398 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1953 



50 is however a nucleus with an odd number of protons and an odd 

 number of neutrons. Such nuclei, of which there are only a few stable 

 examples, (in Part I we met with two, the deuteron and N^^), are not 

 bound by the usual rule. 



FERROMAGNETIC RESONANCE 



Ferromagnetic bodies owe their distinctive feature to uncompensated 

 electrons. This suggests that the magnetic resonance of electrons will 

 be discernible in such bodies, and so indeed it is. In this case it is com- 

 monly known as "ferromagnetic resonance." However, unless the sample 

 is in the shape of a sphere, the resonance-peak will be found in what 

 appears to be very much the wrong place. This is due to the magnetiza- 

 tion of the substance, which produces a remarkable effect upon the 

 location of the resonance. The field strength in the region occupied by 

 the sample, which would be H if the sample were not there, is changed 

 to a very different value ; and yet in general it would not be right to take 

 the value of Hi the ''internal field strength" and put it in place of H 

 in equation (3). We must understand this effect and make the proper 

 allowance for it before we do anything else with the data (unless, I 

 repeat, Ave confine ourselves to data obtained with spheres). The effect 

 appears to be beyond the power of ''intuition" to conceive, and we must 

 have recourse to the fundamental equations, which describe the pre- 

 cession of the electronic magnets. It will be recalled that in Part I, we^ 

 looked at nuclear magnetic resonance sometimes as the turning-over of 

 nuclear magnets and sometimes as an outcome of precession. Now we 

 are going to treat the electronic resonance as an outcome of precession. 



The fundamental vector equation, which was given in a sort of diluted 

 form as equation (6) of Part I, reads as follows: 



dp/dt = fieX Hi (15) 



Here p and fie stand for the angular momentum and the magnetic mo- 

 ment of the electron, and Hi for the field which operates on the electron. 

 We have seen that m«/p is written as ge/2mc ; we denote this quantity by 

 y; and we give it the minus sign because, for the electron, angular mo- 

 mentum and magnetic moment are antiparallel to one another. Now 

 we have: 



dfie/dt = -TMc X Hi (16) 



This we proceed to write as three scalar equations; but first we replace 

 fXe by M. This will help to do away with the implication that the mag- 

 netic moment varies in magnitude (it is the direction that changes with 



