Relativistic energy shifts of negative-ion bound states: the rational function Thomas–Fermi potential model

Abstract

The rational function Thomas–Fermi (RTF) potential recently used for describing electron–atom scattering interactions is investigated as to its bound (negative-ion) states. Although the (static) RTF potential may account for some relativistic and many-body corrections, this study focuses on (relativistic) dynamical aspects of the ‘extra’ electron in the negative-ion bound states. Some exotic states near threshold are shown to exist in the Dirac equations but not in the Schrödinger equation that neglects the spin of the ‘extra’ electron. Results are presented for the two large atomic charge numbers Z = 54 and Z = 64.