Antiproton-Hydrogen annihilation at sub-kelvin temperatures

The unique features of the LEAR (low-energy antiproton ring) facility at CERN made recently possible the synthesis of few antihydrogen atoms [1]. This effort would be pursued with the antiproton deccelerator (AD) project [2] and would make possible the storage of sensible amounts of antihydrogen. This project reinforces the already active interest to investigate several theoretical and experimental problems in the physics of antimatter [3–7]. In view of storing antimatter in traps, it would be interesting to have some theoretical calculations of the rate at which antiprotons (p̄) and antihydrogen (H̄) annihilate with the residual gas. This process should be evaluated at subkelvin temperatures, the optimal energy domain for an effective synthesis and trapping of antimatter. From a theoretical standpoint, a specific feature of systems like H + p̄ or H + H̄ , containing pairs of unlike charged heavy particles (p and p̄), is the possibility of rearrangement followed by Protonium (Pn) formation. Indeed even at zero p̄ kinetic energy Protonium can be produced in states with principal quantum number n ≤ 30. Since the pioneer work of E. Fermi and E. Teller [8] in 1947, this problem has been treated by several authors [9,10,12] in the energy range going from a fraction to tens a.u.. The usual approach is based on the following two assumptions: i) the separation of electronic and nuclear motion and ii) the classical treatment of the antiproton dynamics. The aim of the present work is to provide a correct description of the ultra-low energy limit, i.e. Tp̄ < 10−6 a.u., an energy domain in which the above mentioned assumptions are no longer valid. As a consequence we are definitely faced to a quantum threeor four-body problem. We will consider in what follows the annihilation of ultra slow antiprotons with atomic hydrogen in the framework of an unitary coupled channel approach. This process will be identified to the free Pn formation: