TRACON controller described a loss of separation event and TCAS RA. Contributing factors listed incl...

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.

Original NASA ASRS Text

Title: 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.

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.

Data retrieved from NASA's ASRS site as of July 2013 and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.

Attributes
ACN	1017380
Time
Date	201206
Local Time Of Day	1201-1800
Place
Locale Reference	ZZZ.Airport
State Reference	US
Environment
Light	Daylight
Aircraft 1
Make Model Name	B737 Undifferentiated or Other Model
Operating Under FAR Part	Part 121
Flight Phase	Descent
Route In Use	STAR ZZZZZ
Flight Plan	IFR
Aircraft 2
Make Model Name	MD-83
Operating Under FAR Part	Part 121
Flight Phase	Cruise
Route In Use	Vectors
Flight Plan	IFR
Person 1
Function	Departure Approach
Qualification	Air Traffic Control Fully Certified
Person 2
Function	Pilot Not Flying First Officer
Events
Anomaly	ATC Issue All Types Conflict NMAC
Miss Distance	Horizontal 0 Vertical 400

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.