How to extract the lifetime of pionium and |$a^{0}_{0}−a^{2}_{0}$| from the measurements of the pionium ionization probability

The goal of this note is to describe the algorithms used in DIRAC to estimate the lifetime τ and the difference in scattering lengths |$a^{0}_{0}−a^{2}_{0}$|. This note could then be used as a reference, saving lengthy explanations in the physics publications.