Comparison of the Reactionsp+d→H3+π+,p+d→He3+π0as a Test of Charge Independence

The pair of reactions $p+d\to {\mathrm{H}}^3+{\pi }^{+}$ and $p+d\to {\mathrm{He}}^3+{\pi }^0$ have been investigated experimentally to see if the predictions of the theory of charge independence are fulfilled. Because of the low cross section (a few microbarns) and large background (heavy particles emitted at ∼10° lab) the results do not provide as critical a test as might be hoped. We find that there is a 50% chance that the ratio of the reaction cross sections $\frac{(p+d\to {\pi }^{+}+{\mathrm{H}}^3)}{(p+d\to {\pi }^0+{\mathrm{He}}^3)}$ is between 2.0 and 2.6. Charge independence predicts that the ratio should be exactly two. The experimental difficulties would be less at higher proton energies; this method would seem to provide a very stringent test of charge independence if the comparison could be made with sufficient accuracy.