Influence of the p-p Nuclear Interaction on the Rate of the Low-Energy p+Hμ → (pp)α +μ- Reaction

The influence of an additional strong p-p nuclear interaction in a three-charge-particle system with arbitrary masses is investigated. Specifically, the system of p, μ-, and p is considered in this paper, where p is an antiproton, μ- is a muon and p is a proton. A numerical computation in the framework of a detailed few-body approach is carried out for the following protonium (antiprotonic hydrogen) formation three-body reaction: p + Hμ(1s) → ( pp)α + μ-. Here, Hμ(1s) is a ground state muonic hydrogen, i.e., a bound state of p and μ-. A bound state of p and its antimatter counterpart p is a protonium atom in a quantum atomic state a, i.e., Pn = ( pp)α. The low-energy cross sections and rates of the Pn formation reaction are computed in the framework of coupled Faddeev-Hahn-type equations. The strong p-p interaction is included in these calculations within a first order approximation. It was found, that the inclusion of the nuclear interaction results in a quite significant correction to the rate of the three-body reaction.