Microwave spectroscopic study of the hyperfine structure of antiprotonic $^3$He

In this work we describe the latest results for the measurements of the hyperfine structure of antiprotonic $^3$He. Two out of four measurable super-super-hyperfine {SSHF} transition lines of the $(n,L)=(36,34)$ state of antiprotonic $^3$He 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 $^3$He [S. Friedreich {\it 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 $\gamma_e = 3.41 \pm 0.62$~MHz and an inelastic collision rate of $\gamma_i = 0.51 \pm 0.07$~MHz