1. Three-body quantum Coulomb problem: Analytic continuation.
- Author
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Turbiner, A. V., Lopez Vieyra, J. C., and Olivares Pilón, H.
- Subjects
THREE-body problem ,COULOMB barriers (Nuclear fusion) ,ANALYTIC continuation ,COULOMB'S law ,IONIZATION energy - Abstract
The second (unphysical) critical charge in the three-body quantum Coulomb system of a nucleus of positive charge and mass , and two electrons, predicted by Stillinger has been calculated to be equal to and for infinite and finite (proton) mass , respectively. It is shown that in both cases, the ground state energy (analytically continued beyond the first critical charge , for which the ionization energy vanishes, to ) has a square-root branch point with exponent 3/2 at in the complex -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 ). The first critical charge is found accurately for a finite proton mass in the Lagrange mesh method, . [ABSTRACT FROM AUTHOR]
- Published
- 2016
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