608 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



other things on the initial state of the system. Equation (13.1) is based 

 on the assumption that the number of charged scatterers decays as a 

 first order process, and that cr is a linear function of this number, relative 

 to the exponential dependence on time. 



The first order character of pairing is fortunate for it renders the 

 measurement of r independent of a knowledge of $, i.e. independent of 

 the initial state of the system. This is not only fortunate from the point 

 of view of calculation but from experiment, since it is almost impossible 

 to prepare a specimen in a well defined initial state. 



The unimportance of <l> is best seen by plotting the logarithm of 

 (T„ — (T against time. According to (13.1) this plot is specified by 



log (o-« - cr) = log * + - 



T 



(13.1) 



Thus the reciprocal of its slope measures r, and $ is not involved. Fig. 

 27 illustrates the data for a typical run plotted in this manner. The sam- 

 ple is one containing about 9 X lO'^ cm~^ gallium and the experiment 

 was performed at 195°K (dry ice temperature). Notice that the curve is 

 absolutely straight out to 3500 minutes, demonstrating beyond a doubt 

 that the process is first order. The relaxation time computed from its 

 slope is 1.51 X 10 seconds as against a value calculated by the methods 



1 



I 



I 

 o 



l.Or-: 



0.6 



0.4 



0.2 



0.1 



'.!• 



500 1000 1500 2000 



TIME IN MINUTES 



2500 



3000 



3500 



Fig. 27 — Plot of log (o-„ — <r) as a function of time showing first order kinetics 

 of pairing. 



