Electron Theory of the Metallic State. 749 



order unity, or perhaps two or three times greater than 

 unity. We can regard this fact as a further support for 

 our theory. As is well known, it is a rather great difficulty 

 for the classical electron theory. 



§ 4. Potential Energy of the Metallic Space-lattice. 



In full analogy with the theory of Born and Lande> 

 the work done in bringing an electron or an atom from 

 infinity to their place in the lattice is —€(j) e or 4-e</> , where 

 the potential functions cf) e and </> a due to the surrounding- 

 electrons and atoms are given by , 



^STST ^ 



where R denotes the distance between an electron and 

 its nearest atomic neighbour, so that for a metal of the 

 type NaCl 



"A 



2W P ' < 3 > 



The terms ~ arise from the forces between electrons 



and atoms regarded as point charges. The terms ^ x arise 



from the repelling forces on an electron from the nearest 

 atom-ions or on an atom from the nearest electrons, due 

 to the arrangement of a number of electrons around and at 

 an appreciable distance from a positive nucleus in the atom. 



The term — jyix arises from the attracting forces on the 



positive charge of the atom-ions caused by the mentioned, 

 arrangement of the electrons in the nearest atoms, and 

 vice versa. For <j> e there is, of course, no term corre- 

 sponding to this. A term arising from the repelling forces 

 between the neutral parts of the atoms is to be neglected, 

 if the atoms' dimensions are sufficiently smaller than their 

 distances. 



The constant a may be calculated by a method of 

 Madelung, and is for a lattice of the simple type NaCl, 

 which we have adopted for our trial. 



a - 1-742 e (4) 



The constants b and l> are deduced from the condition 



k-v; 



