On eta-pi mixing close to the eta-Helium threshold

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A K-matrix formalism is used to relate the amplitudes for the three reactions pd --> 3He eta, pi- 3H --> 3He eta and pd --> 3H pi+. Free parameters are fitted to the available experimental data and an extrapolation below the eta 3He threshold is made to see the origin of the eta 3He threshold enhancement. The existence of a virtual -- and not a quasi-bound -- state finds support in the data. The K-matrix permits a discussion of eta-pi mixing. A mixing parameter of 0.010(5), i.e. a mixing angle theta =0.6(3) degrees, is extracted from a best fit to the very recent pd --> 3He pi0 reaction data.