On the Structure of the Nuclei Between Helium and Oxygen

Abstract

In order to test the present assumptions on nuclear forces, the theory is applied to the nuclei in which the first $p$ shell of protons and neutrons is being built up, i.e., to the nuclei with masses between 5 and 16. The Hartree-Fock approximation is used for the numerical calculations, but the more qualitative results are independent to a large degree of the approximations used. The angular momenta of the ground states appear to be given correctly by the theory. Although the wave functions used do not correspond to preformed alpha-particles, the first-order energies exhibit a marked four-shell structure. The experimental energy difference between the nuclear pairs ($N,N+1$), ($N+1,N$) may possibly be somewhat larger than the difference in the electrostatic energies. Support for the use of spin exchange (Heisenberg) forces to account for the singlet-triplet separation in the deuteron is found in the singlet-triplet separation inferred from the ${\mathrm{Li}}^{6}$-${\mathrm{He}}^{6}$ normal state energy difference. However, the ${\mathrm{B}}^{10}$-${\mathrm{Be}}^{10}$ and ${\mathrm{N}}^{14}$-${\mathrm{C}}^{14}$ normal state differences do not fit the simple theory which is adequate for the singlet-triplet spacing in the two and six particle problems.