  In this work we describe the latest results for the measurements of the
hyperfine structure of antiprotonic helium-3. Two out of four measurable
super-super-hyperfine SSHF transition lines of the (n,L)=(36,34) state of
antiprotonic helium-3 were observed. The measured frequencies of the individual
transitions are 11.12548(08) GHz and 11.15793(13) GHz, with an increased
precision of about 43% and 25% respectively compared to our first measurements
with antiprotonic helium-3 [S. Friedreich et al., Phys. Lett. B 700 (2011)
1--6]. They are less than 0.5 MHz higher with respect to the most recent
theoretical values, still within their estimated errors. Although the
experimental uncertainty for the difference of 0.03245(15) GHz between these
frequencies is large as compared to that of theory, its measured value also
agrees with theoretical calculations. The rates for collisions between
antiprotonic helium and helium atoms have been assessed through comparison with
simulations, resulting in an elastic collision rate of gamma_e = 3.41 +- 0.62
MHz and an inelastic collision rate of gamma_i = 0.51 +- 0.07 MHz.
