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The H${}^-$ type isoelectron system: second critical charge, second bound state of H${}^-$ and analytic continuation | | A.V. Turbiner
; J.C. Lopez Vieyra
; H. Olivares Pilon
; | | Date: |
23 Jun 2015 | | Abstract: | The second critical charge in the 3-body quantum Coulomb system $(Z, e, e)$
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. In both cases, the ground state energy
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, 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 in the
Lagrange mesh method, $Z^{m_p}_{c} = 0.911, 069, 724, 655$. | | Source: | arXiv, 1506.7403 | | Services: | Forum | Review | PDF | Favorites | |
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