EMB145 CREW REPORTS TCAS RA ON ARRIVAL TO SAT AND THEN FORGETTING TO CONTACT TOWER FOR CLEARANCE TO LAND.

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HIGH CREW WORKLOAD RESULTING FROM AN OVERLOADED ATC SITUATION IN THE SAT AREA; COMPOUNDED BY ADDITIONAL STRESS ON THE FLT CREW RESULTING FROM A NEAR MISS AND A TCAS RA EVENT. THE PRIMARY FOCUS OF THIS REPORT IS FOR PROBABLY LNDG WITHOUT ATC CLRNC AT SAT. THE CREW RESPONDED TO A TCAS RA APPROX 5-10 MINS PRIOR TO LNDG; SO IT IS BEING INCLUDED AS A CONTRIBUTING FACTOR. ZHU WAS WORKING OUR FLT AS WE DSNDED ON THE MARCS ARR INTO SAT. CTR ISSUED OUR FLT NUMEROUS HDG; ALT; AND SPD CHANGES AND AMENDMENTS. BECAUSE OF ALL THE CHANGES BEING ISSUED BY ATC THE CREW GOT BEHIND ON OUR CREW BRIEFING; IN-RANGE CHKLIST; AND PAX BRIEFING DUTIES. ATC'S AND OUR WORKLOAD WAS VERY HIGH. CTR DSNDED US TO 6000 FT. WHEN WE WERE LEVEL THEY HANDED US OFF TO SAT APCH; WITHOUT PROVIDING US WITH A TA FOR THE VFR TFC WHICH WAS ABOUT TO CAUSE OUR TCAS EVENT. WHEN WE SWITCHED TO APCH FREQ WE COULD NOT MAKE CONTACT INITIALLY DUE TO FREQ CONGESTION. BEFORE WE COULD ESTABLISH COM WITH APCH WE RECEIVED A TCAS TA; FOLLOWED QUICKLY BY AN RA TO CLB AT 3000 FPM. THE CREW COMPLIED WITH THE RA AND CLBED 300 FT BEFORE THE RA STOPPED. AT THE TOP OF OUR CLB THE CONFLICT TFC PASSED 400 FT DIRECTLY BELOW OUR ACFT ON OUR TCAS (6 MI DISPLAY). THE FO CAUGHT A GLIMPSE OF THE TFC AS IT PASSED UNDER US AS IT WAS APCHING FROM OUR 2 O'CLOCK POS. AT TOP OF CLB WE ESTABLISHED CONTACT WITH APCH AND ADVISED WE WERE CLBING FOR A TCAS RA. THE APCH CTLR ALSO HAD A VERY HIGH WORKLOAD AND SEEMED TO BE OVERLOADED. WE WERE NOW RUSHED TO COMPLETE OUR REMAINING DUTIES; WITH ADRENALINE STILL PUMPING FROM THE RA EVENT WE WERE QUICKLY VECTORED ON TO A 12 MI FINAL AND CLRED FOR A VISUAL APCH TO RWY 30L. APCH CTL FORGOT TO HAND US OFF TO LCL TWR CTL. WE FAILED TO NOTICE AND LANDED. WE CONTACTED GND CTL AND TAXIED TO THE GATE. AT THE END OF THE LNDG ROLL I REALIZED THAT I WAS STILL LISTENING TO APCH CTL AND HADN'T CONTACTED THE LCL CTL TWR. WE CONTACTED GND CTL. THEY GAVE US NO INDICATION THAT WE HAD LANDED WITHOUT CLRNC AND INSTRUCTED US TO TAXI TO OUR GATE. I SHOULD HAVE OMITTED THE PAX BRIEFING PORTION OF MY DUTIES WHEN IT BECAME APPARENT THAT OUR WORKLOAD WAS GETTING HIGH. I DOUBT IF THAT ALONE COULD HAVE PREVENTED THIS EVENT. THE FAA NEEDS TO TAKE SOME TYPE OF ACTION TO PREVENT THEIR CTLRS FROM BECOMING AS OVERLOADED AS THE ZHU AND SAT APCH CTLRS WERE THAT DAY.