Cluster-cluster potentials for the beryllium isotopes

الملخص EN

Two types of cluster-cluster potentials are obtained for the beryllium isotopes.

The first one of the suggested four-body potentials is an attractive Gaussian interaction and the second is a superposition of repulsive and attractive Gaussian forces.

The ground-state wave functions of the beryllium isotopes 8Be, 9Be and 10Be are expanded in series in terms of products of two wave functions: the first represents the set of A-4 nucleons and the second represents the set of the last four nucleons.

We use the four-particle fractional parentage coefficients to separate the wave function into a function of (A- 4)-nucleons and the other for the remaining alpha particle.

In the construction of these wave functions we have used the basis functions of the translation-invariant shell model.

The expansion coefficients of the factorizations of these wave functions are products of four-particle orbital and spin-isospin fractional parentage coefficients.