Localized Orbitals in Nuclear Structure

A generalization of the alpha-particle model of nuclear structure is developed, in which even-even nuclei or inner cores of odd nuclei are built up from localized spatial cells occupied either by two neutrons or by two neutrons and two protons. The analysis used is based on general properties of solutions of Hartree-Fock equations and on the effects of configuration interaction for a neutron-proton system governed by a Hamiltonian of the form $\Sigma K\left(i\right)+\Sigma Q(i, j)$. It is not necessary to specify the operators $K$ and $Q$ exactly, except that the interaction operator $Q$ is assumed to be primarily an attractive interaction of short range. A semi-empirical binding energy formula is derived which gives close agreement with observed binding energies for stable even-even nuclei lighter than ${\mathrm{Ca}}^{40}$. For a reasonable value of a parameter not determined by these data, the energy formula predicts that ${\mathrm{Ti}}^{44}$ should be unstable.