B737 WAS HIT BY THE JETWAY AS IT WAS POSITIONING AT THE GATE.

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AFTER ENG SHUTDOWN; AND WHILE PERFORMING THE SHUTDOWN FLOW; I WAS CONTACTED BY A RAMPER ON THE INTERPHONE AND INFORMED THAT THE #1 ENG COWL HAD BEEN DAMAGED BY THE JETWAY. POSTFLT CHKLISTS WERE COMPLETED AND MAINT WAS CONTACTED. THE TAXI-IN HAD BEEN NORMAL AND PER COMPANY PROCS. 1 MARSHALLER AND 2 WING WALKERS WERE PRESENT AND OBVIOUSLY VERY VIGILANT. THE JETWAY APPEARED TO BE PARKED SOMEWHAT OUT OF THE NORMAL POS; SO TAXI SPD INTO SPOT WAS SLOW AND DELIBERATE. APPROX 10 FT SHORT OF ESTIMATED STOPPING POINT; I BROUGHT ACFT ALMOST TO A STOP AND TAXIED THE FINAL 6-10 FT EXTREMELY SLOWLY. MARSHALLER MOTIONED THE ACFT TO A STOP; AND CHOCKS WERE INSERTED. AFTER SECURING ENGS; I RELEASED THE PARKING BRAKE PER SOP. I WAS NOTIFIED BY SOMEONE ON THE RAMP THAT THE DAMAGE HAD BEEN DETECTED APPROX 3-5 MI AFTER ENG SHUTDOWN. DURING THAT PERIOD; I OBSERVED THE JETWAY OPERATOR HAVE SOME DIFFICULTY POSITIONING THE JETWAY ON THE ACFT. WHILE NO ONE ACTUALLY WITNESSED THE CONTACT; IT IS BELIEVED TO HAVE OCCURRED AFTER THE ACFT WAS CHOCKED AND WHILE THE JETWAY WAS BEING POSITIONED. I BELIEVE THAT WHILE THE JETWAY WAS PREPOSITIONED SOMEWHAT ABNORMALLY; ALL PROCS AND PRECAUTIONS WERE FOLLOWED; AND THIS ERROR CAN BE ATTRIBUTED TO UNFAMILIARITY WITH A NEW JETWAY AND ITS INITIAL CLOSE PROX TO THE ACFT.