Second Bound State of PsH

The existence of a second bound state of PsH that is electronically stable and also stable against positron annihilation by the normal $2\gamma$ and $3\gamma$ processes is demonstrated by explicit calculation. The state can be found in the ${}^{2,4}S^o$ symmetries with the two electrons in a spin-triplet state. The binding energy against dissociation into the $\mathrm{H}(2p)+\mathrm{Ps}(2p)$ channel was $7.03\times {10}^{-4}\mathrm{hartree}$. The dominant decay mode of the states will be radiative decay into a configuration that autoionizes or undergoes positron annihilation. The NaPs system of the same symmetry is also electronically stable with a binding energy of $1.514\times {10}^{-3}\mathrm{hartree}$ with respect to the $\mathrm{Na}(3p)+\mathrm{Ps}(2p)$ channel.

Figure 1

The binding energy, $\epsilon =-(⟨E⟩+0.1875)$, of the ${}^{2,4}S^o$ state of PsH as a function of $J$. The directly calculated energy is shown as the solid line while the $J\to \infty$ limits using Eq. (4) with 1, 2, 3, or 4 terms are shown as the dashed lines. The $\mathrm{H}(2p)+\mathrm{Ps}(2p)$ dissociation threshold is shown as the horizontal solid line.

Figure 2

The binding energy (in units of hartree) of the ${}^{2,4}S^o$ state of NaPs as a function of $J$. The directly calculated binding energy is shown as the solid line while the $J\to \infty$ limits using Eq. (4) are shown as the dashed lines. The $\mathrm{Na}(3p)+\mathrm{Ps}(2p)$ threshold is shown as the horizontal solid line.