a 



CHAPTER 1 

 PROPERTIES OF NUCLEI 



1.1. Stable Isotopes. Examination of the charge, mass, and abundance of 

 existing isotopes has led to a set of empirical rules governing the structure of 

 stable nuclei so far as the allowed numbers of protons and neutrons in a stable 

 nucleus are concerned [l,2]. x They are understood in a qualitative way from 

 elementary considerations of the binding energies for various combina- 

 tions of neutrons and protons and are strongly supported by the behavior 

 of the radioactive isotopes. 



The fundamental requirement for stability of nuclei is satisfied when the 

 binding energy is a maximum or, alternatively, the exact mass is a minimum 

 for a given total number of nuclear particles. This may be regarded as 

 equivalent to filling the lowest proton and neutron quantum levels in the 

 nucleus. If the transformation of a proton to a neutron results in a greater 

 binding energy or smaller exact atomic weight, the nucleus is unstable and the 

 transformation will occur through K capture or positron emission. Con- 

 versely, positron decay will reduce an excess number of neutrons to protons 

 until the most stable configuration is reached, i.e., until lower lying proton 

 levels are filled. On this basis the isotope rules can be explained and are borne 

 out by the modes of decay of the radioactive isotopes. 



Formulation of the isotope rules is simplified with the aid of several designa- 

 tions expressing the relation between numbers of neutrons and protons. 

 Nuclei with the same number of protons Z but different atomic weights, or 

 A — Z, are referred to as isotopes; nuclei with the same number of neutrons, 

 A — Z, but different Z are isotones; and nuclei with the same A but different 

 Z are isobars. Nuclei with even numbers of both protons and neutrons 

 will be designated by (E, E) and those with even protons and odd neutrons by 

 (E, O). Similar definitions hold for the designations (O, E) and (O, O). 



I. In a first approximation, nuclei contain equal numbers of protons and 

 neutrons, i.e., Z = A/2. For the light elements this rule is followed exactly 

 for the most abundant isotope. This can be understood if it is assumed that 

 the nuclear force binding a neutron and proton (pn) is somewhat greater than 

 the attraction between like particles (pp) and (nn). If the reverse were true, 

 one would expect nuclei to consist wholly of neutrons, or neglecting electro- 

 static repulsion, wholly of protons. Further, if forces between like particles 



1 The numbers in brackets refer to the references at the end of the chapter. The refer- 

 ences for this chapter appear on page 14. 



3 



