Pion Multiplicity in Nucleon-Antinucleon Annihilation

Abstract

In the annihilation problem we have considered the influence of the Ball-Chew model, according to which, at low energies, only a few of the eigenstates of the nucleon-antinucleon system need be considered. The effect of the selection rules that forbid certain pion multiplicities is thereby examined. The energies considered are 50 Mev, 140 Mev, and 0 Mev in the case of protonium---the bound system of a proton and an antiproton. To obtain the multiplicity, we have used the Fermi statistical model but have introduced Lorentz-invariant phase space, thus defining a new interaction volume. It is found that due to selection rules there is a substantial change in the number distribution of the outgoing pions. At 140 Mev and in the case of protonium the two-pion production is decreased considerably. The zero-prong events for the $p\overline{p}$ annihilation are suppressed by about a factor of two for annihilations at rest in the case of protonium compared to the corresponding events for annihilations in flight. The over-all average multiplicity is unchanged, however. The value of the newly defined interaction volume, in units of Fermi volume, for $p\overline{p}$ and $N\overline{p}$ annihilations (where $N$ denotes an "average" nucleon) should be \ensuremath{\sim}10 in order to fit the observed multiplicities.