An exact computation of decay rates is, of course, much more
complicated, since it requires a detailed understanding of the
shape of the potential barrier.  In principle, this is computable
from quantum chromodynamics (an extremely well-tested theory), but
in practice the computation is much too complex to be done exactly.
There are, however, reliable approximations available, and in
addition the shape of the potential can be measured experimentally.

For beta decay, the underlying fundamental theory is different; one
begins with electroweak theory (for which Glashow, Weinberg and
Salam won their Nobel prize) rather than quantum chromodynamics.
Again, though, I don't know of anything here that is "unknown."