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The effect of the strong $\bar{\rm p}$-p nuclear interaction in athree-charge-particle system with arbitrary masses is investigated.Specifically, the ($\bar{\rm p},\ \mu^-$,\ p) system is considered, where$\bar{p}$ is an antiproton, $\mu^-$ is a muon and p is a proton. A numericalcomputation in the framework of a detailed few-body approach is carried out forthe following protonium (antiprotonic hydrogen) formation three-body reaction:$\bar{p} + H_{\mu}(1s) \rightarrow (\bar{p} p)_{\alpha} + \mu^-$. 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 atomin a quantum atomic state $\alpha$, i.e. $Pn = (\bar{p}p)_{\alpha}$. Thelow-energy cross sections and rates of the $Pn$ formation reaction are computedin the framework of a Faddeev-like equation. The strong $\bar{\rm p}$-pinteraction is included in these calculations within a first orderapproximation. It was found, that even in the framework of this approximationthe inclusion of the strong interaction results in a quite significantcorrection to the rate of the three-body reaction. Therefore, the titlethree-body antiprotonic process with participation of muons should be useful,especially at low-energy collisions, in studying the $\bar{\rm p}$-p nuclearforces and the annihilation channels in $Pn$.

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