CONTEMPORARY ADVANCES IN PHYSICS, XXVIII 613 



should not expect a perfect agreement, since the two nuclei are not 

 identical; but we should be disconcerted by a sharp disagreement, 

 since both nuclei belong to elements of which the nuclear charges 

 differ at most by only a few per cent and the nuclear masses by little 

 more. A very great disagreement would in fact be gravely injurious 

 to the theory. Making the test, Gurney and Condon found, however 

 that there is no grave disagreement: the theory survives the test. 



A very similar test was applied with greater minuteness by Gamow. 

 For each element he assumed a potential-hill having a vertical rise on 

 the inward side, and on the outward side a curved slope conforming 

 exactly to the function (Z — 2)/r, where Z stands for the atomic 

 number of the element before the alpha-particle quits it and conse- 

 quently (Z — 2)e stands for the charge of the residual nucleus. In 

 other words, he postulated a classical inverse-square electrostatic field 

 ("Coulomb field") from infinity inward to a distance Tq from the 

 centre of the nucleus, and at ro a discontinuous potential-fall. This is 

 a potential-distribution distinguished by a single disposable constant, 

 to wit, r^; for Vm itself is determined by Tq and Z. 



Gamow proceeded to compute what value must be assigned to ^o 

 in order to achieve agreement between theory and experiment for 

 each of the twenty-three alpha-emitters. Approximations must be 

 made in carrying through the calculations; those which Gamow em- 

 ployed convert equation (28) into this: 



loge r = - loge {h/4:mro~) + 87rVVm (Z - 2)//W2£ 



-f (167rgVm/;0VZ^^Vr^. 



Putting for E the kinetic energy of the alpha-particles and for T 

 the mean lives of the several elements, he evaluated ro. Had the 

 values proved very different for the various alpha-emitters, it would 

 have spoken ill for the theory; but all the values were comprised be- 

 tween 9.5 and 6.3 times 10~^^ cm. The order of magnitude is satis- 

 factory; the differences between the several values are by no means 

 disagreeably great; and there are even signs of a systematic upward 

 trend of the values of ro with the atomic numbers of the nuclei. The 

 quantum-mechanical theory and the crater model of the nucleus so 

 pass their crucial test. 



