A forgotten publication of Ettore Majorana on the improvement of the Thomas-Fermi statistical model

Ettore Majorana proposed an important improvement to the Thomas-Fermi statistical model for atoms, with a communication at the general meeting of the Italian Physical Society, held in Rome, on December 29th, 1928, regularly published on Nuovo Cimento. This communication did not receive any mention, neither in the numerous publications of Fermi and his associates on the subject, nor in the further reconstructions of the life and activity of Ettore Majorana. The Majorana proposal was not accepted by Enrico Fermi for years, and forgotten. However, it was finally exploited, without reference, in the 1934 conclusive paper by Fermi and Amaldi on the statistical model for atoms. We analyze the improved model proposed by Majorana, with the help of unpublished notes, kept in the Majorana Archives in Pisa. Moreover, we trace the path leading Fermi to the eventual late acceptance of Majorana improvement, also with the help of the material in Fermi Archives in Pisa. The conclusion is that Ettore Majorana played an effective leadership in Rome for the very conceptual formulation of the statistical model for atoms.