Expectation values of the $e^{+}\mathrm{He}\left({}^{3}S^e\right)$ system

Close to converged energies and expectation values for $e^{+}\mathrm{He}\left({}^{3}S^e\right)$ are computed using a ground state wave function consisting of 1500 explicitly correlated Gaussians. The best estimate of the $e^{+}\mathrm{He}\left({}^{3}S^e\right)$ energy was $-2.25059508\text{hartree}$, which has a binding energy of $0.00059508\text{hartree}$ against dissociation into $\mathrm{Ps}+{\mathrm{He}}^{+}$. The $2\gamma$ annihilation rate for the spin doublet state was $5.713\times {10}^9{\mathrm{s}}^{-1}$. The estimated annihilation rate with the core ${\mathrm{He}}^{+}$ electron was $2.506\times {10}^6{\mathrm{s}}^{-1}$. The derived enhancement factor for annihilation with the ${\mathrm{He}}^{+}\left(1s\right)$ core was 2.29, just over 10% smaller than the enhancement factor derived from analyses of annihilation during $e^{+}\text{−}{\mathrm{He}}^{+}$ scattering. The diffuse nature of the wave function, with well separated ${\mathrm{He}}^{+}$ and Ps subsystems, is demonstarted to be on the threshold of satisfying the formal criteria that define a quantum halo state.