Self-Consistent Binding Energies and Densities of Protons and Neutrons inBe10andC10

Binding energies, root-mean-square radii, and deformations of the protons and neutrons are calculated for the prolate and the oblate energy minima in ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$ and ${}_{}{}^{10}{}_{}{}^{}\mathrm{C}$, utilizing the Hartree-Fock approach. The nucleons interact via the Volkov and the Coulomb force. The energies are corrected for the c.m. motion. The mass and the charge distribution are surprisingly different: The theoretical charge deformation in ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$ is ${\beta }_C=0.62\mathrm{}$ [${\beta }_C\left(\mathrm{expt}\right)=\pm 0.7\pm 0.1$], while the calculated mass deformation has the value ${\beta }_M=0.41\mathrm{}$. A division of the total binding energy into a proton and a neutron part yields for ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$ twice as large a contribution for the protons as for the neutrons. This puzzle can be understood by means of Wigner's $S{U}_4$ model.