246 



THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



(23) . Combining the two pieces, we find 



M /I — cos x\ 



M -\- m\ T / 



/.(c) 



cdc 



In this expression, the artificial exclusion of small angle scattering is no 

 longer necessary and can be dropped. Completing the integrating of 

 equation (20) we see that the right hand side gives averages over the 

 unperturbed velocity distribution /(c). Combining pieces, using (23) 

 and indices 1, 2, 3 for the x, y and z components we get 



M -{- m 



ji(r, t) = -n(r, t) J^ k, 



M 



/I 



cosx\ 



; / 



l(CiC,) — {Ci){Cy)] 



(143) 



According to (16) and (24), the square bracket in (143) is the diffusion 

 tensor. It has two distinct components which equal respectively 



i), 



D^ = 



(144) 



(145) 



The velocity averages entering are (120), and (121), that is the directional 

 components of the random part of the energy. Substituting we get finally 



{M + m)kT 



Du = 



Mm 



/I - cos x\ 



V 



"/ 



(M + m)'/^^^H^±Ml 



+ a' 



cos x)\ 



/ 



(146) 



^,^ / 3M sin^ X + 4ot(1 - cos x) \/ l - cos x V 



D^ = 



\ 

 (M + m)kT 



/\ 



Mm 



/I 



cos x \ 



; / 



+ a= 



(M + m)*(?i^) 



(147) 



Mhn / 3itf sin' x + 4m(l - cos x) \/l 

 \ r /\ 



cos xV 



r / 



The diffusion coefficients have the simple property that they are ob- 

 tained by adding the low field and the high field limiting expressions. 



