Binding Energy of the Four-Nucleon System with Separable Potential

Abstract

Following the approach of Mitra a four-body formalism is set up for the $\alpha$-particle system under the condition of full antisymmetrization of the four nucleon wave function. The $N-N$ $\alpha$ state interaction considered is of the separable type and the shape is assumed to be Gaussian. The resulting equations are solved (under certain approximations) for the $\alpha$-particle ground-state energy. Using the above simplified interaction it is found that this approach leads to overbinding in the four-nucleon system.