Since you're going to shoot them in the brain (right?), anything that will penetrate the skull will work.
I guess you could do a lung shot, which is reasonably humane, but then they might make it to the neighbor's yard and die there...
Seriously, accuracy is way more important than power (since airguns don't really have any power to speak of) when you're talking about airguns.
Ok, here's a mini-rant. I hate these questions about minimum power for killing this, minimum ft/lbs for this game, minimum caliber for killing that. I don't think it's a useful practice to try to reduce animals to numbers and then if the gun exceeds that animal's number, blaze away. The fact is that the most powerful airgun made can be used to wound a squirrel, while a match rifle (generally pretty anemic in the power department) can make a clean kill with shot placement. IMO, the answer to these questions is always very simple. If you have to ask, don't try shooting the animal with any airgun.
BUT, I realize that such questions come from a desire to be humane, and that I might be a bit oversensitive on the topic, so I'll try to answer as best I can.
Airguns do not kill with power, energy, momentum or shock. They kill by poking TINY little holes in critical parts of animals. If the little bitty holes aren't in the right place, the animals crawl away and suffer. If the little bitty holes are in exactly the right place, the animals die quickly and humanely.
To kill a squirrel with an airgun, you need to figure out how big the target is. NOT the squirrel, but the critical parts that need to be disrupted. The brain, or perhaps the heart/lungs. Then you need to figure out how far away you can CONSISTENTLY hit a target that size from the shooting position(s) you will be likely to use in the situation. You will need to learn how to visualize the specific targets from various angles that you are likely to view the animal.
Generally speaking, by the time a person has practiced enough to have any business using an airgun to hunt animals, they have a good idea of what kind of airgun they should be using. I've seen squirrels taken very cleanly at ranges up to 50 feet with a single shot from an airgun that didn't even make 3ft/lbs at the muzzle. I've also seen them wounded and lost after being shot multiple times with much more powerful airguns.
It is NOT a matter of energy or power. It is PURELY a matter of the skill and knowledge of the shooter.
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