ACR HAS TCASII RA AFTER TA. RESPONDS; THEN TFC SIGHTED.

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DSNDING THROUGH 18300 FT WITH CLRNC TO CROSS LAMMA INTXN AT 12000/250 KTS; ATC ADVISED OF VFR TFC LEVEL AT 17500 FT 12 O'CLOCK 4 MI. SIMULTANEOUSLY; TCASII ISSUED RA OF MIN 2100 FPM DSCNT. CURRENT DSCNT RATE WAS 2000 FPM. RATE OF DSCNT INCREASED TO APPROX 3500 FPM. ATC (DIFFERENT CTLR'S VOICE) CALLED TFC AT 12 O'CLOCK LESS THAN 1 MI. OBSERVED SMT-TWIN WITH WING TIP TANKS DIRECTLY AHEAD SLIGHTLY ABOVE OUR POS. ACFT PASSED DIRECTLY ABOVE AS WE DSNDED THROUGH 17200 FT. IT IS UNKNOWN IF OTHER ACFT WAS IN CONTACT WITH CTR; BUT I BELIEVE I REMEMBER ANOTHER ACFT BEING GIVEN TA (POSSIBLY ADVISING HIM OF OUR POS). PROBLEM MAY HAVE BEEN CAUSED BY INEXPERIENCED CTLR OR MOMENTARY DISTR. COULD HAVE BEEN AVOIDED BY VECTOR/ALT CHANGE. POOR JUDGEMENT WAS OBVIOUSLY USED BY ATC; IF THE CONFLICTING TFC WAS KNOWN TO THEM. SUPPLEMENTAL INFO FROM ACN 204148: MY FIRST REACTION/THOUGHT WAS TO LEVEL OFF ABOVE THE TFC. I'M NOT SURE WE COULD HAVE DONE THAT AT OUR ALT AND DSCNT RATE WHEN WE GOT THE CALL. TCASII COMMANDED A DSCNT SOON AFTER CTR ADVISED US OF THE TFC. WITHOUT TCASII; THE MISS DISTANCE WOULD HAVE BEEN MUCH LESS THAN 300 FT.