The Binding Energy of⁸Be and¹²C

A general group-theoretic method is given for the enumeration of the integrals in the resonating group structure method of the alpha particle model of the alpha nuclei. The general methods are then applied to the calculation of the binding energies of 8 Be and 12 C. These calculations are carried out using Gaussian wave functions and a Gaussian central force potential, which is taken to be the mixture of the Wigner, Bartlett, Heisenberg and Majorana interactions. The variational method is used to fix the parameter determining the separation between the alpha particle clusters. Two types of exchange dependence of the potential are considered corresponding to symmetrical forces and to Serber forces respectively. The former gives no binding (both for 8 Be and 12 C) while the latter overestimates the binding energies. A mixture of about 30% of the symmetric force and 70% of the Serber force gives the correct values for the binding energies. A simple transformation is used to calculate the Coulomb energy from the previously evaluated integrals for the Gaussian potential.