Sec. 1.7] PROPERTIES OF NUCLEI 13 



Without a more detailed knowledge of the structure and the motions of 

 particles in nucleus, the magnetic moment must be determined experi- 

 mentally. Both the proton and neutron themselves have a magnetic moment 

 which also must be determined experimentally because the charge distribu- 

 tion in elementary particles is not known. Although the magnetic moment of 

 the electron is determined directly by its spin and angular momentum, this 

 is not true of the proton and neutron, neither of which have magnetic 

 moments of one nuclear magneton, the value suggested by the ratio of their 

 masses to that of the electron. This discrepancy between nuclear angular 

 moments and the corresponding magnetic moments is taken into account by 

 the formal introduction of a nuclear g factor which is defined as the ratio of 

 the magnetic moment in units of nuclear magnetons, n , to the angular 

 momentum in units of h/2ir. Thus, the magnetic moment in units of nuclear 

 magnetons is n = ig, where i is the nuclear spin in units of h/2ir. Most 

 experimental methods give the nuclear g factor directly, and if the spin is 

 known, ju is given the simple product as indicated above. 



Known experimental values of n are given'in Table 3. 



1.7. Electric Quadrupole Moment. From the theory of electrostatics it is 

 known that the potential field of an arbitrary charge distribution can be 

 expressed in a series of terms of the form 



v = — + -Pi (cos e) + ±p, (cos e) + • • • 



r r- r 



where P< (cos 6) are Legendre polynomials. At large distances compared 

 with the dimensions of the charge distribution, only the first term, represent- 

 ing a spherically symmetric or coulomb field, is important since all other 

 terms diminish as 1/r 2 or faster. Thus, at distances large compared with the 

 nuclear radius the electrostatic field is equivalent to a point source of charge 

 eZ. The second term, representing an electric dipole, does not exist for 

 nuclei since it vanishes for radially symmetric charge distributions containing 

 charge of only one sign. 



The third term, representing the electric quadrupole, may, however, exist 

 for nuclei in which protons are not distributed throughout the nucleus with 

 strict spherical symmetry. A small contribution to the electric field is then 

 made by the quadrupole moment which in effect alters the spherically 

 symmetric form of the stronger coulomb field but only within a distance of a 

 few times the nuclear radius. It is reasonable to assume in a first approxi- 

 mation that the asymmetry takes the simplest form of distortion of a sphere 

 which is that of an ellipsoid of rotation. Then from electrostatics the 

 nucleus will be cigar-shaped or a prolate spheroid when q is positive, and 

 platter-shaped or an oblate spheroid when q is negative. 



