Alpha-Cluster Structure of Light Self-Conjugate4nNuclei in Their Ground States

Abstract

From phenomenological considerations, a mass formula is derived to calculate the interaction energy among the last two neutrons and last two protons in a nucleus. This interaction energy is the intra-$\ensuremath{\alpha}$-cluster energy of the last $\ensuremath{\alpha}$ cluster in the nucleus. Then from a proper analysis of these intra-$\ensuremath{\alpha}$-cluster energies, a separation of the intra- and inter-$\ensuremath{\alpha}$-cluster energies out of the total binding energy of the nucleus is made. Clear ideas about the sizes of the $\ensuremath{\alpha}$ clusters relative to the size of the free $\ensuremath{\alpha}$ particle and also about the degree of $\ensuremath{\alpha}$ clustering in each $\ensuremath{\alpha}$ nucleus are obtained. Positive evidence supporting the additive nature of the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$-cluster interaction is found. Finally, the intra-$\ensuremath{\alpha}$-cluster interaction energies are compared with the $\mathrm{nn}$-, $\mathrm{pp}$-, and $\mathrm{np}$-interaction energies in the same even-even self-conjugate nuclei in order to explore the similarities between the nature of two-body and four-body interactions.