Primary Populations of Metastable Antiprotonic ${}^{\mathrm{4}}\mathrm{H}\mathrm{e}$ and ${}^{\mathrm{3}}\mathrm{H}\mathrm{e}$ Atoms

Initial distributions of metastable antiprotonic ${}^{\mathrm{4}}\mathrm{H}\mathrm{e}$ and ${}^{\mathrm{3}}\mathrm{H}\mathrm{e}$ atoms over principal ($n$) and angular momentum ($\ell$) quantum numbers have been deduced using laser spectroscopy experiments. The regions $n=37–40$ and $n=35–38$ in the two atoms account for almost all of the observed fractions [$(3.0\pm 0.1)\%$ and $(2.4\pm 0.1)\%$] of antiprotons captured into metastable states.

Figure 1

Energy level diagrams of $\overline{p}{{}^{\mathrm{4}}\mathrm{H}\mathrm{e}}^{+}$ and $\overline{p}{{}^{\mathrm{3}}\mathrm{H}\mathrm{e}}^{+}$ atoms. Wavelengths of the studied transitions are indicated in nanometers. The one at $\lambda =670.8\mathrm{n}\mathrm{m}$ was not observed.

Figure 2

Three delayed annihilation time spectra of $\overline{p}{{}^{\mathrm{4}}\mathrm{H}\mathrm{e}}^{+}$ with annihilation spikes of the transition $(n,\ell )=(33,32)\to (32,31)$ induced at $t_1=1.4\mu \mathrm{s}$ (a), $5.4\mu \mathrm{s}$ (b), and $10.4\mu \mathrm{s}$ (c).

Figure 3

Time evolutions of the populations in 12 $\overline{p}{{}^{\mathrm{4}}\mathrm{H}\mathrm{e}}^{+}$ [filled circles with error bars in (a)–(l)] and eight $\overline{p}{{}^{\mathrm{3}}\mathrm{H}\mathrm{e}}^{+}$ [filled triangles in (m)–(t)] states. The best fit of a cascade model is shown in solid lines.

Figure 4

Measured delayed annihilation time spectra of $\overline{p}{}^{\mathrm{4}}\mathrm{H}\mathrm{e}$, compared with simulated spectra for cases where the states are populated up to $n_{\mathrm{m}\mathrm{a}\mathrm{x}}=39$ (dashed lines), $40$ (solid lines), $41$ (dot-dashed lines), and $50$ (dotted lines).

Figure 5

Measured distributions of primary populations in $\overline{p}{{}^{\mathrm{4}}\mathrm{H}\mathrm{e}}^{+}$(filled circles with error bars) and $\overline{p}{{}^{\mathrm{3}}\mathrm{H}\mathrm{e}}^{+}$ (filled triangles). Theoretical $\overline{p}{{}^{\mathrm{4}}\mathrm{H}\mathrm{e}}^{+}$populations derived from diabatic state [20] (solid lines) and semiclassical coupled-channel [21] (dashed lines) calculations are shown.