The three-cluster ?fish bone? model

Abstract

The resonating group interaction of three clusters, in the single channel no-distortion approximation, is split into a leading part and a residual part. In norm kernel eigenstate representation, the leading part exhibits a peculiar, fish bone like symmetry. An off-shell transformation, which leads to an energy-independent interaction, also reduces the strength of the three-body Pauli potential. The smallness of this potential is related to the possibility of interpreting cluster relative motion wave functions as probability density amplitudes. Neglecting all residual interactions and introducing, instead, fitting parameters into the two-cluster direct interactions leads to a three-cluster optical model, In this model the on-shell behaviour of two-cluster interactions is determined by experimental data, while their off-shell behaviour, as well as the three-cluster Pauli potential, are determined by the Pauli principle.Nuclear Reactions: Scattering theory, nuclear models, optical models, composite particle interactions, symmetry of interactions.

The concept of a Pauli barrier in nucleus-nucleus scattering

“…The model is considered a possible extension of the orthogonality condition model. It agrees with the resonating group model up to the omission of some residual interaction [8,9]. We want to study the effect of the partly Pauli-forbidden states in the fish bone optical model.…”

Reexamination of theα−α“fishbone” potential

“…We can extend the two-body fishbone model to three clusters by embedding the two-body fishbone potential into the three-body Hilbert space [6]. We use the usual configuration space Jacobi coordinates.…”

“…In the method of Buck, Friedrich and Wheatley [4] a deep potential is adopted, and it is assumed that the lowest few states are forbidden by the Pauli principle. The fishbone model by Schmid [5,6] goes beyond previous mod-els as it introduces the concept of partially Pauli forbidden states.…”

Negative parity states and ground state properties of the????n system calculated by different forces

“…The KS forces gives 2.2 MeV overbinding. According to the theory of the three-cluster fishbone model [22], there should be a repulsive threebody force due to the Pauli-principle. The reason for the existence of the three-body force can be easily understood.…”