The delayed annihilation time spectra (DATS) of antiprotonic helium atoms have been studied in isotopically pure low temperature ^3He and ^4He gas at various densities. The DATS taken at 5.8~K and 400~mbar are very similar in shape except for i) a small difference in the time scale and ii) the presence of a distinct fast decay component in the case of ^3He. The ratio of overall trapping times (mean lifetimes against annihilation), R = T_{\mathrm{trap}}(\mbox{^{4}He})/T_{\mathrm{trap}}(\mbox{^{3}He}), has been determined to be 1.144 \pm 0.009, which is in good agreement with a theoretical estimate yielding R = [(M^*(\mbox{\overline{\mathrm{p}}}\mbox{^{4}He})/ M^*(\mbox{\overline{ \mathrm{p}}}\mbox{^{3}He})]^2=1.14, where M^* denotes the reduced mass of the \mbox{\overline{\mathrm{p}}}\mbox{He^{++}}\ system. The presence of a short-lived component with a lifetime of (0.154\pm 0.007)\ \mbox{\mus} in the case of \mbox{^{3}He}\ suggests that the \mbox{\overline{\mathrm{p}}}\mbox{^{3}He^{+}}\ atom has a state of intermediate lifetime on the border between a metastable zone and an Auger-dominated short-lived zone. The fraction of antiprotons trapped in metastable states at 5.8~K and 400~mbar is lower by 22.2(4)\% for \mbox{^{3}He}\ than for \mbox{^{4}He}. All the data can be fitted fair
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