The interaction of alpha-particles and the binding energy of 8Be

A calculation of the binding energy of 8Be is given, based upon the separation of the eight nucleons into two groups of four, using Gaussian functions and a Yukawa central force. The calculation is considerably simplified by the use of an integral identity between the Gaussian potential and the Yukawa potential. The energy is calculated with a Gaussian potential, and the identity used to convert the result to that which would have been obtained by direct use of the Yukawa potential. The results of the variational calculation show that unless the saturation conditions usually adopted in the theory of heavy nuclei are abandoned, there can be no binding, confirming an earlier result of Margenau, obtained with a Gaussian potential. The results do not depend essentially on the range of the force, nor on the central two-body type of force adopted. When the old saturation conditions are abandoned, quite reasonable results are obtained. The magnitude of the energies due to the exchange of single particles and pairs of particles indicates that the force between alpha-particles is not additive. A discussion of the saturation conditions and of the alpha-particle model in the light of the results is given.