# Influence of the Pauli principle on two-cluster potential energy

### Submission summary

 As Contributors: Yuliya Lashko Arxiv Link: https://arxiv.org/abs/1910.05046v1 (pdf) Date accepted: 2019-11-22 Date submitted: 2019-10-14 02:00 Submitted by: Lashko, Yuliya Submitted to: SciPost Physics Proceedings Proceedings issue: 24th European Few Body Conference (University of Surrey, U.K.) Academic field: Physics Specialties: Nuclear Physics - Theory Quantum Physics Approach: Theoretical

### 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.

Published as SciPost Phys. Proc. 3, 021 (2020)

### Submission & Refereeing History

Submission 1910.05046v1 on 14 October 2019

## Reports on this Submission

### Anonymous Report 1 on 2019-11-18 (Invited Report)

• Cite as: Anonymous, Report on arXiv:1910.05046v1, delivered 2019-11-18, doi: 10.21468/SciPost.Report.1325

### Strengths

1) Authors demonstrated that for the non-compact cluster shapes the eigenvalues of the exact and folding potential energy matrix coincide.

2) For the compact cluster shapes with small relative distances between clusters, authors found a number resonance states with the exact cluster-cluster potential. In contrast, these resonance states are absent in the case of folding potential.

No weakness

### Report

In the present manuscript, the influence of the Pauli principle on the cluster-cluster potential energy of the two-cluster nuclear system was studied in the algebraic version of the resonating-group method. Authors used three well-known nucleon-nucleon potentials: Volkov N2, modified Hasegawa-Nagata, and Minnesota potentials. A few interesting results were obtained by authors. For the lightest nuclei of $p$-shell, $^{5}$He, $^{5,6,7}$Li and $^{7,8}$Be considered as two-cluster systems, the eigenvalues and eigenfunctions of the exact (with full anti-symmetrization) and folding (without full anti-symmetrization)
potential energy matrix were compared. Authors demonstrated that for the non-compact cluster shapes the eigenvalues of the exact and folding potential energy matrix coincide. For the compact cluster shapes with small relative distances between clusters, the exact cluster-cluster potential shows a number resonance states. In contrast, these resonance states are absent in the case of folding potential.

So, there is no doubt that the subject studied in the manuscript is very important and actual for the nuclear cluster community to justify publication.

In total, the manuscript is written very well and cleanly. There are no typos. The reference list is complete. Therefore, the manuscript certainly deserves a publication.

### Requested changes

No changes

• validity: high
• significance: high
• originality: high
• clarity: top
• formatting: excellent
• grammar: good