ON REFLECTION OF ELECTRONS BY METALLIC CRYSTALS 897 



(h = o{el) 



,3 4. + geos2.4-|(-^V5cos4.) 



+ ^4 ( - ^ COS 2(7+7 cos 6o- j + • . . 

 el , 461 . , dt /82 , 155\ , 



^' 192 ■ (9)(83) 



^' = (I8)V) "^ (12^^ 

 ' (180) (8^) "^ 



The calculated terms which are exhibited here enable us to calculate the 

 solution ^(z) to a certain accuracy, and this accuracy proved to be sufficient 

 for our purposes. 



Although this method is very complicated analytically, it was found to 

 be quite convenient for purposes of numerical calculation. 



5. The Reflection Coefficient for Large Values of E 



This work is concerned chiefly with the reflection coefficient for small 

 values of E (actually up to 20 electron volts). However, it is interesting that 

 we can obtain a simple approximate formula for R for indefinitely large 

 values of E in the intervals between the diffraction bands. 



For this purpose we go back to Brun's method, and we write the dependent 

 variable in equation (5) in the form (p = — i6o -{- o). We find that the new 

 dependent variable co satisfies the equation 



-^ - lidoo) + 60^ + 2(9i cos 2z = 0, 

 dz 



and we seek a solution of this equation in the form 



ccijz) CC2(Z) 



0) ^= coo KZ) -r a + ""^2" -h • • • . 

 VO VQ 



The functions con(3) are easily computed, and we finally arrive, in an entirely 

 straight-forward way, at the result 



o(^/4) = -ido + ^i + %+ '". (7) 



