CONTEMPORARY ADVANCES IN PHYSICS, XXVIII 607 



In Fig. 19 the abscissa is not K, but a quantity (the range of the 

 impinging alpha-particles) which increases more rapidly than K\ but 

 this does not affect the meaning of the peaks. Moreover, there is 

 abundant indication that quantities of such curves are simply waiting 

 for someone to take the data and plot them; for this is the phenomenon 

 of "resonance" to which many pages ^^ were devoted in the Second 

 Part, and which has chiefly been observed by the other methods there 

 described, but should always manifest itself in this way when the 

 proper experiments are performed. 



If we wish to interpret this without letting go of the classical theory, 

 we must say that either or both of the functions /i and/2 have maxima 

 at certain values of K. But here again, the adoption of quantum 

 mechanics may make this step superfluous. For consider the one- 

 dimensional potential-distribution of Fig. 16, a valley between two 

 hills, with energy-values reckoned from the bottom of the valley. 

 If the wave-equation be solved for this potential-distribution and for 

 any such value of particle-energy E as the dashed line of. Fig. 16 

 indicates — such a value, that according to classical theory a particle 

 possessing it might either be always within the valley or always beyond 

 either hill, but never could pass from one of these three zones to 

 another — a curious result is found. For the solutions which the laws 

 of quantum mechanics demand and accept, the ratio of squared- 

 amplitude ^^* within the valley to squared-amplitude ^^* beyond 

 either hill is usually low, but for certain discrete values of E it attains 

 high maxima! 



Now the three-dimensional nucleus-model of which I am speaking 

 resembles this case more than it does the other one-dimensional cases 

 of Figs. 14 and 15, because it consists of a potential-valley surrounded 

 on all sides by a potential-hill. One may therefore expect the prob- 

 ability of entry or penetration to pass through maxima such as are 

 symbolized by the dips in the "fence" of Fig. 13, entaiUng maxima 

 in the curve of probability-of-transmutation P« plotted as function 

 of K. Such is the quantum-mechanical explanation of the phe- 

 nomenon of "resonance," which indeed derives its name from this 

 theory; for the values of X" or £ at which the maxima occur are those 

 for which the amplitude of the oscillations of the ^P-function in the 

 valley within the barrier are singularly great. 



One wants next to know what quantitative successes have been 

 achieved in predicting or explaining such things as the actual locations 

 of the resonance-maxima, or the precise trend of the curve of Prvs-X 



27 "Nucleus, Part II," pp. 148-153; more fully treated in Rev. Set. Inst., 5, 66-77 

 (Feb. 1934). 



