Sec. 1.3] PROPERTIES OF NUCLEI 7 



unoccupied proton level will transform by beta emission until the lowest 

 levels are filled. The converse holds for isobars with an excess of protons 

 compared with the stable configuration. Such nuclei capture electrons or 

 undergo positron emission transforming protons to neutrons in order to fill 

 lower lying neutron levels. 



The binding energy of nuclei with even A must be represented by two 

 parabolas on the same E axis: one containing (0, O) nuclei and a lower curve 

 containing (E, E) nuclei, as shown in Fig. 1. From the possible combination 

 of A particles, (Z, N), (Z - 1, N + 1), (Z - 2, N + 2) etc., and (Z + 1, 

 N — 1), (Z + 2, N — 2) etc., which can form isobars, those with odd Z lie 

 on the upper curve and can always transform to a nucleus on the lower curve 

 by beta emission or K capture. By the same processes, isobars lying far up 

 on the Z-even curve can cross to a lower level on the Z-odd curve. By 

 successive transformations of this kind the isobar is brought finally to one of 

 two possible stable nuclei occupying the lowest levels on the Z-even curve. 

 If two points are stable, they must differ by two charge units. These nuclei 

 cannot transform into each other despite a possible energy difference since 

 either beta emission or K capture would take them first to a higher level on 

 the Z-odd curve, which is energetically impossible, and no process is known 

 for the simultaneous transformation of two charge units without also a 

 change in mass. 



An exception to this is found only in the light nuclei H 2 , Li 6 , B 10 , and N 14 . 

 Here, the Z-even and Z-odd curves are nearly superimposed because the 

 contribution of the electrostatic field to the binding energy is negligible. 

 The lowest state, therefore, lies at the apex of the Z-odd curve and 

 Z = A - Z = N. 



1.2. Mass Defect. Mass spectrographic measurements of the exact 

 weight of nuclei indicate a consistent variation from the integral values of 

 atomic weight. The difference between the integral atomic weight and the 

 exact mass of an isotope, M, relative to O 16 (A = 16.00000) is referred to as 

 the mass defect AM. 



AM = M - A 



The mass defect is positive only for elements lighter than O 16 and for the very 

 heaviest elements. In all other cases it is negative. The variation in the 

 mass defect over the entire mass range is of the order of 0.5 per cent or less. 



1.3. Packing Fraction. The packing fraction/ or mass defect per elemen- 

 tary particle is a quantity most frequently employed in experimental practice 

 to express the deviation of the exact isotope weight from the integral atomic 

 mass number. It is defined by the relation 



M - A AM 

 f ~ A A 



