Charge and isospin symmetry breaking via external $\pi^{0}-\eta$ meson mixing

A simple model of isospin and charge symmetry breaking due to external$pi^0-eta$ meson mixing is presented. It is based on amplitudes extracted from the available experimental data for pd$rightarrow^3$He$pi^0$, pd$rightarrow^3$He$eta$ and dd$rightarrow^4$He$eta$ reactions. Predictions of the strength of isospin symmetry breaking in pd$rightarrow^3$H$pi^+$/$^3$He$pi^0$ reactions are given. Within the same model, the cross section for the charge symmetry breaking dd$rightarrow^4$He$pi^0$ reaction is calculated