ON REFLECTION OF ELECTRONS BY METALLIC CRYSTALS 905 



For fixed values of Vo and Fi, the reflection coefficient tends to decrease 

 with increasing E over most of the range between any two successive 

 diffraction bands. For fixed values of Vo and E, E being in a range between 

 two diffraction bands, R tends to decrease with increasing Vi. This is a re- 

 sult which was not anticipated when the work was begun. As was expected, 

 we find a tendency for R to increase with Vo when E and Fi/Fo are held 

 fixed. 



The most interesting feature of the results is the behavior of R in the neigh- 

 borhoods of the edges of the diffraction bands. Unfortunately, the range of 

 values of E considered is not great enough to reveal this behavior very com- 

 pletely. (The failure to consider a greater range of values of E was the result 

 of our reluctance to embark again on the difficult numerical computations 

 relating to the PF±x,i(±^) functions. Since the necessary computations 

 had been performed earlier for values of E up to 20 electron volts, we de- 

 cided, unfortunately as it now appears, to confine ourselves to this range.) 



The behavior of the curves near the edges of the diffraction bands which 

 occur in the neighborhood oi E = 19 electron volts (when Fo is 18 or 20 

 electron volts) does not require much discussion. The reader will observe a 

 small dip in the curves for Vi = Fo/10 just below these diffraction bands. 

 The accuracy of the computations is believed to be high enough that we are 

 justified in taking this dip to be entirely genuine. 



When Vo is 10, 12, or 14 electron volts the behavior of the curves for 

 values of E in the neighborhood of zero is rather complicated. Herring and 

 Nichols consider this behavior to be one of the most significant features of 

 the results, and they have given a full discussion of it from the physical 

 point of view.* In view of the availability of their discussion, we may con- 

 fine ourselves here to a few brief remarks. 



In some of the cases which we are referring to now there are diffraction 

 bands extending from £ = to certain positive values of E. (These dif- 

 fraction bands are shown in a self-explanatory way in the figures.) When 

 such a diffraction band exists the complicated behavior of R for small val- 

 ues of £ is a result of the existence of the diffraction band, and it is com- 

 parable with the behavior of R in the upper part of the range of values of 

 E in the case in which Fo = 20 electron volts. 



In the cases in which we do not have diffraction bands extending upward 

 from £ = we have to explain the complicated behavior of R in somewhat 

 different terms. 



Assuming that we have such a case, let us momentarily ignore the fact 

 that the physically significant values of £ are non-negative, and consider 

 £ as an unrestricted real parameter. Under this convention concerning £, 



* Herring and Nichols, footnote 2, pp. 248-249. 



