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-$\alpha$-cluster energy of the last $\alpha$ cluster in the nucleus. Then from a proper analysis of these intra-$\alpha$-cluster energies, a separation of the intra- and inter-$\alpha$-cluster energies out of the total binding energy of the nucleus is made. Clear ideas about the sizes of the $\alpha$ clusters relative to the size of the free $\alpha$ particle and also about the degree of $\alpha$ clustering in each $\alpha$ nucleus are obtained. Positive evidence supporting the additive nature of the $\alpha -\alpha$-cluster interaction is found. Finally, the intra-$\alpha$-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.

• Received 24 March 1972

DOI:https://doi.org/10.1103/PhysRevC.6.476