Classical analytical description of negative hydrogen ions

Studies of negative hydrogen ions (NHI), such as, H– and D–, are important from both practical and fundamental points of view. One of the reasons for their practical importance has to do with heating tokamak plasmas by external beams of NHI. Another practical use is the injection of NHI in high-power proton accelerator facilities to enhance their performance. In addition, NHI are also important for studies of opacities of the atmospheres of the Sun and of A-type stars. We present a classical analytical description of NHI in the situation where the underlying hydrogen (or deuterium) atom constitutes a rapid subsystem while the outer electron represents a slow subsystem. We focus on the case where the inner electron is in a circular state, so that the subsystem “nucleus plus inner electron” does not have the average electric dipole moment — in distinction to previous studies where the presence of the average dipole moment was the crucial requirement. By using the separation of rapid and slow subsystems, we show analytically that there is a classical bound state in such system and studied its parameters. In particular, we calculate analytically the primary frequency of the radiation of such system. This could be used for its experimental detection. The states that we found for the above systems could be considered as classical counterparts of the double-excited states of NHI previously studied in the literature in frames of quantum mechanics. The existence of classical counterparts of the double-excited states of NHI is a counterintuitive result.