Effect of strong $\bar{\mathrm{p}}$-p nuclear forces on the rate of the low-energy three-body protonium formation reaction: $\bar{p}+H_{\mu }(1s)\to (\bar{p}p{)}_{\alpha }+{\mu }^{-}$

Abstract

The effect of the strong $\bar{\mathrm{p}}$-p nuclear interaction in a three-charge-particle system with arbitrary masses is investigated. Specifically, the ($\bar{\mathrm{p}},{\mu }^{-}$,\ p) system is considered, where $\bar{p}$ is an antiproton, ${\mu }^{-}$ 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: $\bar{p}+H_{\mu }(1s)\to (\bar{p}p{)}_{\alpha }+{\mu }^{-}$. Here, $H_{\mu }(1s)$ is a ground state muonic hydrogen, i.e. a bound state of p and ${\mu }^{-}$. A bound state of $p$ and its counterpart $\bar{p}$ is a protonium atom in a quantum atomic state $\alpha$, i.e. $Pn=(\bar{p}p{)}_{\alpha }$. The low-energy cross sections and rates of the $Pn$ formation reaction are computed in the framework of a Faddeev-like equation. The strong $\bar{\mathrm{p}}$-p interaction is included in these calculations within a first order approximation. It was found, that even in the framework of this approximation the inclusion of the strong interaction results in a quite significant correction to the rate of the three-body reaction. Therefore, the title three-body antiprotonic process with participation of muons should be useful, especially at low-energy collisions, in studying the $\bar{\mathrm{p}}$-p nuclear forces and the annihilation channels in $Pn$.

arXiv commentPreprint: 33 pages, 11 figures, 1 Table