Abstracts of Bell System Technical Papers* 

 Not Published in this Journal 



Anderson, P. W./ and P. R. Weiss^ 



Exchange Narrowing in Paramagnetic Resonance, Revs. Mod. Phys., 

 25, pp. 269-276, Jan., 1953. 



In this paper the problem of the Une shape in paramagnetic resonance when 

 large exchange interaction is present is discussed from the standpoint of a 

 simplified mathematical model. The mathematical model can be called the 

 model of "random frequency modulation": It is assumed that the atom ab- 

 sorbs a single frequency, which varies over a distribution determined by the 

 dipolar local fields, but that this frequency varies randomly in time at a rate 

 determined by the exchange interactions. The predicted line shape in the 

 case in which exchange is large is of resonance type in the observable center 

 of the line, but falls off more rapidly in the wings. This line shape has been 

 verified experimentally in a number of cases. This conclusion seems quite 

 independent of any assumption about the type of random frequency modula- 

 tion, etc. 



The quantitative conclusions are reached in the following way: It is sus- 

 pected, since the exchange motion is the superposition of the effects of a 

 number of neighbors which is not particularly small, that a good approxima- 

 tion to the modulation function is Gaussian noise with a Gaussian spectrum. 

 This, of course, is what would result from the superposition of a large number 

 of rather small effects. Under this assumption both the second moment (which 

 is independent of exchange) and the fourth moment of the line shape can be 

 calculated. This kind of modulation is the simplest one which does give a 

 finite fourth moment; a Markoffian, or "jump", type of modulation, which 

 might seem more reasonable at first, does not. These moments are then com- 

 pared with the moments computed by Van Vleck [Phys. Rev. 74, 1168 (1948)] 

 to fix the two adjustable parameters, mean square frequency, and average 

 rate of change of frequency, of the theory. 

 The. result as to line breadth, which is essentially 



((Aa)2))Av dipole-dipole 



A ^^^ 



~" J/h 



* Certain of these papers are available as Bell System Monographs and may be 

 obtained on request to the Publication Department, Bell Telephone Laboratories, 

 Inc., 463 West Street, New York 14, N. Y. For papers available in this form, the 

 monograph number is given in parentheses following the date of publication, and 

 this number should be given in all requests. 



1 Bell Telephone Laboratories. 



• Rutgers University, New Brunswick, N. J. 



1257 



