Stability of Relativistic Matter via Thomas-Fermi Theory

TL;DR

This paper introduces a Thomas-Fermi-Weizsaecker type theory to prove the stability of relativistic matter, improving bounds on the fine structure constant and nuclear charge, with a simpler approach inspired by Lieb-Thirring methods.

Contribution

It develops a new theoretical framework that simplifies the proof of relativistic matter stability and extends the bounds on key physical constants.

Findings

Critical alpha value raised to 0.77

Maximum nuclear charge for alpha=1/137 is 59

Method parallels Lieb-Thirring proof, offering new perspective

Abstract

A Thomas-Fermi-Weizsaecker 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, alpha, is raised to 0.77 (recall that the critical value is known to be less than 2.72). When alpha =1/137, the largest nuclear charge is 59 (compared to the known optimum value 87). Apart from this, our method is simple, for it parallels the original Lieb-Thirring proof of stability of nonrelativistic matter, and it adds another perspective on the subject.