The $\Lambda^{0}$ baryon has two possible decays, the first is $\Lambda^{0} \to \pi^{0} + n^{0}$ and the second $\Lambda^{0} \to \pi^{-} + p^{+}$.
I've been asked to determine the ratio of protons to neutrons observed in the decay.
Properties: $$ \begin{array}{cccc} \text{Particle} & \text{Spin} & \text{Charge} & \text{total isospin} \\\hline \Lambda^0 & \frac12 & 0 & 0 \\ \rm n^0 & \frac12 & 0 & \frac12 \\ \rm p^+ & \frac12 & +1 & \frac12 \\ \pi^- & 0 & -1 & 1 \\ \pi^0 & 0 & 0 & 1 \\ \end{array} $$
Charge and angular momentum are conserved in the decay, but the total isospin changes by $\frac{1}{2}$. I'm supposed to ignore all relativistic effects.
How do I even begin with this question? I don't understand how these conservations lead to the number of particles observed in the decay...
