Majorana: From atomic and molecular, to nuclear physics

In the centennial of Ettore Majorana's birth (1906-1938?), we re-examine some aspects of his fundamental scientific production in atomic and molecular physics, including a not well known short communication. There, Majorana critically discusses Fermi's solution of the celebrated Thomas-Fermi equation for electron screening in atoms and positive ions. We argue that some of Majorana's seminal contributions in molecular physics already prelude to the idea of exchange interactions (or Heisenberg-Majorana forces) in his later works on theoretical nuclear physics. In all his papers, he tended to emphasize the symmetries at the basis of a physical problem, as well as the limitations, rather than the advantages, of the approximations of the method employed.