Unified treatment of hadronic annihilation and protonium formation in slow collisions of antiprotons with hydrogen atoms

Abstract

Antiproton ($\overline{p}$) collisions with hydrogen atoms, resulting in the hadronic process of particle-antiparticle annihilation and the atomic process of protonium ($\overline{p}p$) formation (or $\overline{p}$ capture), are investigated theoretically. As the collision energy decreases, the collision time required for the $\overline{p}$ capture becomes necessarily longer. Then, there is the possibility that the $\overline{p}$-$p$ annihilation occurs significantly before the $\overline{p}$ capture process completes. In such a case, one can no longer consider the annihilation decay separately from the $\overline{p}$ capture process. The present study develops a rigorous unified quantum-mechanical treatment of the annihilation and $\overline{p}$ capture processes. For this purpose, an $R$-matrix approach for atomic collisions is extended to have complex-valued $R$-matrix elements allowing for the hadronic annihilation. Detailed calculations are carried out at low collision energies ranging from ${10}^{\ensuremath{-}8}$ to ${10}^{\ensuremath{-}1}$ eV, and the annihilation and the $\overline{p}$ capture (total and product-state selected) cross sections are reported. Consideration is given to the difference between the direct annihilation occurring during the collision and the annihilation of $\overline{p}p$ occurring after the $\overline{p}$ capture. The present annihilation process is also compared with the annihilation in two-body $\overline{p}+p$ collisions.