US law places no limits on the purchase of barrels- they are parts, not firearms.
HOWEVER- we cannot EXPORT parts of firearms (and scopes suited for military usage) without a permit issued by the US State Dept. There are international treaties regarding the movement of weapons from one country to another.
That can be a relatively complex process that is not cheap. A friend of mine just donated a SMLE to a military museum in Australia, and it was quite a production.