Three-Body Protonium Formation in a Collision Between a Slow Antiproton (p) and Muonic Hydrogen: Hμ—Low Energy p + (pμ)1s→(pp)1s+ μ Reaction

Abstract

A bound state of a proton, p, and its counterpart antiproton, (Formula presented.), is a protonium atom (Formula presented.). The following three-charge-particle reaction: (Formula presented.)- is considered in this work, where (Formula presented.)- is a muon. At low-energies muonic reaction (Formula presented.) can be formed in the short range state with α = 1s or in the first excited state: α = 2s/2p, where (Formula presented.) and p are placed close enough to each other and the effect of the (Formula presented.) nuclear interaction becomes significantly stronger. The cross sections and rates of the Pn formation reaction are computed in the framework of a few-body approach based on the two-coupled Faddeev-Hahn-type (FH-type) equations. Unlike the original three-body Faddeev method the FH-type equation approach is formulated in terms of only two but relevant components: (Formula presented.) and (Formula presented.), of the system’s three-body wave function (Formula presented.), where (Formula presented.). In order to solve the FH-type equations (Formula presented.) is expanded in terms of the input channel target eigenfunctions, i.e. in this work in terms of the (Formula presented.)) eigenfunctions. At the same time (Formula presented.) is expanded in terms of the output channel two-body wave function, that is in terms of the protonium (Formula presented.) eigenfunctions. A total angular momentum projection procedure is performed, which leads to an infinite set of one-dimensional coupled integral–differential equations for unknown expansion coefficients.