Intensity and the angular and momentum distributions of pions and positrons emitted from a nucleus in proton decay

Perturbation theory in the Hamiltonian of the decay p → π0+e+ is used to study the decay of bound protons accompanied by the emission of pions from the nucleus. The pion-nucleus interaction is described using the optical model. For the case of the quasi-free decay of protons in the 16O nucleus we obtain the pion and positron emission-angle distributions and the pion momentum spectra, which can be useful in setting up correlation experiments to search for proton instability. It is shown that the shape of the curves is determined mainly by the momentum distribution of the nucleons in the nucleus. The pion interaction with the nucleus leads to a decrease of the probability for the emission of correlated particles by roughly a factor of 3 in the emission-angle range 150--1800 and the total probability for pion emission from the nucleus is decreased by roughly a factor of 1.5