Flight Crew Air Transport Pilot (ATP)
Distraction; Situational Awareness
Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Other / Unknown
Flight Crew Became Reoriented
Human Factors
Told a family with 3 young kids that I would allow them in the cockpit after the flight since we were short on time leaving.  Landed with a request for two wheelchairs; and meet and assist for vision impaired.  After being marshalled in I asked for GPU power.  I set the brake; chocks were installed; stairs were placed on the aircraft; and we were given a signal to open the door.  We began deplaning while I was on the radio calling for a second wheelchair (there was only one outside); and requesting the meet and assist come to the aircraft (Ops told me they were waiting at the gate; but how is a vision impaired to make it from the plane to the top of the jet way with two sets of stairs?).  After 2-3 min with no GPU I started the APU.  Soon after the kids I had promised to show the flight deck to stopped at the flight deck door.  I got up to allow the kids to sit in my seat.  There were three; so my First Officer got up to allow all three in the cockpit.  My First Officer exited the flight deck and I stayed hunched over the center console in the flight deck to answer their questions.  As soon as the First Officer began doing his walk around he realized engine 2 was still running; he signaled to me.  I shut it down immediately; and then we completed the parking checklist.  While my intentions were good (wheelchair for passenger; guide for passenger; GPU for cost savings; and entertaining the children) they caused me to be distracted and I deviated from SOP and common sense inadvertently.  Not completing the Parking checklist before exiting the flight deck.  Ramp placing stairs on the plane and signaling ok to open with beacon running.  Engine running with three kids and a pilot in flight deck! Use increased awareness during high workload situations and distractions.  Strict adherence to checklist policy.  Standardization among ground crew.  GPU should be provided when available.  Ground crew said they sent for it after I asked for it; but I asked for it in range.  Ground crew should not approach the aircraft while an engine is running.  This rule is broken 99% of the time and needs to be addressed.  This situation made the importance of such a rule very obvious.  If the rule were followed; the door never would have been opened and the undesired aircraft state would have been avoided.  Ultimately; it is the crew's responsibility to ensure safe operation of the aircraft; but this broken link could have prevented the situation from ever happening.   Lastly; please forgive my typos.  I'm typing on an iPad as fast as possible before my password times out and I lose all data!
EMB-145 Captain reports forgetting to shut down the second engine after gate arrival due to multiple distractions. The running engine is detected by the First Officer during his walk around.