58 N. F. Mott N(E) FIGURE 1.(a)Intensity of X-ray emission spectra plotted against energy in volts for certain ght metals ( from H. M. O'Bryan h. w. B, Skinner(1934), Phys. Rev. 45, 379 (b)Theoretical form of bands long as the transition was to the Lnr state(of p-symmetry)so that no selection rule prohibited the transition from the s-like states at the bottom of the band. On the other hand, what was observed as as in figure la. The sharp cut-off at high energies was in fact very marked, as was its broadening at high temperatures pre dicted by Fermi-Dirac statistics, but the low energy limit showed a marked tail In a paperd published in 1934, Jones, Skinner and I put forward the explanati of the fact that the term e/r1 did not destroy the sharp cut-off, but did affect the low-energy limit: an electron excited just above the Fermi energy(by an energy AE)and could interact (collide)with an electron just below it, so that both changed their states, by a kind of Auger effect. but the number of electrons with which it could do this was proportional to AE, so the lifetime of such an excited electron was long, varying(as we found)as 1/(AE)2. This tended to infinity as AE became small, so the Fermi energy was sharp, even when electron-electron interaction was Lken into account. On the other hand, a ',in the Fermi distribution near the bottom of the band could be filled by a process in which any electron with above it moved down into it, giving up its energy to another electron. Thus the lifetime would be short, and the electron's energy according to the uncertainty principle would be weakly defined, leading to the observed tail There are two comments that I should like to make on this. The first is that Sommerfeld's prediction of a linear electronic specific heat, and equally Jones' theory of alloys, really did imply that the idea of a sharp Fermi energy was some thing that corresponded to physical reality and not just a consequence of neglecting the interaction between electrons. But it needed the visual evidence provided by Skinners work to make me(at any rate)see that there was something here that we really had to explain. The second is that we failed to go on and show that the Fermi surface was a real concept. This awaited the work of Landau(e)(1956), and its exper nental determination(for copper, @3) by Pippard in 1957)and the development of the de Haas-van Alphen effect for the purpose, mainly by Shoenberg, t together f An excellent account of experimental methods of measuring the Fermi surface is give by N. w. Ashcroft N. D. Mermin, Solid state physics, (New York: Holt, Rinehart Winston, 1976),p,263-281