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 are to be reconsidered.