Relativistic total energy and chemical potential of heavy atoms and positive ions

Abstract

The relativistic Thomas-Fermi theory, with a finite nucleus, is used to study the variation of the chemical potential mu with atomic number Z and number of electrons N(N<or=Z). This is done by solving a suitable dimensionless form of the differential equation for the self-consistent field for the semiclassical radius of the positive ions. Integrating the relation mu =( delta E/ delta N)Z the difference between the total energy of positive ions and that of the corresponding neutral atom has been obtained. The scaling predictions of Marconi and one of the authors are confirmed by their numerical calculations, since the dependence on the nuclear radius for any reasonable variation of this quantity is of negligible consequence. Finally, attention is given to bringing the first principles calculation of the relativistic Thomas-Fermi total energy of neutral atoms which they have carried out into contact with the Dirac-Fock results of Desclaux. To do so, it proves necessary to correct the energy contributions of the K- and L-shell electrons by means of the Sommerfeld formula, thereby generalising the non-relativistic boundary correction of Scott.