The threshold laws for electron-atom and positron-atom impact ionization

The Coulomb-dipole theory is employed to derive a threshold law for the lowest energy needed for the separation of three particles from one another. The study focuses on an electron impinging on a neutral atom, and the dipole is formed between an inner electron and the nucleus. The analytical dependence of the transition matrix element on energy is reduced to lowest order to obtain the threshold law, with the inner electron providing a shield for the nucleus. Experimental results using the LAMPF accelerator to produce a high energy beam of H- ions, which are then exposed to an optical laser beam to detach the negative H- ion, are discussed. The threshold level is found to be confined to the region defined by the upper bound of the inverse square of the Coulomb-dipole region. Difficulties in exact experimental confirmation of the threshold are considered.