Ground state of the hydrogen negative ion

Based on recently developed variational many-body Schr\"{o}dinger equation for electrons with Coulomb interactions [1], we provide first numerical results for the ground state electron structure of the hydrogen negative ion. It is shown that Fermi-Teller promotion effect together with non-adiabatic screening effects due to the Pauli's exclusion principle are responsible for the weak binding of the anion. The calculated ionization potential $J=-1/2 - 2 \lambda + \langle 1/r_{12} \rangle$ of the hydrogen negative ion is compared with the experiment, where $\lambda$ is the mean binding energy per one electron in the ground state.\\[0pt] [1] B.~D.~Obreshkov , Phys.~Rev.~A {\bf 78}, 032503 (2008).