1016 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



-8 



-8 -6 



mc 



-4 -2 



smc 



6 amc 



8 

 6 

 4- 



(c) 



5n=-i 



J L 



lPil= mc 



© 



J L 



-8-6-4-2 2 4 6 8mC -8 -6-4-2 2 4 

 Px-^ Px-*^ 



CRYSTAL MOMENTUM 



amc 



Fig. Al— Initial and Final Values of P for Transitions which conserve energy. 



(a) The two nearly spherical surfaces for | K I = 6 mc. 



(b) The two surfaces for | /-*, | = 3 mc. 



(c) For an electron with \P^\ = mc, energy loss is impossible. 



(d) The case of | K I = 0. 



waves. Inserting this in the expression (A2.14) for PF12 dZi, we obtain 

 Wx. J82 = (F/27rM) m \^inP-,cl\Vcu\ 



X (2;h + 1 + ^ny){Py/P,) dPy (A4.2) 



= (1/0(1/8WP1)(2«^ + 1 + 8ny){cPy/kT)PydPy 



where we have used the symbol / to represent 



^ = irh* culrrC-^xn kT (A4.3) 



because, as we shall shortly show, t is the mean free path for electrons. 



