12 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 1 



half-integer value. In most stable, unexcited nuclei the spin is less than 

 4///27T, and for all nuclei of the even-even type it is zero. The resultant 

 angular momentum of a nucleus is presumably the vector sum of the orbital 

 angular momenta of all the particles and the intrinsic spin of each particle, 

 added according to the vector rules of quantum theory. The orbital angular 

 momentum is always an integer multiple of h/2ir if the same quantum condi- 

 tions hold here as for the orbital electrons. The vector sums therefore are 

 also integers. The spin of both the neutron and proton are known from 

 experimental evidence to be one-half, and if two such particles occupy the 

 same quantum state, their spins must be orientated parallel or antiparallel. 

 The contribution of the particle spins to the total nuclear spin will therefore 

 be an integer or half-integer for even or odd numbers of particles, respectively. 



A sufficiently detailed and consistent model of the nucleus has not yet been 

 formulated which will provide the exact magnitude of the spin for a nucleus 

 containing a prescribed number of protons and neutrons. But the qualita- 

 tive conclusions outlined above regarding the origin and the necessary magni- 

 tudes of nuclear spin are borne out by experiment. Further, if the spin of a 

 stable isotope (Z, A) is known, it is safe to conclude that the spin of a stable 

 nucleus with which it is isotopic will differ by one-half the number of excess 

 neutrons, i.e., i = (i /2)(A — A ), where i is the known spin for the isotope 

 of atomic weight A , and A, the atomic weight of a stable isotopic nucleus. 



The spin of a radioactive nucleus, on the other hand, will depend on its 

 state of excitation and will differ from the ground state, usually by integral 

 units of spin. If a beta particle, for example, is emitted, the nuclear spin 

 always changes by an integral value, including zero, since the ejected beta 

 particle and neutrino each have an intrinsic spin of one-half. In any nuclear 

 reaction, spin and angular momentum must be conserved as well as mass and 

 energy. Known values of nuclear spins in units of h/2x are given in Table 3 

 page 22 for stable nuclei. 



1.6. Magnetic Dipole Moment. Assuming the particles within a nucleus 

 to be in motion, it is to be expected that a magnetic field will be produced by 

 the current distribution of at least the charged particles. A single proton 

 moving in a circular orbit with a frequency v and angular momentum lh/2ir 

 represents a circulating current of magnitude equal to i — ev and produces a 

 field equivalent to a magnetic shell with a magnetic moment of 



leh . 



The unit n is referred to as the nuclear magneton. Because of the relative 

 magnitudes of the masses of the electron and proton it is smaller than the 

 Bohr magneton by the factor 1,840. 



