In this paper we obtain an estimate for the Thomas{Fermi density which plays a role in the analysis of the atomic energy asymptotics. Such estimate has obvious number{theoretic features related to the radial symmetry of a certain Schrr odinger operator, and we use number{theoretic methods in our proof. From the technical viewpoint, we also simplify and improve some of the original estimates in ...

Using Thomas-Fermi-Dirac equation within the exchange-correlation scheme and a Z-dependent trial solution, the ground state binding energy for neutral, positively, and negatively charged atoms are calculated. Comparing to the results obtained in earlier works, the values of the binding energy estimated here for both light and heavy atoms agree nicely with the Hartree-Fock values. We have also c...

A Thomas-Fermi-Weizsäcker type theory is constructed, by means of which we are able to give a relatively simple proof of the stability of relativistic matter. Our procedure has the advantage over previous ones in that the critical value of the fine structure constant, α, is raised to 0.77 (recall that the critical value is known to be less than 2.72). When α = 1/137, the largest nuclear charge ...

In this paper, a newly proposed analytical scheme by the authors namely the improved di erential transform method is employed to provide an explicit series solution to the Thomas Fermi equation. The solution procedure is very straightforward, requiring merely elementary operations together with di erentiation, and ends up in a recursive formula involving the Adomian polynomials to a ord the unk...