The Binding Energy ofO16

A perturbation calculation has been made to determine the binding energy of the ${\mathrm{O}}^{16}$ nucleus. Zero-order eigenfunctions constructed from harmonic oscillator functions in a central field were used in conjunction with a symmetrical form of the Hamiltonian involving space exchange, space-spin exchange, nonexchange and spin exchange terms and only one range function of Gaussian form. The coefficients of the interactions were selected to give agreement with the scattering results and the observed energies of ${\mathrm{H}}^2$ and ${\mathrm{He}}^4$, and to satisfy the requirement of the upper limit of nuclear masses. The interaction so selected leads to a very small first-order binding energy, $19m{c}^2$. Second-order contributions to the energy were calculated from the interaction of excited states with the ground state. The energy is thus estimated to be about $79m{c}^2$ in second order. The third-order contributions were found to be disturbingly large, amounting to perhaps half of the second-order contributions, but of opposite sign. The procedure does, however, appear to converge and it is believed that the end result is indicated sufficiently well to show that the assumed interactions are inadequate to produce the required binding energy of ${\mathrm{O}}^{16}$.