power supply - Automatically switching from 9V battery to DC wall adapter on insertion

I have a simple circuit that runs off of a 9V battery. I'm re-designing it so that it can also run off of an external 12V DC source (ie: a wall adapter). I want to design the circuit so that if both the battery and the wall adapter are connected simultaneously, the wall adapter is used, and the battery is effectively disconnected from the circuit.

I've found a few circuits online that might work, but they unfortunately might allow a trickle of current into the battery, and since it could be a non-rechargeable (ie: alkaline) cell, this could be disastrous.

I've considered the using a barrel jack with a normally-closed three-terminal contact configuration, but I'm not quite sure how to start. How would I go about designing such a circuit?

Answer

The NC (normally closed) terminals (2 & 3 in the sheet) must connect the battery. When you plug in the adapter, this terminals opens. Try to determine on which pin (in addition to pin 1) the adapter connects (i can't determine the number from the sheet).

Edit: The battery connects between pins 1 & 2.

^{simulate this circuit – Schematic created using CircuitLab}