Highly negative crystal ions in a Thomas–Fermi ab initio theory with exchange

Abstract

The existence of solutions describing highly negative ions together with the charge distribution and the electron affinity of these ions are examined in the case of the ions bound with the other atomic species, for example in a crystal lattice. The examination is done on the basis of a Thomas–Fermi statistical theory with exchange. The electrons obey the Fermi statistics and no empirical parameters are used in calculations. It is shown that solutions for the statistical ions whose nuclear charge is Z may exist in the presence of the amount of the negative charge equal at least to (3/2)Z. A similar existence of solutions for highly negative ions is obtained on the basis of a modified Englert–Schwinger statistical theory of the atomic systems.