Effect of screening due to free mobile charges on the binding energy of an H- ion

A calculation of the binding energy of a negative hydrogen ion (H-), defined as the energy required to remove one of the two electrons from the H- ion to infinity in the presence of other free mobile charges, is reported. The effective interactions between the constituent particles of H- ion are assumed to be described by Dingle-Mansfield potentials. This potential is valid for a Fermion gas of an arbitrary degeneracy. The variation of the binding energy of an H- ion as a function of the screening parameter delta is calculated, using a variational approach. It is shown that the binding energy of an H- ion goes to zero for adelta = 0.87, where a is the Bohr radius. The binding energy of a hydrogen atom itself in the presence of free mobile charges goes to zero for adelta = 1.2. The relative significance of these two values is discussed