The estimation of production rates of ${\pi }^{+}{K}^{-}$, ${\pi }^{-}{K}^{+}$ and ${\pi }^{+}{\pi }^{-}$ atoms in proton–nucleus interactions at 450 GeV c^–1

Short-lived ($\tau \sim 3\times {10}^{-15}s$) ${\pi }^{+}{K}^{-}$, $K^{+}{\pi }^{-}$ and ${\pi }^{+}{\pi }^{-}$ atoms as well as long-lived ($\tau ⩾1\times {10}^{-11}$ s) ${\pi }^{+}{\pi }^{-}$ atoms produced in proton–nucleus interactions at 24 GeV c^–1 are observed and studied in the DIRAC experiment at the CERNProton Synchroton. The purpose of this paper is to show that the yields of the short-lived ${\pi }^{+}{K}^{-}$, $K^{+}{\pi }^{-}$ and ${\pi }^{+}{\pi }^{-}$ atoms in proton–nucleus interactions at 450 GeV c^–1 and ${\theta }_{lab}=4^{\circ }$ are estimated to be, respectively 67 ± 13, 31 ± 6 and 15 ± 2 times higher. This may allow a significant improvement of the precision of their lifetime measurement and $\pi \pi$ and $\pi K$ scattering length combinations $|a_0-a_2|$ and $|a_{1/2}-a_{3/2}|$. The yields of the long-lived ${\pi }^{+}{K}^{-}$, $K^{+}{\pi }^{-}$ and ${\pi }^{+}{\pi }^{-}$ atoms at 450 GeV c^–1 are estimated to be 265 ± 53, 120 ± 24 and 60 ± 9 times higher per time unit than at 24 GeV c^–1. This may allow the resonance method to be used for measuring the Lamb shift in the $\pi \pi$ atom and a new $\pi \pi$ scattering length combination $2a_0+a_2$ to be obtained. (paper)