NMAC BTWN A LEARJET 55; CLBING OUT THROUGH 11000 FT; AND A MOONEY PASSING OVER IN THE OPPOSITE DIRECTION. NO TIME FOR EVASIVE ACTION.

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WE WERE DEPARTING JACKSON HOLE; WY; AND GOING TO PUEBLO; CO. WE DEPARTED JACKSON HOLE ARPT TO THE S (RWY 17?). WE WERE CLRED TO 15000 FT AND BEGAN A L TURN ON TKOF TO A HDG OF 135 DEGS AS PRESCRIBED FOR NOISE ABATEMENT. WE CONTACTED CTR OUT OF 9000 FT WHEN TWR HANDED US OFF. MY COPLT WAS RUNNING A CHKLIST AND I WAS FLYING. CLBING OUT OF 11000 FT; I NOTICED SOMETHING MOVING IN THE WINDSCREEN OUT OF THE CORNER OF MY EYE. I LOOKED R AND ALL I SAW WAS THE BOTTOM OF A MOONEY PASSING R OVERHEAD OF US. I DID NOT HAVE TIME TO TAKE ANY EVASIVE ACTION. I IMMEDIATELY ASKED CTR IF HE HAD ANY TFC NEARBY AND THAT WE HAD A MOONEY PASS 50 FT OVERHEAD OF US GOING THE OPPOSITE DIRECTION. HIS RESPONSE (CTR) WAS 'WE HAVE NUMEROUS TARGETS IN YOUR AREA.' CTR CALLED 'RADAR CONTACT' JUST AFTER MOONEY PASSED OVERHEAD. I BELIEVE THIS COULD HAVE BEEN AVOIDED IF THE COPLT HAD WAITED TO ACCOMPLISH CHKLIST UNTIL IN RADAR CONTACT; AND BEEN LOOKING OUTSIDE FOR TFC. I SHOULD HAVE BEEN SCANNING FOR TFC BETTER AS WELL. CTR SHOULD NOTIFY ACFT OF 'NUMEROUS TARGETS IN AREA.' I BELIEVED THERE WAS NO OTHER TFC IN AREA BECAUSE NEITHER TWR NOR CTR ADVISED OF ANY. BE EXTREMELY ALERT IN A RESORT/VACATION AREA FOR TFC SIGHT-SEEING OR PASSING OVER THE AREA.