Measurements of the reaction $\overline{p}p \to \phi \eta$ of antiproton annihilation at rest at three hydrogen target densities

The proton-antiproton annihilation at rest into the $\phi\eta$ final state was measured for three different target densities: liquid hydrogen, gaseous hydrogen at NTP and at a low pressure of 5 mbar. The yield of this reaction in the liquid hydrogen target is smaller than in the low-pressure gas target. The branching ratios of the $\phi\eta$ channel were calculated on the basis of simultaneous analysis of the three data samples. The branching ratio for annihilation into $\phi\eta$ from the $^3S_1$ protonium state turns out to be about ten times smaller as compared to the one from the $^1P_1$ state.