Theoretical predictions for pionium searches

Characteristic properties of pionium $A_{2\pi }$ and associated low energy $s$-wave cross sections $\sigma ({\pi }^0{\pi }^0\to {\pi }^0{\pi }^0)$, $\sigma ({\pi }^{+}{\pi }^{-}\to {\pi }^0{\pi }^0)$, and $\sigma ({\pi }^0{\pi }^0\to {\pi }^{+}{\pi }^{-})$ are investigated with a coupled-channels potential model. Some experimental results and conclusions should be reconsidered.