The power core is the most important system on a ship, as it provides power to every other system. The table below lists the ship size each core is designed for, as well as the PCU it provides and its cost.
A power core doesn't "recharge." Think of it as a generator or a reactor that produces the given number of PCU whenever it is active. If it goes down, it needs to be fixed or replaced; as soon as it is back online, the PCU output is available.
The recharging of backup batteries (see below) is not defined, but would probably add a level of complexity that is not needed.
A power core typically has a backup battery system for use in emergencies that can provide limited power—enough for life support, gravity, and comms (see page 430), but no other systems—for 2d6 days.
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Agreed with Dragonchess Player - it sounds like your initial assumption is flawed. There's nothing that has to be "recharged". It effectively runs forever.
That said, could some space battle damage lead to an emergency landing and being stuck there while the core recharges as a plot device for an adventure? Sure I guess. But that's all it would be - a plot device.