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- W1800010310 abstract "The second (unphysical) critical charge in the 3-body quantum Coulomb system $((Z,m_p), (e,m), (e,m))$ 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 $m_p$ of charge $Z$, respectively. It is shown that in both cases, the ground state energy $E(Z)$ (analytically continued beyond the critical $Z_c$ to $Z < Z_c$) 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 -0.515541 a.u. (-0.515311 a.u. for the proton mass $m_p$). The first critical charge for which the ionization energy vanishes is found for a finite proton mass $m_p$ in the Lagrange mesh method, $Z^{m_p}_{c} = 0.911, 069, 724, 655$." @default.
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- W1800010310 date "2015-06-23" @default.
- W1800010310 modified "2023-09-27" @default.
- W1800010310 title "Two-electron sequence: second critical charge, second bound state of H${}^-$ and analytic continuation" @default.
- W1800010310 hasPublicationYear "2015" @default.
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