Direct calculation of the probability of pionium ionization in the target

The goal of the DIRAC experiment at CERN is the lifetime measurement of pionium ($π^+ π^−$ atom). Its lifetime is mainly defined by the charge-exchange process $π^+ π^−$ → $π^0 π^0$. The value of the lifetime in the ground state is predicted in the framework of chiral perturbation theory with high precision: $τ_{1S} = (2.9 \pm 0.1) × 10^{−15}$ s. The method used by DIRAC is based on analysis of $π^+ π^−$-pair spectra with small relative momenta in their center-of-mass system in order to find out the signal from pionium ionization (breakup) in the target. Pioniums are produced in proton-nucleus collisions and have relativistic velocities (γ > 10). For fixed values of the pionium momentum and the target thickness, the probability of pionium ionization in the target depends on its lifetime in a unique way; thus, the pionium lifetime can be deduced from the experimentally defined probability of pionium ionization. On the basis of ionization cross sections of pionium with target atoms, we perform the first direct calculation of the pionium ionization probability in the target.