Test of $\overline{\mbox N}$ N potential models: Isospin relations in $\overline{\mbox p}$ d annihilations at rest and the search for quasinuclear bound states

We have determined branching ratios for antiproton annihilations at rest on protons or neutrons in liquid deuterium which we compare to frequencies of isospin-related processes in antiproton-proton annihilations. Using the annihilation rates into $\pi^0\pi^0$ and $\pi^-\pi^0$ where the annihilation took place on the proton or neutron, respectively, we discuss the fraction of S-wave and P-wave annihilation in liquid D $_2$ . The frequencies for $\pi^-\omega$ and $\rho^-\pi^0$ , and $\pi^-\eta$ and $\pi^-\eta'$ and the corresponding frequencies for $\overline{\mbox p}$ p annihilations are used to determine isoscalar and isovector contributions to the protonium wave function. The isospin decomposition of the annihilating $\overline{\mbox p}$ p system in the $^3$ S $_1$ or $^1$ S $_0$ state is consistent with both, pure $\overline{\mbox p}$ p initial wave function and with the predictions of $\overline{\mbox N}$ N potential models. For the $^3$ P $_0$ state of the $\overline{\mbox p}$ p atom we find consistency with a pure $\overline{\mbox p}$ p system at annihilation while $\overline{\mbox N}$ N potential models predict large $\overline{\mbox n}$ n contributions. We observe $\rho$ - $\omega$ interference in $\overline{\mbox p}$ p $\rightarrow \pi^+\pi^-\eta$ and $\pi^+\pi^-\pi^0$ annihilation which we compare to $\rho$ - $\omega$ interference in $e^+e^-$ annihilation. The interference patterns show striking similarities due to similar phase relations; the interference magnitude depends on the $\omega$ - $\rho$ production ratio. The similarity of the phase in all 3 data sets demonstrates that isovector and isoscalar parts of the protonium ( $\overline{\mbox p}$ p atomic) wave function are relatively real, again in conflict with $\overline{\mbox N}$ N potential models. The annihilation rate for $\overline{\mbox p}$ d $\rightarrow$ K $^-$ K $^0$ p confirms the dominance of the isovector contribution to $\overline{\mbox N}$ N $\rightarrow$ K $\overline{\mbox K}$ annihilations. No complications due to initial state interactions are required by the data. Furthermore, we searched for narrow quasinuclear bound states close to the $\overline{\mbox N}$ N threshold, also predicted by $\overline{\mbox N}$ N potential models, but with negative outcome. We conclude that $\overline{\mbox N}$ N potential models are not suited to provide insight into the dynamics of the annihilation process.