﻿S4t2 Mr. J. H. Van Vleck on the normal Helium Atom 



In this paper and its predecessor we have discussed the 

 relation of statistical theory to thermodynamics in detail 

 only for a rather limited class of systems, though it is 

 practically the class in which alone success has been attained 

 by anyone. It is at least doubtful how much further the 

 combinatory calculus can be pushed ; as soon as the multi- 

 nomial theorem ceases to apply (as it would for imperfect 

 gases) great difficulties are encountered in our method, 'but 

 these difficulties are largely inherent in such problems. 

 In spite of these limitations, it would appear that the 

 potentialities of the method are by no means exhausted. 



LXXII. The normal Helium Atom and its relation to the 

 Quantum Theory. By J. H. Van Vleck, Jefferson 

 Physical Laboratory, Harvard University, Cambridge, 

 Mass. (U.S.A.).* 



PART I. of this paper is of a non-mathematical character, 

 and is concerned with the difficulties associated with 

 finding a satisfactory quantum theory model of normal 

 helium. After a resume of existing models, a study is made 

 of the model suggested by Dr. E. C. Kemble in which the 

 two electrons are arranged with axial symmetry, the one 

 symmetrical type whose energy has not yet been computed. 

 As the result of a rather laborious calculation, a value is 

 obtained for the ionization potential of this model which is 

 not in agreement with experiment, the discrepancy being 

 slightly greater than for the Bohr model. 



Because of the failure of this model with axial symmetry, 

 it does not seem possible to devise a satisfactory symmetrical 

 model of helium based on the conventional quantum theory 

 of atomic structure, and the remainder of Part I. therefore 

 deals with the modifications in the ordinary conception of 

 the quantum theory or of the electron which may be 

 necessary in order to escape from this dilemma. Two 

 suggestions on reformulation of the quantum conditions made 

 by Lungmuir are criticized, and a frankly empirical rule for 

 determining the stationary states is suggested which leads lo 

 approximately the correct energy values for ihe helium 

 atom, the hydrogen molecule, and the positively charged 



* Communicated by Prof. Lyman. 



