Antiproton (p) collisions with hydrogen atoms, resulting in the hadronic process of particle-antiparticle annihilation and the atomic process of protonium (pp) formation (orp capture), are investigated theoretically. As the collision energy decreases, the collision time required for thep capture becomes necessarily longer. Then, there is the possibility that thep-p annihilation occurs significantly before thep capture process completes. In such a case, one can no longer consider the annihilation decay separately from thep capture process. The present study develops a rigorous unified quantum-mechanical treatment of the annihilation andp 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 −8 to 10 −1 eV, and the annihilation and thep 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 ofpp occurring after thep capture. The present annihilation process is also compared with the annihilation in two-bodyp + p collisions.