Importance of the three-body Pauli potential in three-cluster systems

Abstract

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.

Three-body Pauli potential in then p ? system

“…In systems of three clusters, the transformation has been introduced for the reduction of three-body forces [8,9]. In fact, three-body forces have been seen to be extremely large when this transformation is not carried out [2]. In our present study, the transformation will always be carried out.…”

“…It is a desirable feature, when three-and multibody forces are small, despite the compositeness of the interacting bodies, or when they can be made small by certain transformations. In the previous study [2] the Pauli principle was only approximately taken into account by the fish bone optical model, in which a residual interaction term of the resonating group equation is replaced by a modification of the local potential part. In nuclear multi-cluster systems, an important origin of multibody forces is the Pauli principle.…”

The two- and three-cluster fish bone model with saturation

“…But in a first survey, one may study them separately. The three-body Paul/potential has been defined and studied in systems without hard core correlations, both in the fish bone optical model [2,6] and in the resonating group model [13]. The three-body potential arising from hard core correlations has been studied in the AAa system [8].…”

“…Also, we expect an effective three-cluster force arising from the fact that a third cluster takes away configuration space from an interacting pair of clusters, when it is present in the region of interaction. In dealing with effective three-body forces we have to be careful, however 9 If we allow microscopic function bases to be nonorthogonal, and potentials to be energy-dependent due to the overlap-or norm kernel, three-cluster forces may arise which are very strong and should be called artificial three-cluster forces rather than physical ones [2,6,7]. In the resonating group model as well as in the fish bone optical model, it is strongly recommended, therefore, to orthonormalize function bases by off-shell transformations 9 Collecting terms we can write down the wave equation of the fish bone optical model with saturation,…”

The non-orthogonality problem of the coupled reaction channels method

“…Some consideration has already been given to the first two points [2][3][4]. In the present paper we are dealing with the third point.…”