Nuclear critical charge for two-electron ion in Lagrange mesh method

Abstract

The Schroedinger equation for two electrons in the field of a charged fixed center $Z$ is solved with the Lagrange mesh method for charges close to the critical charge $Z_{cr}$. We confirm the value of the nuclear critical charge $Z_{cr}$ recently calculated in Estienne et al. {\em Phys. Rev. Lett. \bf 112}, 173001 (2014) to 11 decimal digits using an inhomogeneous (non-uniform) three-dimensional lattice of size $70\times 70\times 20$. We show that the ground state energy for H${}^{-}$ is accurate to 14 decimals on the lattice $50\times 50\times 40$ in comparison with the highly accurate result by Nakashima-Nakatsuji, {\it J. Chem. Phys. \bf 127}, 224104 (2007).

6 pages, no figures

References in corpus (3)

• Dipole transitions in the bound rotational-vibrational spectrum of the heteronuclear molecular ion HD${}^{+}$
• Quadrupole transitions in the bound rotational-vibrational spectrum of the deuterium molecular ion
• Quadrupole transitions in the bound rotational-vibrational spectrum of the tritium molecular ion

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• Three-body quantum Coulomb problem: analytic continuation
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• Helium-like ions in $d$-dimensions: analyticity and generalized ground state Majorana solutions
• Ultra-Compact accurate wave functions for He-like iso-electronic sequences and variational calculus. IV. Spin-singlet states $(1sns)$ $n{}^{1}S$ family of the Helium sequence