The estimation of production rates of $\pi^+K^-, \pi^-K^+$ and $\pi^+\pi^-$ atoms in proton-nucleus interactions at 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 PS. 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 per time unit. This may allow significantly improving the precision of their lifetime measurement and ππ and πK scattering length combinations |a0 − a2| and |a 1/2 − a3/2| . The yields of the long-lived π+ K− , K+ π− and π+ π− atoms at 450 GeV/c are estimated to be 370, 1600 and 750 times higher 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 2 a0 + a2 to be obtained.