Isospin bounds for energy partition in $\overline{\e}$ and $\overline{N}$ annihilation

In reactions such as ee to anything, NN to anything, the final state (neglecting secondary isospin violating decays) is customarily supposed to have isospin zero or one. It is shown that for such states the average fraction (X) of the energy carried away by neutral pions is bounded by X<(9+ square root 41)/20 approximately=0.77, when I/sub 3/=0 (e.g., for ee, pp, nn) and by X>(11- square root 41)/40 approximately=0.115, when I/sub 3/=+or-1 (e.g., for pn or np). (4 refs).