1012 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



it is necessary to reproduce a large amount of the material dealt with in or- 

 dinary conductivity theory. We do this in a somewhat abbreviated form ex- 

 panding the exposition on the points particularly pertinent to the theory 

 of energy losses. 



For convenience we reproduce here a number of the more important sym- 

 bols. The references indicated refer to places where they are discussed in the 

 text. 



a = lattice constant; Fig. 3. 



c = speed of longitudinal acoustical wave; Equ. (3.2). 

 C(e = average longitudinal elastic constant; Equ. (A4.1). 



e = base of Naperian logarithms. 



E = electric field. 



8 = energy. 



Sin and Son; Equ. (A4.1) and (A7.9). 



h = Iw h = Planck's constant. 



k = Boltzmann's constant. 



/ = mean free path for electron due to scattering by acoustic phonons; 

 (A4.3). 

 Z^op = describes scattering by optical phonons; (A7.19). 



m = e£Fective mass of electron. 



M = mass in equivalent mass treatment; (A5.8). 



P = "crystal momentum" of electron = It times its wave number. 



V = volume of crystal. 



A = dilation; (A4.1) and (A7.10). 



V = frequency of normal mode, 

 j/op = frequency of optical mode (used in Section 4 only); Equ. (4.5). 



A 2 The Probability of Transition into Energy Range 5S2 



In this section we consider an electron initially with energy Z\ and mo- 

 mentum Pi, which for convenience we take to be along the P^-axis, and 

 we evaluate the probability that it make a transition to states with ener- 

 gies in the range S2 to S2 + 5S2. We shall assume that the crystal is elas- 

 tically isotropic so that for the spherical energy surface approximation 

 employed, i.e. equation 3.6, the scattering will be symmetrical about the 

 Pz-axis. The end states, P2, may, therefore, be considered in groups lying 

 in the range dZi, dd where 6 is the angle between Pi and P2. These states 

 lie in a ring in P-space whose volume is 



27rP2 sin 6 P2 dd dP^ = 27rmP2 sin 6 dd dSz (A2.1) 



