Coulomb Energy of Light Nuclei

The Coulomb energy is calculated by determining the nuclear radius so that the energy difference between ${\mathrm{N}}^{13}$ and ${\mathrm{C}}^{13}$ agrees with observation. Two different assumptions are investigated: (a) that the nuclear radius is simply proportional to the cube root of the number of particles, (b) that the wave function of the last neutron or proton extends beyond the surface of the residual nucleus by an amount determined by its binding energy. The latter assumption accounts very well for the irregularities of the positron energies in the series ${\mathrm{C}}^{11}$ ${\mathrm{N}}^{13}$ ${\mathrm{O}}^{15}$ ${\mathrm{F}}^{17}$, and agrees quantitatively with observation within 0.15 milli-mass-units. Theoretically and experimentally, the actual Coulomb energy should lie between the results of (a) and (b). Application of these considerations to unknown nuclei shows that ${\mathrm{C}}^{10}$ and ${\mathrm{O}}^{14}$ are highly stable, ${\mathrm{Be}}^6$ certainly and ${\mathrm{B}}^9$ almost certainly unstable, while the stability of ${\mathrm{B}}^8$ and ${\mathrm{N}}^{12}$ is doubtful.