Stability of Relativistic Matter via Thomas-Fermi Theory
  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. 
E. H. Lieb, M. Loss, H. Siedentop