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- W2899465026 abstract "The second (unphysical) critical charge in the 3-body quantum Coulomb system of a nucleus of positive charge $Z$ and mass $m_p$, and two electrons, predicted by F~Stillinger has been calculated to be equal to $Z_{B}^{infty} = 0.904854$ and $Z_{B}^{m_p} = 0.905138$ for infinite and finite (proton) mass $m_p$, respectively. It is shown that in both cases, the ground state energy $E(Z)$ (analytically continued beyond the first critical charge $Z_c$, for which the ionization energy vanishes, to $Re Z < Z_c$) has a square-root branch point with exponent 3/2 at $Z=Z_B$ in the complex $Z$-plane. Based on analytic continuation, the second, excited, spin-singlet bound state of negative hydrogen ion H${}^-$ is predicted to be at -0.51554 a.u. (-0.51531 a.u. for the finite proton mass $m_p$). The first critical charge $Z_c$ is found accurately for a finite proton mass $m_p$ in the Lagrange mesh method, $Z^{m_p}_{c} = 0.911, 069, 724, 655$." @default.
- W2899465026 created "2018-11-09" @default.
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- W2899465026 date "2015-06-23" @default.
- W2899465026 modified "2023-09-27" @default.
- W2899465026 title "The H${}^-$ type isoelectron system: second critical charge, second bound state of H${}^-$ and analytic continuation" @default.
- W2899465026 hasPublicationYear "2015" @default.
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