HAVE SEEN; BUT IT WAS NOT ENOUGH. AS THE PNF; I SAW THE TFC JUST AFTER THE 'CLB' COMMAND. IT WAS A WHITE CESSNA; C172; SLIGHTLY BELOW OUR NOSE AT A MI OR LESS ON A TRACK THAT HAD JUST AT HIS 12 O'CLOCK POS. WE LEVELED AT 12000 FT FOR A FEW MOMENTS AND STARTED BACK DOWN TO 11000 FT. DURING THIS TIME; I AGAIN ADVISED THE CTLR THAT WE HAD RESPONDED TO THE RA AND WE WERE DSNDING OUT OF 12000 FT FOR 11000 FT. HE ACKNOWLEDGED THE RESPONSE AT THIS TIME. ALL OF THIS TIME; THE ALTDEV WARNING WAS SOUNDING CONTRIBUTING TO THE TENSENESS OF THE SIT. THE CTLR HANDED US OFF TO NORCAL SHORTLY THEREAFTER WITH NO FURTHER COMMENT. I SUSPECT HE WAS AS UNNERVED AS WE.