A schematic drawing of the laser–microwave–laser method

<p><strong>Figure 1.</strong> A schematic drawing of the laser–microwave–laser method. The dashed arrows indicate the laser transitions between the SHF levels of the radiative decay-dominated state (<em>n</em>, <em>L</em>) = (36, 34) and the Auger-decay-dominated state (37, 33) of \bar{\mathrm{p}}^{3}He<sup>+</sup>. The wavy lines illustrate the microwave-induced transitions between the SSHF levels of the long-lived state.</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>