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There are many types of AA battery cells. There are also rechargeable ones. You forgot to say which one.
A lithium non-rechargeable AA battery cell made by Energizer has a current limiter inside to prevent a Lithium fire. The datasheet shows an excellent output of 1A and says 3A is fine and 5A can be in pulses.
A new Ni-MH cell can produce 10A when shorted and a Ni-Cad can produce more. The internal resistance shown on Energizer's datasheet for their Ni-MH cell is 30 milli-ohms.