Radii of Mirror Nuclei

Abstract

A nuclear model is used in which the nucleon density is a constant out to the core radius $R$ and then decreases as $\frac{e^{-\alpha r}}{r^2}$, where ${\alpha }^2=\frac{8MW}{{\hslash }^2}$, in which $W$ is taken as the average binding energy per nucleon. Values of $R$ are determined from the measured energy differences between mirror nuclei by calculating the Coulomb energy difference on the above model. If one assumes that the density of the core is constant with changing $A$, then $R=\frac{1.36\times {10}^{-13\mathrm{}}{A}^{\frac{1}{3}}}{{(1+\frac{3}{\alpha R})}^{\frac{1}{3}}}$ and fits the data well. This also gives values of nuclear radii in agreement with those obtained from the recent electron scattering measurements of Lyman, Hanson, and Scott even for large $A$. For light elements, a good approximation to the average nuclear radius, $R+\frac{1}{\alpha }$, is $1.4\times {10}^{-13\mathrm{}}{A}^{\frac{1}{3}}$. Nearly half of the nucleons are in the exponential tail.