Date: 201206
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Light: Daylight
Aircraft: B737 Undifferentiated or Other Model
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Flight phase: Descent
Airspace: Class E ZZZ
ATC / advisory: TRACON ZZZ
Second aircraft: MD-83
Reporter organization: Government
Reporter function: Departure; Approach
Reporter qualification: Air Traffic Control Fully Certified
Human factors: Distraction; Communication Breakdown; Situational Awareness; Workload
Second reporter function: Pilot Not Flying; First Officer
Anomaly: ATC Issue All Types; Conflict NMAC
Detector: Automation Aircraft RA; Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Air Traffic Control Separated Traffic; Flight Crew FLC complied w / Automation / Advisory
Contributing factors: Human Factors; Staffing
Primary problem: Human Factors

Narrative: Air Carrier X was inbound to ZZZ from the northeast; assigned 12;000 FT from the Center. When I got control I issued Air Carrier X a 170 heading for sequencing and a descent to 10;000 FT due to crossing VFR traffic descending from 10;500 to 8;500 FT. Air Carrier Y was inbound from the southeast descending via the RNAV arrival from 12;000 to 8;000 FT. At this time the aircraft where approximately 50 miles apart; but on a converging courses to meet 30 [miles] east of ZZZ with Air Carrier Y crossing that area at 10;000 FT. To avoid this situation I issued Air Carrier X 9;000 FT once the VFR aircraft was no longer a factor. A departure [aircraft] had to return immediately after departure due to an emergency. When I issued 9;000 FT to Air Carrier X; I thought they received it and read it back. Apparently; what I heard was Air Carrier X was actually another aircraft checking in and Air Carrier X never received the clearance and remained level at 10;000 FT and still on converging course with Air Carrier Y. The emergency aircraft was then shipped to my frequency for sequencing and there was confusion as to what runway the aircraft would be landing on. This took away from my timing and sequencing plan with Air Carrier Y and Air Carrier X. When I went back and scanned I noticed Air Carrier Y and Air Carrier X approximately 7 miles apart converging with Air Carrier Y now descending out of 10;800 FT. I issued a safety alert to Air Carrier Y and a preventive vector. I should not have issued Air Carrier X 10;000 FT in the first place and been more attentive to the hear-back/read-back. There should have been an assist position open. With the traffic being as it was and TMU tagging aircraft I believe they should be answering the [approval requests] when there is no assist working.


Second narrative: I was the pilot not flying. We were cleared to descend via the [RNAV arrival] into ZZZ. We were switched to TRACON [and] after initial check-in; TRACON responded; 'Company flight # slow to 210 KIAS.' We acknowledged and began to slow to 210 KIAS; while continuing the profile for the [Arrival]. We noticed that there was communication saturation due to TRACON handling an emergency flight landing on [Runway] XXR. About five miles south of ZZZZZ descending through 10;500 FT; we heard TRACON querying a flight about an aircraft at twelve o'clock. The other carrier was at 10;000 FT and told to descend to 9;000 FT; which they replied; 'Roger; aircraft in sight; descending to 9;000 FT.' At that time; I picked up the aircraft visually; while simultaneously we received a TCAS Alert. The alert quickly became a Climb RA to which the pilot flying executed our procedures immediately. I requested the pilot flying to increase climb rate because of the attitude of the other carrier's flight; which was climbing toward us. At approximately 11;700 FT the other carrier's flight passed beneath our aircraft. After landing; we contacted TRACON. They acknowledged it was their error on the loss of separation due to an emergency aircraft saturating the airwaves and Controller loss of situational awareness. They informed us that our closest point of approach was 400 FT vertically. We landed on XXL with no further incidents. As a crew; it helps to recognize when TRACON is handling an emergency aircraft. They are out of their habit patterns and tend to lose track of additional aircraft in the sky. The pilot flying did a marvelous job executing TCAS avoidance procedures. Training situations definitely help when the real situation is encountered in the air.


Synopsis: TRACON Controller described a loss of separation event and TCAS RA. Contributing factors listed include the handling of an emergency aircraft needing an immediate return to the airport; along with the lack of an open assist controller position.