Resonance states of unnatural parity in positronic atoms

Abstract

Resonance states of unnatural parity ${P}^{e}$ and ${D}^{o}$ in the positronic atoms ${e}^{+}\text{H}$ and ${e}^{+}{\text{He}}^{+}$ are calculated and discussed in detail in terms of the coupled-channel scheme in the hyperspherical coordinate system. New resonances emerge in the analysis of the eigenphase sum. The time-delay matrix eigenvalues prove to be useful in unraveling overlapping resonances. Many resonances are identified as belonging to some infinite series of Feshbach resonances supported by an adiabatic hyperspherical potential. Some Feshbach resonances independent of any infinite series are also identified to be supported by an adiabatic potential. The positions and widths of higher-lying members of the infinite series are known to be expressible as geometric progressions. Their common ratios are obtained theoretically, including those for the series failing to appear in the present calculation. Several resonances unassociated with a minimum in any adiabatic potential are found in the region of avoided crossing. The diabatic picture is invoked for understanding the resonance mechanism, the resonance energy, and the trend in the widths for all those exceptional cases. The lowest-order $2\ensuremath{\gamma}$ and $3\ensuremath{\gamma}$ pair annihilation in these unnatural-parity states is shown to be forbidden.