Effects of Fermi motion and secondary particle collisions for proton decay in nuclei

The effects of Fermi motion and secondary particle collisions on the ${\pi }^0{e}^{+}$ produced from proton decay in nuclei are investigated using a Monte Carlo program based on the intranuclearcascade model. The calculations indicate probabilities of 39%, 23%, and 15% for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, and ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$, respectively, for ${\pi }^0$ and $e^{+}$ to emerge simultaneously with angles 180° ± 13°. These probabilities are insensitive to total energy cuts provided $E_T<~0.95M_p$.