Many-Body Perturbation Theory for the Hydrogen Negative Ion

Linked-cluster many-body perturbation theory is applied to study the stability of the ground state of the ${\mathrm{H}}^{-}$ ion. A diagrammatic approach is made to analyze the role of various polarization effects. A complete set of states obtained in the $V^{N-1\mathrm{}}$ potential is used to evaluate the diagrams. The total energy of ${\mathrm{H}}^{-}$ is calculated to be -0.027 66 a.u., leading to the binding energy 0.527 66 a.u., in good agreement with the most accurate value, 0.027 75 a.u., due to Pekeris. The result of our investigation shows conclusively the crucial importance of monopole and dipole polarization effects for the stability of this ion in particular and negative ions in general. A comparison with the results from earlier work is also made.