Influence of the Pauli principle on two-cluster potential energy

TL;DR

This paper investigates how the Pauli principle influences the potential energy in two-cluster nuclear systems, revealing its significant impact on eigenfunctions and the formation of resonance and trapped states.

Contribution

It introduces a detailed analysis of the Pauli principle's effects on potential energy matrices in light p-shell nuclei, emphasizing eigenfunction modifications.

Findings

Pauli principle significantly alters eigenfunctions

Resonance and trapped states are formed due to Pauli effects

Eigenvalues are less affected than eigenfunctions

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 $\alpha$-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.