608 



BELL SYSTEM TECHNICAL JOURNAL 



as it rises away from the axis of abscissse. Here it must be admitted 

 that almost everything remains to be done. The locations of the 

 resonance-maxima must be expected to depend upon the details of the 

 potential-distribution within the valley, of which there is as yet no 

 notion. The precise trend of Pi as actually observed cannot be the 

 same as that of (27) however good the theory may be, first because 

 not all of the impacts are central (page 596), then because in most (not 

 quite all) of the experiments the bombarded substance is in a thick 

 layer instead of a thin film (page 597), and finally because of the 

 functions /i and f^ of equation (20). Much as we should like for 

 simplicity to put these functions equal to unity and zero respectively, 

 and even though quantum mechanics has removed some of the ob- 

 stacles to doing so, yet we are obliged to take them into account — the 

 most striking and cogent reason being that with a variety of elements, 

 Pt is not the same for impact of protons as for impact of deutons, 

 though ne is the same for both ! -^ 



The situation being such, one cannot ask as yet for accurate state- 

 ments about the values of r^ and F™, the constants of the "crater 

 model" exhibited in Figs. 12 and 13. These must wait upon a 

 thoroughgoing fitting of the theory to the experimental curves of 

 Pt-vs-K, involving a decision as to the magnitude of fi. The values 

 of Vm for several of the lighter elements have been estimated from the 

 data on transmutation, but the procedure of arriving at the estimates 



12|- 

 10 



8 



6 - 



4 - 



2- 



Be 



Mg Al 



6 8 



ATOMIC NUMBER 



Fig. 20— Resonance-levels and (estimated) heights of potential-barriers for some 

 of the lighter elements, deduced from observations of transmutation. (Pollard; 

 Phys. Rev.) 



has not (so far as I know) been published. I reproduce as Fig. 20 a 

 graph of Pollard's, the circles along the uppermost line showing the 

 estimated values of eVm and the crosses along the other two lines 



^^ Also it has been said that the shapes of the best experimental curves of Pt-vs-K 

 imply that as K is increased, /i increases at first and then becomes constant; but 

 there is a great lack of published theory on these matters. 



