## This graph summarizes the results for the two measured SSHF transitions u _{mathrm{HF}}^{--} and u _{mathrm{HF}}^{-+} as well as the frequency difference Delta u _{mathrm{HF}}^{pm } (mathrm{E}_{^{prime }10} [6], mathrm{E}_{^{prime }10/^{prime }11}) for the first measurement period in 2010 and the combined result of all data recorded in the years 2010 and 2011

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**Figure 7.** This graph summarizes the results for the two measured SSHF transitions \nu _{\mathrm{HF}}^{--} and \nu _{\mathrm{HF}}^{-+} as well as the frequency difference \Delta \nu _{\mathrm{HF}}^{\pm } (\mathrm{E}_{^{\prime }10} [6], \mathrm{E}_{^{\prime }10/^{\prime }11}) for the first measurement period in 2010 and the combined result of all data recorded in the years 2010 and 2011. It further provides a comparison of these values with the respective theoretical calculations (Korobov [12, 27], Kino [11]). The frequency difference of the experimental data for the 11.157 73 GHz resonance between the first year of measurements and the combined results of all recorded data may be explained by the slightly different microwave power used for the measurement period in 2010 and also by the lower statistics for this transition in the first year.

**Abstract**

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 11.125 48(08) GHz and 11.157 93(13) GHz, with the increased precisions of about 43% and 25%, respectively, compared to our first measurements with antiprotonic ^{3}He (Friedreich *et al* 2011 *Phys. Lett.* B **700** 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 0.032 45(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 γ_{e} = 3.41 ± 0.62 MHz and an inelastic collision rate of γ_{i} = 0.51 ± 0.07 MHz.