Proton-Antiproton Annihilation in Protonium

Abstract

Using the model for the nucleon-antinucleon interaction proposed by Ball and Chew, we have calculated the capture rates for the various eigenstates of protonium—the bound system of a proton and an antiproton. It is found that these rates depend sensitively on spin, isotopic spin, and total angular momentum eigenvalues of protonium, not just on orbital angular momentum, as is usually assumed. The average capture rates for the $\mathrm{nS}$ and $\mathrm{nP}$ states are $5.3\times \frac{{10}^{18}}{n^3}$ and $4.3\times \frac{{10}^{14}}{n^3}$ ${\sec }^{-1\mathrm{}}$, respectively. This $P$ capture rate is two orders of magnitude larger than in the case of the ($K^{-}-p$) atom because of the relatively long range of interaction in the Ball-Chew model. The problem of the Stark effect collisions, studied by Day, Snow, and Sucher in connection with the ($K^{-}-p$) atom, is therefore re-investigated and at the same time we have considered certain important effects which were not considered by these authors. Rough calculations indicate that for protonium also the capture will take place predominantly from $S$ states.