Why does a He atom's atomic radius increase when it is trapped inside a buckyball?

I'm not learned on what you are speaking of, but I would venture to say that the electron cloud of the Helium atom grows very large, rather than the nucleus. The electron cloud would be the envelope (of vacuum area around the nucleus) where the electrons can be found at any point in time. By placing it in a buckyball the surroundings lead themselves to draw the electrons possible locations farther away from the nucleus than normally found, either by repulsion from electrons in the shell, or be attraction to the nuclei and bonds within the shell, (behavior I am mentioning is to similar to how a Cooper Pair is formed.)