LXXIX. Energy band shapes and band widths in metals

Abstract The density of states curve given by the recent theory of Bohm and Pines is compared with those of the Sommerfeld and Hartree-Fock theories. It is found that the Bohm and Pines curve shows a rudimentary ‘tail’, and the effect of this on the interpretation of the experimental soft x-ray emission data is discussed, with particular reference to the metals sodium, magnesium and aluminium. Although the Bohm and Pines band width is a great improvement on that of the Hartree-Fock theory, it is still much larger than the observed width. It is suggested that this may be partly due to the neglect of the short-range correlation energy: a lower bound to the narrowing of the band from this cause is calculated, and found to be 0·1 ev for sodium.