Aβ-Decay Energy Systematics

A $\beta$-decay energy systematics is presented which exhibits linear relations for disintegration energies between atoms ($Z, N$) and ($Z+1, N-1\mathrm{}$) when plotted as a function of $N$ keeping $Z$ constant. Separate plots are necessary for odd and even values of $A$. The disintegration energy lines show marked discontinuities for $N=50, 82, \mathrm{and} 126$. There is also considerable indication of a discontinuity at $N=28\mathrm{}$, and in the region of $N=20\mathrm{}$ sharp changes in slope are observed. Proton magic numbers at 50, 82, and possibly 28 are indicated by gaps in the spacing of the disintegration energy lines. No definite submagic numbers are at present identifiable. Changes in the even-odd differences of neutron and proton binding energies show up as changes in the line separation pattern. The most striking pattern changes can be interpreted as due to decreases in the even-odd differences for both neutrons and protons after their respective magic numbers. The systematics is useful in estimating disintegration energies in cases where measurements have not yet been made. Part of a systematics for double $\beta$ decay is also shown.