Determination of the branching ratios $\Gamma (K_L \to 3 \pi^0) / \Gamma (K_L \to \pi^+ \pi^- \pi^0)$ and $\Gamma (K_L \to 3 \pi^0) / \Gamma (K_L \to \pi e \nu )$

Improved branching ratios were measured for the $K_L \to 3 \pi^0 $ decay in a neutral beam at the CERN SPS with the NA31 detector: $\Gamma (K_L \to 3 \pi^0) / \Gamma (K_L \to \pi^+ \pi^- \pi^0) = 1.611 \pm 0.037$ and $\Gamma (K_L \to 3 \pi^0) / \Gamma (K_L \to \pi e \nu ) = 0.545 \pm 0.010$. From the first number an upper limit for $\Delta I =5/2$ and $\Delta I = 7/2 $ transitions in neutral kaon decay is derived. Using older results for the Ke3/K$\mu $3 fraction, the 3$\pi^0$ branching ratio is found to be $\Gamma (K_L \to 3 \pi^0 )/ \Gamma_{tot} = (0.211 \pm 0.003)$, about a factor three more precise than from previous experiments.