The electronic specific heat and X-ray absorption of metals, and some other properties related to electron bands

According to the electron theory of metals the energies of the possible stationary states of the electrons in a metal form a continuum; it is usual to denote by N(E) dE the number of such states with energies between E and E+dE per unit volume. In a metal at the absolute zero of temperature all states are occupied up to a maximum energy E=ζ0. It is the purpose of this note to discuss the quantity N(E) in connexion with the crystal structure, specific heat and X-ray absorption spectra of metals.