Solution
= Solution
The four direct <beta decay> <branching fractions> exhaust the parent decays in the model, so
$$
\boxed{\Gamma_0+\Gamma_1+\Gamma_2+\Gamma_3=1.}
$$
Here the question's $\Gamma_i$ are dimensionless <branching fractions>, despite the conventional use of $\Gamma$ for a dimensionful <decay width>. Its “zeroth excited state” means the daughter <ground state>. Cascades through an excited level do not count as an additional direct beta branch to it.