Coulomb Energies of Light Nuclei

The Coulomb energy differences of light nuclei, determined mostly from $\beta$ decay, are fitted to a formula $\Delta E_c=a\left(\frac{Z}{A^{\frac{1}{3}}}\right)+b$, where $b$ is an exchange term. With modern data, the nuclear series $A=4n, 4n+1, 4n+2, 4n+3$ all yield surprisingly consistent values: $a=1.46\mathrm{}$ Mev, $b=-1.11\mathrm{}$ Mev. The data very clearly exhibit the presence of the exchange term; the value of $a$ corresponds to a square well radius, $R=1.18\mathrm{}{A}^{\frac{1}{3}}\times {10}^{-13\mathrm{}}$ cm. The $\Delta E_c$ formula is combined with $\beta$-decay energies to determine the spacing ${\Delta }_{T{T}^{\prime }}$ of the lowest-lying states of isotopic spins $T$, $T^{\prime }$ for a given $A$. The observed behavior of the $\Delta$ provides qualitative evidence for dominant supermultiplet structure in light nuclei.