LETTER TO THE EDITOR The importance of the nucleon-nucleon correlations for the ηα S-wave scattering length, and the π-η mixing angle in the low energy ηα scattering length model

Using the new set of dd → ηα near threshold experimental data, the estimate of the importance of the nucleon-nucleon correlations for the ηα S-wave scattering length in the multiple scattering theory is obtained using the low energy scattering length model. The contribution turns out to be much bigger then previously believed. The π-η mixing angle is extracted using the experimental data on the dd → ηα and dd → πα processes. The model is dominated by the subthreshold extrapolation recipe for the ηα scattering amplitudes. When the recipe is chosen the model is completely insensitive to the ηα parameters for the subthreshold value of the η cm momentum of p η = −(0.46)2 fm. Provided that the subthreshold extrapolation recipe is correct, a good estimate of the π-η mixing angle is obtained if the experimental cross sections for the dd → πα reaction at the corresponding deuteron input energy are taken from the literature. PACS numbers: 13.60.Le, 13.75.n, 25.10.+s, 25.40.Ve Short title: LETTER TO THE EDITOR