High-statistics measurements of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>Λ</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>Σ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mi mathvariant="normal">c</mml:mi><mml:mo>.</mml:mo><mml:mi mathvariant="normal">c</mml:mi><mml:mo>.</mml:mo><mml:mn/></mml:math>reactions at threshold (2000)

We report on precision measurements of the cross sections for the reactions $\overline{p}\stackrel{\ensuremath{\rightarrow}}{p}\overline{\ensuremath{\Lambda}}\ensuremath{\Lambda},$ $\overline{p}\stackrel{\ensuremath{\rightarrow}}{p}\overline{\ensuremath{\Lambda}}{\ensuremath{\Sigma}}^{0},$ and $\overline{p}\stackrel{\ensuremath{\rightarrow}}{p}{\overline{\ensuremath{\Sigma}}}^{0}\ensuremath{\Lambda}$ in the region below 5 MeV excess kinetic energy above reaction threshold. For the $\overline{p}\stackrel{\ensuremath{\rightarrow}}{p}\overline{\ensuremath{\Lambda}}\ensuremath{\Lambda}$ measurement, the data represent a third and definitive scan through the threshold region by this experiment. Improvements in the detector system and analysis techniques, coupled with greatly increased statistics, have negated the question of the existence of a near-threshold resonance as had been indicated in our earlier, lower-statistics studies. The high statistics permit the first extraction of the polarization information at these low energies. We also report the first measurement of the cross section for the complementary reactions $\overline{p}\stackrel{\ensuremath{\rightarrow}}{p}\overline{\ensuremath{\Lambda}}{\ensuremath{\Sigma}}^{0}+\mathrm{c}.\mathrm{c}.$ at excess energies up to 2.5 MeV. This allows a comparison of the onset of $\overline{\ensuremath{\Lambda}}\ensuremath{\Lambda}$ production to that of $\overline{\ensuremath{\Lambda}}{\ensuremath{\Sigma}}^{0}$ and ${\overline{\ensuremath{\Sigma}}}^{0}\ensuremath{\Lambda}.$ The data show no evidence for near-threshold resonance structures in either reaction channel. Further, the $\overline{p}\stackrel{\ensuremath{\rightarrow}}{p}\overline{\ensuremath{\Lambda}}{\ensuremath{\Sigma}}^{0}+\mathrm{c}.\mathrm{c}.$ reactions exhibit a larger P-wave fraction close to threshold compared to $\overline{p}\stackrel{\ensuremath{\rightarrow}}{p}\overline{\ensuremath{\Lambda}}\ensuremath{\Lambda}.$