NMAC BTWN DEP ARR TFC AT ACK.

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DEP INSTRUCTIONS WERE RWY HDG TO 2000 FT. JUST AFTER TKOF; TWR ALERTED US TO TFC AT OUR 10 O'CLOCK; DIRECTED A TURN TO A HDG OF 010 DEGS; AND INSTRUCTED US TO CHANGE TO THE APCH FREQ. THIS INTERRUPTED OUR AFTER TKOF FLOW; INCLUDING OUR '1000 FT TO GO' CALLOUT. AT THE SAME TIME; OUR TCASII GAVE US BOTH A VISUAL AND AURAL TA; WITH THE TFC IN QUESTION AT OUR 10-12 O'CLOCK; AT THE ALT THROUGH WHICH WE WERE PASSING AND SHOWING VERY CLOSE; ALMOST ON TOP OF; OUR CURRENT POS. BOTH OF US PLTS RESPONDED TO THE TA; LOOKING INSIDE AT THE TCASII SCREEN AS WELL AS OUTSIDE FOR THE TFC WHILE I WAS TURNING TO THE NEWLY ASSIGNED HDG. MEANWHILE; WE CONTINUED TO CLB AT TKOF PWR AND 200 KIAS IN THE ATA. AS WE WERE ABOUT TO PASS THROUGH 2000 FT; THE PNF ALERTED ME WITH A CALLOUT. IN AN EFFORT TO NOT OVER-CONTROL THE LEVEL OFF FROM OUR CLB RATE OF 4000-5000 FPM; I REDUCED PWR STEADILY BUT NOT QUICKLY; AND PUSHED THE NOSE OVER; DSNDING BACK TO 2000 FT. AT OUR HIGHEST POINT; WE REACHED 750 FT ABOVE OUR ASSIGNED ALT. I BELIEVE THIS EXCURSION WAS CAUSED BY (1) THE INTERRUPTION OF OUR AFTER TKOF FLOW AND CALLOUTS; ESPECIALLY THE '1000 FT TO GO' CALLOUT; (2) THE ATTEMPT BY BOTH PLTS TO ANALYZE THE TCASII ALERT IN ORDER TO LOCATE AND AVOID THE TFC; AND (3) DIVERSION OF ATTN AS PF FROM MAINTAINING ASSIGNED HDGS; ALTS; AND AIRSPDS. INTERRUPTIONS FROM EXTERNAL SOURCES ARE A GIVEN IN THE COURSE OF ANY FLT AND CANNOT BE PREVENTED BY THE CREW; SO I CANNOT RECOMMEND A CORRECTIVE ACTION FOR THAT. FOR THE OTHER TWO FACTORS; CHANGES IN OUR OPERATIONAL PROCS ARE POSSIBLE TO MINIMIZE CHANCES OF A RECURRENCE. ON FUTURE FLTS UNDER IFR; WE WILL NOT OPERATE THE TCASII IN THE TERMINAL AREA DURING DEP; BUT INSTEAD RELY UPON ATC AS WE HAVE IN THE PAST TO KEEP US CLR AS WE FLY ASSIGNED HDGS AND ALTS UNTIL SUCH TIME AS WE ARE ABLE TO GIVE TCASII ALERTS OUR ATTN WITHOUT DEGRADATION TO OUR FLT PARAMETERS. DURING VFR DEPS WHERE WE ARE NOT ARTIFICIALLY LIMITED TO A LOW INITIAL LEVEL OFF ALT OR A SPECIFIC HDG AND MAY NOT HAVE THE FULL ASSISTANCE OF ATC; WE WILL CONTINUE TO USE THE TCASII FOR COLLISION AVOIDANCE. AS PF; I WILL NOT PERMIT MY ATTN TO BE DIVERTED FROM HDG; ALT; OR AIRSPD UNTIL AT LEAST THE ACFT IS STABILIZED AT INITIAL CRUISE. INSTEAD I WILL BRIEF AND RELY UPON THE PNF TO HANDLE ANY INTERRUPTIONS WHICH MAY ARISE.