596 BELL SYSTEM TECHNICAL JOURNAL 



inverse-square field, do not extend far enough inward for the integral to 

 surpass the value Ko/le. 



2. When particles of charge ne {n = any integer) are projected at 

 a sheet of any specific element, they cannot enter the nuclei at all 

 unless their kinetic energy exceeds the critical value neVm', and if the 

 curve of number-entering-nuclei vs. kinetic-energy can in any way be 

 deduced from any experiments, it should rise fairly sharply from the 

 axis of kinetic energy at this critical abscissa. 



(It will have been noticed that I expressed both of these predictions 

 as though the escape or the entry of a particle made no difference to 

 the height of the potential-barrier, which is the universal practice. 

 This is obviously too crude an assumption; the error in it must be 

 graver the smaller the atomic number of the element, therefore graver 

 in theorizing about the transmutation of light elements than in 

 theorizing about the radioactivity of heavy ones; it must be rectified in 

 future.) 



The former of these predictions can be sharply and unquestionably 

 tested; and it proves to be wrong. Uranium I. emits alpha-particles of 

 kinetic energy Kq equal to 4 MEV; but Rutherford suspected from 

 scattering-experiments on other heavy elements, and subsequently 

 proved by such experiments upon uranium itself, that the inverse- 

 square force-field extends so far inwards as to involve a height of 

 potential barrier at least twice as great as Ko/2e; so that an emerging 

 alpha-particle should possess at least 8 MEV of kinetic energy derived 

 from coasting down the hill, and even this is merely a lower limit to 

 the estimate, since the hill may be higher and the particle might 

 come with some excess of energy over its brow! 



The second prediction is not so readily tested. If all of the charged 

 particles (protons or deutons or alpha-particles, say) projected at the 

 postulated sheet of matter were directed straight towards the centres 

 of nuclei, and arrived at the potential-hills without suffering any 

 prior loss of energy elsewhere, the fraction entering through the 

 potential barriers would rise suddenly from zero to unity as the kinetic 

 energy K of the particles was raised to neVm, and any phenomenon 

 depending solely upon entry would make its advent suddenly if at all. 

 Unfortunately this does not occur in any experiment now possible or 

 likely ever to become possible. If the sheet of matter is a monatomic 

 layer, most of the oncoming particles will be going towards the gaps 

 between the nuclei, and the initial directions of the rest will be pointed 

 towards all parts of the cross-sections of the nuclei, only an infinitesimal 

 fraction going straight toward the centres. Designate by p the 

 perpendicular distance from a centre to the line-of -initial-motion of 



