Abstract
We study effects of the Pauli principle on the potential energy of two-cluster systems. The object of the investigation is the lightest nuclei of p-shell with a dominant \boldsymbol{\alpha}𝛂-cluster channel. For this aim we construct matrix elements of two-cluster potential energy between cluster oscillator functions with and without full antisymmetrization. Eigenvalues and eigenfunctions of the potential energy matrix are studied in detail. Eigenfunctions of the potential energy operator are presented in oscillator, coordinate and momentum spaces. We demonstrate that the Pauli principle affects more strongly the eigenfunctions than the eigenvalues of the matrix and leads to the formation of resonance and trapped states.
Highlights
In the present paper, we have considered how the Pauli principle affects a cluster-cluster interaction
We have studied influence of the Pauli principle on the interaction between two clusters within a microscopic method – an algebraic version of the resonating group method
Due to the Pauli principle, a cluster-cluster interaction is a nonlocal potential within the standard version of the resonating group method
Summary
We have considered how the Pauli principle affects a cluster-cluster interaction. We follow a microscopic method, an algebraic version of the resonating group method [1], and consider the lightest nuclei of p-shell with a dominant α-cluster channel. Correct account of the Pauli principle is known to be of paramount importance in description of bound and low-energy resonance states in light nuclei with a prominent cluster structure. Proper account of the antisymmetrization of nucleons belonging to different cluster is quite a tricky problem. Popular cluster models, which treat the antisymmetrization approximately, use a folding cluster-cluster potential. It is necessary to know what the difference between the folding and exact cluster-cluster potential is. We found an unexpected impact of the Pauli principle on the potential energy
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