Electron Density in Interior Far from Metal Surfaces

概要

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This paper deals with the validity of te relation p_1=k_F^3/(3π^2) in an interior of metal, where p_1 is the density of free electrons in the metal and k_F is the Fermi wave number. Both k_F and p_1 are expressed in terms of phase shifts with accuracy of the order in (k_FL_0)^<-2>, where L_0 is the thickness of the metal. In calculation of p_1, the sum of wave functions over a quantum number is approximated by an expansion formula for summation of trigonometrical series but not by the usual integration over the k-space. The relation is proved to be valid to the order (k_FL_0)^<-1> but not valid to the order (k_FL_0)^<-2>. The validity to the order (k_FL_0)^<-1>, however, is suffcient for a confirmation of the validity of the phase shift sum rule for surface problems. The present expression for p_1 to order (k_FL_0)^<-2> shows the usual Friedel oscillation near the surgaces.
社団法人日本物理学会の論文
1974-12-15