The single ionization cross sections for He and H-2 by positron impact
have been measured in the first few eV above threshold and found to e
xhibit a different energy dependence from the corresponding electron r
esults. If the data, between 1 and 3 eV above threshold, are fitted by
a power law, exponents of 1.99 +/- 0.19 and 1.70 +/- 0.11 are obtaine
d for He and H-2, respectively. This agrees qualitatively with extensi
ons of the Wannier theory in that the exponent is larger than for elec
tron impact. The quantitative disagreement with the predicted value of
2.65 might indicate that the range of validity of this theory is smal
ler than expected.