598 BELL SYSTEM TECHNICAL JOURNAL 



by fi{K){\ — Pe{K)) the number of cases in which this happens. 

 The least which we can take for granted is some general relation of 

 the form, 



Pt^MK)-P.iK) -^MK){1 - P.{K)), (20) 



and the variations of /i and f^ may contribute still further to blotting 

 out all signs of the hypothetical vertical rise in the ideal curve. More- 

 over, /2 might be appreciable at values of K smaller than neVm, thus 

 blotting out every sign of the critical energy-value at which entry 

 commences. 



Thus with regard to the second prediction, the situation is this: 

 the experimental curves of number-of-observed-transmutations vs. 

 kinetic-energy-of-impinging-particles rise so smoothly and so gradually 

 from the axis as to give not the slightest support to the idea that 

 entry into the nucleus commences suddenly at a critical value of K; 

 moreover, transmutation commences to be appreciable — -for several 

 elements, at least — when K is still so small that K/ne is only a small 

 fraction of the least value which can reasonably ^* be ascribed to Vm, 

 in view of what we know from alpha-particle-scattering about the 

 circumnuclear fields of these or similar elements. This again might be 

 due to the hypothetical effect to which the term fiiK) in the equation 

 alludes, but it seems far too prominent for that! With it is to be 

 linked the fact that alpha-particles emerge from nuclei with kinetic 

 energy less than 2eVm. The potential-hill seems not to be so high 

 either for entering or for emerging particles, as it is for those which 

 only ^kirt its slopes ! 



Now if in theorizing about potential-hills and particles we substitute 

 quantum mechanics for classical mechanics, these phenomena cease 

 to be things contrary to expectation, and become instead the very 

 things to be expected. 



This is one of the situations — regrettably frequent in the present-day 



theoretical physics — where neither pictures nor words are adequate. 



The nearest description which can be made with words is probably 



somewhat as follows: We set out to ascertain whether a particle of 



charge ne and kinetic energy K, coming from infinity straight toward 



the nucleus (I simplify the problem as much as possible) will surmount 



the potential-hill of height Vm- Were we to conceive it as a particle 



conforming to classical mechanics, we should arrive at the answers: 



yes, ii K = neVm — no, \l K < neVm- But we are to turn away from 



^^ It is true that the elements of which the circumnuclear fields have been most 

 carefully explored by alpha-particles are not in general the same as those for which 

 transmutability has been observed down to very low values of K; but boron and 

 carbon figure on both the lists, Riezler having studied the scattering of alpha- 

 particles by these {Proc. Roy. Soc, 134, 154-170, 1932). 



