On the Constitution of Metallic Sodium. II

The present work represents an extension to a previous development by the same authors, on the theory of metallic sodium. In the first part of this paper a completely self-consistent solution of Fock's equations for the sodium lattice is carried through indirectly, this being the approximation in which one-electron functions are employed. The question of the correlations between electrons with parallel spin is investigated quantitatively and the Fermi "zero-point energy" is calculated using the proper effective field. The results show that the electrons behave almost exactly as if they were entirely free, the binding energy being 9 kg cal and the lattice constant 4.86A, as compared with the observed values 26.9 kg cal and 4.23A. To complete the picture, the correlations between electrons with anti-parallel spins are investigated in the latter part, since these are not included in the Fock picture. A general discussion of this question is presented and a quantitative treatment of its effect is made which yields a new binding energy of 23.2 kg cal and a lattice constant of 4.75A. The source of the remaining discrepancy is discussed.