The estimation of production rates of $π^+ K^−, π^− K^+$ and $π^+π^−$ atoms in proton-nucleus interactions at 24 and 450 GeV/c

Short-lived ( τ ∼ 3 × 10 − 15 s ) π + K − , K + π − and π + π − atoms as well as long-lived ( τ ≥ 1 × 10 − 11 s) π + π − atoms produced in proton-nucleus interactions at 24 GeV/c are observed and studied in the DIRAC experiment at the CERN P S. The purpose of this paper is to show that the yields of the short-lived π + K − , K + π − and π + π − atoms in proton-nucleus interactions at 450 GeV/c and θ lab = 4 ◦ are estimated to be, respectively, 17, 38 and 16 times higher. This may allow sign ificantly improving the precision of their lifetime measurement and ππ and πK scattering length combinations | a 0 − a 2 | and | a 1 / 2 − a 3 / 2 | . The yields of the long-lived π + K − , K + π − and π + π − atoms at 450 GeV/c are estimated to be 180,800 and 370 times higher p er time unit than at 24 GeV/c. This may allow the resonance method to be used for measuring the Lamb shift in the ππ atom and a new ππ scattering length combination 2a0 + a2 to be obtained.