The ground state energies of the 3 e system and of the A-c~-e system are calculated in the three-cluster fish bone optical model [1]. It is found that the three-cluster Pauli potential is very strong in the M-version of the model and weak in the (off-shell transformed) 57-version. Its influence on the A-c~-e binding energy and ground state wave function is almost negligible in the M-version. The present results indicate that phenomenological three-cluster models with energy-independent two-cluster interactions are not necessarily in contradiction with more microscopic models. It seems to be important, however, to use potentials which contain in their off-shell behaviour both Pauli-principle and saturation character of the nuclear forces.

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In recent years predictions on the off-shell behavior of composite particles interactions have been made by some theoretical models. The goal of this paper is to test them by using 9Be nucleus. The bound state problem of 9Be considered as a e-~-n threecluster system is solved in configuration space. Several on-shell equivalent local and nonlocal forces for the e-e and n-e interactions are used for calculation of the low lying negative parity spectrum of 9Be, and also of the charge density, quadrupole moment, and the correlation density of 9Be ground state. The contributions to the calculated quantities of different partial waves of the two-body forces are examined and discussed.

In case of the p-~ system, the Coulomb exchange potential of the resonating group model and of the fish bone optical model are compared with each other. It is seen that the difference between the two approximations arises mainly from the unrealistic shortdistance behaviour of the proton-proton eZ/r potential, which has been assumed in both models. In case of the c~-~60 system, it is demonstrated that the importance of the Coulomb exchange potential can be very much reduced by an off-shell transformation.

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