Cartesian analysis of angular distributions ine+e−→ψ′→ψγγ′→μ+μ−γγ′

Angular distributions for the cascade ${\psi }^{\prime }\to \chi {\gamma }^{\prime }\to \psi \gamma {\gamma }^{\prime }\to {\mu }^{+}{\mu }^{-}\gamma {\gamma }^{\prime }$ are calculated for $S_{\chi }=0, 1, 2$. In a nonrelativistic quark model the ratio of the partial rates $\frac{{\Gamma }_{M2\mathrm{}}}{{\Gamma }_{E1\mathrm{}}}$ can be calculated and is independent of the shape of the central binding potential. This ratio is of the order of ${\mathrm{}(\mathrm{p}\mathrm{h}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}/\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{k}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s})\mathrm{}}^2$ and is numerically ≲0.0025. This supports the use of the dipole approximation for the radiation. The use of Cartesian tensors simplifies the determination of the angular distributions significantly.