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BELL SYSTEM TECHNICAL JOURNAL 



entry! (This energy E will be the same as the initial kinetic energy 

 K already so often mentioned, which the particle has before it starts 

 to climb the hill.) Perhaps it is not too fanciful to think of these 

 lines as the posts of a fence standing up vertically from the curve, the 

 varying height of which is a rough indication of the varying difftculties 

 which particles of various energies have in getting through. 



To predict successfully how the height of this metaphorical fence, 

 the probability of transmission or of penetration, varies with V or E 

 would be a magnificent triumph of nuclear theory, but it is vain to 

 hope for such a success in the immediate future. Almost certainly the 

 top of the fence curves much more rapidly upward than the drawing 

 suggests, and also there is good reason to think that there may be gaps 

 in the fence somewhere like those depicted in Fig. 13, where the 



Fig. 



13 — Nuclear potential-curve postulated for explaining transmutation, with 

 allowance for " resonance." 



probability of penetration rises to values remarkably near to unity. 

 Such at least are the features of certain one-dimensional potential- 

 fields (do not forget that Figs. 12 and 13 refer to three-dimensional 

 potential-fields having spherical symmetry!) which have isolated 

 potential-hills or hills-adjoined-by-valleys. 



Three of these cases are displayed in Figs. 14, 15, 16. Take the first 

 for definiteness. One plunges in medias res by writing down at once 

 Schroedinger's wave-equation : 



(p-^ldx- + (87r2m//z2)[£ - neV{x)']^ = 0, 



(21) 



in which V{x) stands for the potential-function exhibited in the 

 figure,25 while the meanings of ne, m and E have probably already been 



2^ I deviate from the otherwise-universal usage of employing V for the potential 

 energy of the particle, for the reason that the latter depends on the charge of the 

 particle, while the potential-function is supposed (no doubt inaccurately) not to 

 depend on it. 



