The table displays the uncorrected fit results u _{mathrm{HF}}^mathrm{u} for the fitting of the raw data, together with the reduced χ<sup>2</sup>/<em>ndf</em> and ν<sub>HF</sub> after inflating the errors of the individual data points by sqrt{chi ^2/ndf}

<p><b>Table 1.</b> The table displays the uncorrected fit results \nu _{\mathrm{HF}}^\mathrm{u} for the fitting of the raw data, together with the reduced χ<sup>2</sup>/<em>ndf</em> and ν<sub>HF</sub> after inflating the errors of the individual data points by \sqrt{\chi ^2/ndf}. The fit transition frequencies are displayed for the two different fitting methods, ASF and ISF. At higher resonance, the frequency points differed slightly between 2010 and 2011. These data can only be combined in the averaging over all single scans. The microwave power for the 11.157 GHz resonance was further lower by about 2.5 W compared to 2011. Therefore, the values obtained by the ISF method were used as final results.</p> <p><strong>Abstract</strong></p> <p>In this work, we describe the latest results for the measurements of the hyperfine structure of antiprotonic <sup>3</sup>He. Two out of four measurable super–super-hyperfine (SSHF) transition lines of the (<em>n</em>, <em>L</em>) = (36, 34) state of antiprotonic <sup>3</sup>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 <sup>3</sup>He (Friedreich <em>et al</em> 2011 <em>Phys. Lett.</em> B <strong>700</strong> 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<sub><em>e</em></sub> = 3.41 ± 0.62 MHz and an inelastic collision rate of γ<sub><em>i</em></sub> = 0.51 ± 0.07 MHz.</p>